{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0001","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4df8288b8d3a152777ef5f9b9b53cd236a8c5ba015949cfcfa4827aedc34e5d9","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157001,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[0,0],[1,0],[0,-1],[-1,1]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[0, 0], [1, 0], [0, -1], [-1, 1]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([0, 1, 0, -1], [0, 0, -1, 1], [Yes, Yes, No, No], [Yes, No, Yes, No], [origin, x-axis, y-axis, II])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([0, 1, 0, -1], [0, 0, -1, 1], [Yes, Yes, No, No], [Yes, No, Yes, No], [origin, x-axis, y-axis, II])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0002","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dcb77b054f70c2cf2768b70442f0c8d01ff58ccb79d9cc75f97fd657582aa94b","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157002,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[1,1],[-1,1],[-1,-1],[1,-1]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[1, 1], [-1, 1], [-1, -1], [1, -1]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([1, -1, -1, 1], [1, 1, -1, -1], [No, No, No, No], [No, No, No, No], [I, II, III, IV])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([1, -1, -1, 1], [1, 1, -1, -1], [No, No, No, No], [No, No, No, No], [I, II, III, IV])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0003","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5e481bd645c55be92dc7d98d46e4a1873e2c1acb0a838c3f8472fad578fff504","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157003,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[-10,1],[1,0],[0,1],[-1,-2]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[-10, 1], [1, 0], [0, 1], [-1, -2]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([-10, 1, 0, -1], [1, 0, 1, -2], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-10, 1, 0, -1], [1, 0, 1, -2], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0004","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1d1e72e4dc08a1852f6dc9ccc446ca076a079d8d33ec3ae6aaa30b34782f9322","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157004,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[-9,1],[1,0],[0,1],[-1,-3]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[-9, 1], [1, 0], [0, 1], [-1, -3]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([-9, 1, 0, -1], [1, 0, 1, -3], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-9, 1, 0, -1], [1, 0, 1, -3], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0005","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4053e4dc20b7317f8f15c89c5860331db33a4835bda23643eec4e8a3f34ee46c","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157005,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[-8,1],[1,0],[0,1],[-1,-4]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[-8, 1], [1, 0], [0, 1], [-1, -4]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([-8, 1, 0, -1], [1, 0, 1, -4], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-8, 1, 0, -1], [1, 0, 1, -4], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0006","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b311b8737ea21e99c40ff6e418c626bd2988a6de73d5b7ed9a76bdd33b5adfa1","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157006,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[-7,1],[1,0],[0,1],[-1,-5]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[-7, 1], [1, 0], [0, 1], [-1, -5]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([-7, 1, 0, -1], [1, 0, 1, -5], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-7, 1, 0, -1], [1, 0, 1, -5], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0007","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e4cbb6e325b1e8add4f0097a5ef3302a1e96bc32a809da0f3e8753f15cfa89f7","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157007,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[-6,1],[1,0],[0,1],[-1,-6]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[-6, 1], [1, 0], [0, 1], [-1, -6]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([-6, 1, 0, -1], [1, 0, 1, -6], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-6, 1, 0, -1], [1, 0, 1, -6], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0008","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"509aa9637ca4a598cc338df646fc7feb09ae20179035fd6192146ca8d0c1bb01","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157008,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[-5,1],[1,0],[0,1],[-1,-7]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[-5, 1], [1, 0], [0, 1], [-1, -7]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([-5, 1, 0, -1], [1, 0, 1, -7], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-5, 1, 0, -1], [1, 0, 1, -7], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0009","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d6d54ccea1bc1168e918c48dd06f9d74d6ab177b9c030592c6a15e792e211dd6","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157009,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[-4,1],[1,0],[0,1],[-1,-8]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[-4, 1], [1, 0], [0, 1], [-1, -8]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([-4, 1, 0, -1], [1, 0, 1, -8], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-4, 1, 0, -1], [1, 0, 1, -8], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0010","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"76fcba3ce01346ea961567f92fb2c5dd17cf561bee62c4318636dca2307b9eac","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157010,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[-3,1],[1,0],[0,1],[-1,-9]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[-3, 1], [1, 0], [0, 1], [-1, -9]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([-3, 1, 0, -1], [1, 0, 1, -9], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-3, 1, 0, -1], [1, 0, 1, -9], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0011","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b8409ff999c6bdc54610736cf966256a4aada1c779ad690346393f450bb71785","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157011,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[-2,1],[1,0],[0,1],[-1,-10]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[-2, 1], [1, 0], [0, 1], [-1, -10]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([-2, 1, 0, -1], [1, 0, 1, -10], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-2, 1, 0, -1], [1, 0, 1, -10], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0012","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"03d8c30f675abb2af015958c7d5867cadff6e25d5bb2b5a79d89b350337bf616","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157012,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[-1,1],[1,0],[0,1],[-1,-11]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[-1, 1], [1, 0], [0, 1], [-1, -11]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([-1, 1, 0, -1], [1, 0, 1, -11], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([-1, 1, 0, -1], [1, 0, 1, -11], [No, Yes, No, No], [No, No, Yes, No], [II, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0013","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"474b563c77a00bb90c1e81e162a48fe883432c0efcef1a95562ace6f0b2b847d","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157013,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[0,1],[1,0],[0,1],[-1,-12]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[0, 1], [1, 0], [0, 1], [-1, -12]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([0, 1, 0, -1], [1, 0, 1, -12], [No, Yes, No, No], [Yes, No, Yes, No], [y-axis, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([0, 1, 0, -1], [1, 0, 1, -12], [No, Yes, No, No], [Yes, No, Yes, No], [y-axis, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0014","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6f91c2d89e78acfa3d5ef08ce02ca1fd923ab2b8321debd58eabb9426791fd25","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157014,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[1,1],[1,0],[0,1],[-1,-13]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[1, 1], [1, 0], [0, 1], [-1, -13]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([1, 1, 0, -1], [1, 0, 1, -13], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([1, 1, 0, -1], [1, 0, 1, -13], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0015","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f7a38aadfc7983629644f2b897f4e872a86730a9441bc39cf8e4d830cfdfe6e3","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157015,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[2,1],[1,0],[0,1],[-1,-14]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[2, 1], [1, 0], [0, 1], [-1, -14]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([2, 1, 0, -1], [1, 0, 1, -14], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([2, 1, 0, -1], [1, 0, 1, -14], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0016","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9b91e8709bb350c4eee473f6a04cb87c15d1cce3f02734ab9b040ecc594de650","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157016,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[3,1],[1,0],[0,1],[-1,-15]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[3, 1], [1, 0], [0, 1], [-1, -15]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([3, 1, 0, -1], [1, 0, 1, -15], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([3, 1, 0, -1], [1, 0, 1, -15], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0017","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"12dfe2e80e9c709724ed4acc90485126133f6f21ad3ba821210c2f635c12d970","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157017,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[4,1],[1,0],[0,1],[-1,-16]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[4, 1], [1, 0], [0, 1], [-1, -16]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([4, 1, 0, -1], [1, 0, 1, -16], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([4, 1, 0, -1], [1, 0, 1, -16], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0018","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"69b3fdfb6da3e55d5847515053e47800697722a6d00d1ccd4f00384f83e6415b","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157018,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[5,1],[1,0],[0,1],[-1,-17]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[5, 1], [1, 0], [0, 1], [-1, -17]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([5, 1, 0, -1], [1, 0, 1, -17], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([5, 1, 0, -1], [1, 0, 1, -17], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0019","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"212e13233377b31faa384a05180af9a8b15ea1d7db07f951cd5a0f5cbc71e109","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157019,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[6,1],[1,0],[0,1],[-1,-18]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[6, 1], [1, 0], [0, 1], [-1, -18]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([6, 1, 0, -1], [1, 0, 1, -18], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([6, 1, 0, -1], [1, 0, 1, -18], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0020","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5584ece9f94438b92d19855f820cefefad25f648d87cad3ec88f89b0babda681","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157020,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[7,1],[1,0],[0,1],[-1,-19]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[7, 1], [1, 0], [0, 1], [-1, -19]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([7, 1, 0, -1], [1, 0, 1, -19], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([7, 1, 0, -1], [1, 0, 1, -19], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0021","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e67ab639097c975120d78fcb8f19a6978b182cd3fec5e77b8ad75ef5bc791c1d","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157021,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[8,1],[1,0],[0,1],[-1,-20]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[8, 1], [1, 0], [0, 1], [-1, -20]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([8, 1, 0, -1], [1, 0, 1, -20], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([8, 1, 0, -1], [1, 0, 1, -20], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0022","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"dc799aa17d56b9d61a3b830bc93e6b2fe6a87ff701f4da5d022641552bcc3683","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157022,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[9,1],[1,0],[0,1],[-1,-21]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[9, 1], [1, 0], [0, 1], [-1, -21]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([9, 1, 0, -1], [1, 0, 1, -21], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([9, 1, 0, -1], [1, 0, 1, -21], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0023","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"98588f6bb5fafae4634707789d91b219d784257b65c546b8037853adf00892eb","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157023,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[10,1],[1,0],[0,1],[-1,-22]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[10, 1], [1, 0], [0, 1], [-1, -22]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([10, 1, 0, -1], [1, 0, 1, -22], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([10, 1, 0, -1], [1, 0, 1, -22], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0024","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1125d85dac8353f100edc9653214a1924602d9f3672e9dc8a3822db3c068cfb1","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157024,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[11,1],[1,0],[0,1],[-1,-23]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[11, 1], [1, 0], [0, 1], [-1, -23]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([11, 1, 0, -1], [1, 0, 1, -23], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([11, 1, 0, -1], [1, 0, 1, -23], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0025","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"baa57b8c32686e1be58d276093afdb158c3b9e93aba04bf3da62a927f91d0c25","family_id":"qf-density15-coordinate-four-point-axis-masks","seed":202610157025,"semantic_template":"qf-density15-coordinate-four-point-axis-masks/[[12,1],[1,0],[0,1],[-1,-24]]"},"fields":{"title":"Four Ordered Coordinate Columns, Axes, and Locations","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Four ordered points=[[12, 1], [1, 0], [0, 1], [-1, -24]]. Give (x column, y column, x-axis mask, y-axis mask, origin/x-axis/y-axis/I/II/III/IV classifications).","answer":{"kind":"expression","value":"([12, 1, 0, -1], [1, 0, 1, -24], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])","explanation":"Read both ordered columns, check zero components before quadrants, and then use signs; component data do not determine distances or rendered dimensions. The exact result, retaining the requested order, is ([12, 1, 0, -1], [1, 0, 1, -24], [No, Yes, No, No], [No, No, Yes, No], [I, x-axis, y-axis, III])."},"skills":["Four Ordered Coordinate Columns, Axes, and Locations"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0026","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1215937f8098eb9485eeda4b0ebfeea81bb28933c57a3b7450b4f8d753692767","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157026,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"0\",\"0\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[0, 0], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(0, 0, Yes)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (0, 0, Yes)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0027","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"86488e014e77735e8c8f1aea5258b5d873fb80c32807d5e052ced1d36222a857","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157027,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-1\",\"1\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[1, 2], Q=[2, 1]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(-1, 1, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-1, 1, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0028","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4c92914314a4589301b6ece26f274798e4e0be5cd7c17c5f85b694c34ee1f98f","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157028,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-10\",\"3\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-10, 3], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(-10, 3, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-10, 3, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0029","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"abe36981ab716cc47721afe691878ef6e5ada3b3a19719f77ca9ae4d5e7be2cf","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157029,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-9\",\"4\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-9, 4], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(-9, 4, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-9, 4, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0030","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"84c10167e1e13c689eff2ad95eb9711d69f6aafde708ddad7aba63d0ecc30878","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157030,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-8\",\"5\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-8, 5], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(-8, 5, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-8, 5, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0031","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"20415bd2d4c969ee1e4dcf1257daefcef97174d1812739a0fa99671493ed52fb","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157031,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-7\",\"6\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-7, 6], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(-7, 6, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-7, 6, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0032","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1d413c494764e63ef63f11e7674d04c918483d5ea7409d28ec3d3eaaa28e5735","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157032,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-6\",\"7\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-6, 7], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(-6, 7, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-6, 7, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0033","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1c54924714473cae442d6f432386a5924bde6c6d206fce68e84cc2120bb5658c","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157033,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-5\",\"8\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-5, 8], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(-5, 8, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-5, 8, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0034","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a75586831fd92367801620a76a2ce2c29dd9d6fb64034f1bbc1562abd9669799","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157034,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-4\",\"9\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-4, 9], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(-4, 9, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-4, 9, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0035","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3bb8e3d1659281200bd17c6c2c1284d68161e77d8e2ce451ccbac3ea105ba465","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157035,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-3\",\"10\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-3, 10], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(-3, 10, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-3, 10, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0036","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a12cf883f7923c37760c03e6caf3bbcc05de3c7fa9cedc59907126ec72a95cae","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157036,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-2\",\"11\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-2, 11], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(-2, 11, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-2, 11, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0037","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0e92410eb62bdfbfb1a87e91328ce2e1b82a6e3d510eec396c90b1644c269a38","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157037,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"-1\",\"12\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-1, 12], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(-1, 12, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (-1, 12, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0038","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6b9be39b223faa2997f08213580623f5bc14ea9370a00170d08ccdf7974f2d83","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157038,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"0\",\"13\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[0, 13], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(0, 13, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (0, 13, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0039","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8856d1bbbf6f2d0e60f678564f678437550e0a3cdc37f2952ae201844feec0ce","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157039,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"1\",\"14\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[1, 14], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(1, 14, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (1, 14, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0040","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5faff0acb50a7a7da3e8ad89ed5b6e36957f2662f4eaf980ce4068cdbab9e335","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157040,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"2\",\"15\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[2, 15], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(2, 15, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (2, 15, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0041","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5c77fb3d111e2a3e22240fe71a89bd0ff4ed97fc82bf8dc6c7815a95576b314b","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157041,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"3\",\"16\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[3, 16], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(3, 16, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (3, 16, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0042","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d97cedc35a1f5318300fc90b579bf5b4848792bc082d729f8e17e17bb4bff3e1","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157042,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"4\",\"17\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[4, 17], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(4, 17, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (4, 17, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0043","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b8e2938c2ed29f9968a9517ce0cce2509a822ca6991c9fcc950b98d2aeae6030","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157043,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"5\",\"18\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[5, 18], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(5, 18, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (5, 18, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0044","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"78638540c5561c1363403d2d26bd4881a8ef7ba247be726a7059d31d37b11502","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157044,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"6\",\"19\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[6, 19], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(6, 19, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (6, 19, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0045","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a78f168dcfbd27f12919977fa77a2d603a6f78edabe3800ab80d984723f49c5f","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157045,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"7\",\"20\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[7, 20], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(7, 20, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (7, 20, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0046","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"66f6ae9de00dbfc3e0047e7907bd994a3584da7c7fce094848f021e12c350c17","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157046,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"8\",\"21\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[8, 21], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(8, 21, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (8, 21, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0047","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"36415ee389c50ef251cc3179043051b7dd0d1671ed28655747e9883e32e6d44b","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157047,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"9\",\"22\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[9, 22], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(9, 22, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (9, 22, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0048","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2337947c9a55c30eeb93038a9b043219307ab08ea1ea1faf8ee4ebaa8927e482","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157048,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"10\",\"23\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[10, 23], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(10, 23, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (10, 23, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0049","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5d013a57e7cb266379e14a6d26353f4771d4fde695b4b9f5ee783b40660707ad","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157049,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"11\",\"24\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[11, 24], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(11, 24, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (11, 24, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0050","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ab688d3e70bbf43865da7afdad27c3cbc733a9dde8440db071ffb8fe98e9673d","family_id":"qf-density15-coordinate-ordered-pair-compare","seed":202610157050,"semantic_template":"qf-density15-coordinate-ordered-pair-compare/[\"12\",\"25\"]"},"fields":{"title":"Componentwise Coordinate Differences and Equality","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[12, 25], Q=[0, 0]. Give (P.x−Q.x, P.y−Q.y, are the points equal?), not an L2 distance.","answer":{"kind":"expression","value":"(12, 25, No)","explanation":"Subtract corresponding components and require both defects to vanish for equality in the same frame. The exact result, retaining the requested order, is (12, 25, No)."},"skills":["Componentwise Coordinate Differences and Equality"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0051","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5cd926f992f1fe2b512b216b509077ee526d0e5f6db8059e001ebe79ffec56d6","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157051,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[0,0],[\"0\",\"0\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[0, 0], candidate=[0, 0], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([0, 0], [0, 0], Yes, Yes)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([0, 0], [0, 0], Yes, Yes)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0052","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1b7ff5a410ef0757fa82a957f7c3c80dc0d058fae80a92c70429739aed305dcf","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157052,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[1,1],[\"0\",\"0\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[1, 1], candidate=[1, 1], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([1, 1], [0, 0], Yes, Yes)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([1, 1], [0, 0], Yes, Yes)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0053","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6723125c16b066fd4e2702a59a38529a730c5fab89ab57119a8348face50f2ad","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157053,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[1,2],[\"0\",\"0\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[1, 2], candidate=[2, 1], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([2, 1], [0, 0], Yes, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([2, 1], [0, 0], Yes, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0054","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d07a73a44d0ebaea89ac303ef2b3fd18dc493874801811386fb096b965d05b52","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157054,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[1,2],[\"-1\",\"1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[1, 2], candidate=[1, 2], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([2, 1], [-1, 1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([2, 1], [-1, 1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0055","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9457ed1bc9465be88087fe7ca2dee09c6eda14a9749dd5a09383c68c64dfd829","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157055,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[-8,5],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-8, 5], candidate=[6, -9], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([5, -8], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([5, -8], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0056","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"030194b84695ba082ea0d0c3f4129e14ba25770cf34bcdedb0e29bad1be8e582","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157056,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[-7,6],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-7, 6], candidate=[7, -8], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([6, -7], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([6, -7], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0057","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8b41b582aaad3b08b2daf5661c752444bde2c8b346f44b0988d91ae0db841ae8","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157057,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[-6,7],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-6, 7], candidate=[8, -7], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([7, -6], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([7, -6], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0058","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4b54d9b38ee01fda7c3a58da04e1e51c806d48f73cec0a2a5a35cf2e0857f8b0","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157058,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[-5,8],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-5, 8], candidate=[9, -6], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([8, -5], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([8, -5], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0059","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"577d2ad9f74dc9ccac366c3553ef5bc000ef20b39b7b0b4a34bc84ff8de4e9c4","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157059,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[-4,9],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-4, 9], candidate=[10, -5], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([9, -4], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([9, -4], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0060","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5d6db8a33583fa7e2412048039c6b6dff5289e3851cc3a94cd56b30dc527d9ad","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157060,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[-3,10],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-3, 10], candidate=[11, -4], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([10, -3], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([10, -3], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0061","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9e9f76b18ed2578ad2bd499a33da7139f0620a13e8e4f946e7bc665aebf41d44","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157061,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[-2,11],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-2, 11], candidate=[12, -3], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([11, -2], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([11, -2], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0062","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1387315b1bdbfb9289988612a219b55f19169626ea3deb95a3830d7db743e982","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157062,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[-1,12],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[-1, 12], candidate=[13, -2], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([12, -1], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([12, -1], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0063","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d950ad91aced8faa8ce6d471abf82f6a3edfd1cfc082b26e06dbd47b56aacd86","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157063,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[0,13],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[0, 13], candidate=[14, -1], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([13, 0], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([13, 0], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0064","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7fb542909e19e2130eaff1ebb77a08b134e511e263ff1dadf31f79172678ded5","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157064,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[1,14],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[1, 14], candidate=[15, 0], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([14, 1], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([14, 1], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0065","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d928a8288f94e405a098dd252dba048da1f77bdce9ba885970b5c2602f7d5b60","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157065,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[2,15],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[2, 15], candidate=[16, 1], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([15, 2], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([15, 2], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0066","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"82966cad01059d6ad9c2d3f896feb19cbc95c6e27bff2c8fe83f6a50e6ded501","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157066,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[3,16],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[3, 16], candidate=[17, 2], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([16, 3], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([16, 3], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0067","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3df74ddf9b18a50e6570b9798b2ae616615528f56aec15e494aa2e5e33adc469","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157067,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[4,17],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[4, 17], candidate=[18, 3], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([17, 4], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([17, 4], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0068","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c4907a6b963bc4ff72072e9707d3339d9d612b44984ea606ceec1e2b2653dd7b","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157068,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[5,18],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[5, 18], candidate=[19, 4], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([18, 5], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([18, 5], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0069","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9bc8ca17a5c120015b611d34848a023de2ed31b6293c275791393ebfdba77a87","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157069,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[6,19],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[6, 19], candidate=[20, 5], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([19, 6], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([19, 6], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0070","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b0d794209e5b606fca4425bc7f796f174b0e0ffb0bc4df77f64f605b8312e6c7","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157070,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[7,20],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[7, 20], candidate=[21, 6], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([20, 7], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([20, 7], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0071","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e13a667c135c4de02a2cf32b24f7c3b2a38c9502270731f0cd1955fb4ae6dc8a","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157071,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[8,21],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[8, 21], candidate=[22, 7], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([21, 8], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([21, 8], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0072","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ce1db6c33ce9eb32cce1f8ff99ef1b75efaec178f2bd99cca42a591fee5582e0","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157072,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[9,22],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[9, 22], candidate=[23, 8], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([22, 9], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([22, 9], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0073","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d95cacc20b97c908264e89bfc419c8067e23bbc15845e606c00be5ba1b1ac27b","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157073,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[10,23],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[10, 23], candidate=[24, 9], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([23, 10], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([23, 10], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0074","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d1d97589619744f3a31866cff11dd3cbb8e22df010d8a957ea41b64dcb4c7e48","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157074,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[11,24],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[11, 24], candidate=[25, 10], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([24, 11], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([24, 11], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0075","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"225e3e0b6a9774f5156ce3907f88a11143e7a0dbeec5d0dacd4774f4b1d056fb","family_id":"qf-density15-coordinate-swap-candidate-audit","seed":202610157075,"semantic_template":"qf-density15-coordinate-swap-candidate-audit/[[12,25],[\"1\",\"-1\"]]"},"fields":{"title":"Coordinate-Field Swap Candidate Audit","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. P=[12, 25], candidate=[26, 11], expected=(P.y,P.x). Give (expected list, candidate−expected component pair, is the candidate the true swap?, does P itself equal expected?).","answer":{"kind":"expression","value":"([25, 12], [1, -1], No, No)","explanation":"Swap data fields and check the candidate componentwise, then independently check whether P’s components were equal; this is not a formal geometric-reflection bridge. The exact result, retaining the requested order, is ([25, 12], [1, -1], No, No)."},"skills":["Coordinate-Field Swap Candidate Audit"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0076","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8586fabe72d3eacb17004b8f7e04b1c86f3ebe645a7b9129cd65d27b3811e01a","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157076,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"0\",\"0\"],[\"0\",\"0\"],[\"0\",\"0\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[0, 0], [0, 0]], [[0, 0], [0, 0]], [[0, 0], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[0, 0], [0, 0], [0, 0]], [Yes, Yes, Yes], none)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[0, 0], [0, 0], [0, 0]], [Yes, Yes, Yes], none)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0077","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e27cf732ac0fdb441bfd21a18971c32107de141c6308721cc6b5d9393a3762cf","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157077,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"1\",\"0\"],[\"0\",\"0\"],[\"0\",\"0\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[1, 0], [0, 0]], [[0, 0], [0, 0]], [[0, 0], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[1, 0], [0, 0], [0, 0]], [No, Yes, Yes], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[1, 0], [0, 0], [0, 0]], [No, Yes, Yes], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0078","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7a025c25d256ba5fb83b79a818e56f34a084474114dc5866a9a4dd85cded8e05","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157078,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"0\",\"0\"],[\"0\",\"-1\"],[\"0\",\"0\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[0, 0], [0, 0]], [[0, -1], [0, 0]], [[0, 0], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[0, 0], [0, -1], [0, 0]], [Yes, No, Yes], 1)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[0, 0], [0, -1], [0, 0]], [Yes, No, Yes], 1)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0079","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"53158e1274976e294dd6d5c27d16366c52017cc63be799e419c938a840a92bdf","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157079,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"0\",\"0\"],[\"0\",\"0\"],[\"1\",\"1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[0, 0], [0, 0]], [[0, 0], [0, 0]], [[1, 1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[0, 0], [0, 0], [1, 1]], [Yes, Yes, No], 2)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[0, 0], [0, 0], [1, 1]], [Yes, Yes, No], 2)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0080","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6e091f96608603f14bda823a7bfe51b081f6f3cb7ac4132a1235082c567d225b","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157080,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"-8\",\"1\"],[\"0\",\"4\"],[\"0\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[-8, 1], [0, 0]], [[0, 4], [0, 0]], [[0, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[-8, 1], [0, 4], [0, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[-8, 1], [0, 4], [0, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0081","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b0ab6e88b9c498bd1cf7bb17a7db979ae823b3e8b11a85dbb301d4ce46723cf1","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157081,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"-7\",\"1\"],[\"0\",\"5\"],[\"1\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[-7, 1], [0, 0]], [[0, 5], [0, 0]], [[1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[-7, 1], [0, 5], [1, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[-7, 1], [0, 5], [1, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0082","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b96945b4bc4d4fb7601ab5661a2dd18031c2d9eac9a1c83c87e72de2b2d47a85","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157082,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"-6\",\"1\"],[\"0\",\"6\"],[\"-1\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[-6, 1], [0, 0]], [[0, 6], [0, 0]], [[-1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[-6, 1], [0, 6], [-1, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[-6, 1], [0, 6], [-1, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0083","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e7c74fb352ccd9bd058e46cf2ec812f98ebe4911b68f4d6844698d69e3ae4c2f","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157083,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"-5\",\"1\"],[\"0\",\"7\"],[\"0\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[-5, 1], [0, 0]], [[0, 7], [0, 0]], [[0, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[-5, 1], [0, 7], [0, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[-5, 1], [0, 7], [0, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0084","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cf58ab9d9dc9a9e464142e613d6b84265559c31e5197e4fc8639394795991899","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157084,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"-4\",\"1\"],[\"0\",\"8\"],[\"1\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[-4, 1], [0, 0]], [[0, 8], [0, 0]], [[1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[-4, 1], [0, 8], [1, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[-4, 1], [0, 8], [1, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0085","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"27229f975fa464931770fce8bd22da5e34222bd75a0dfdfdac1b16a3e6f1ca1c","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157085,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"-3\",\"1\"],[\"0\",\"9\"],[\"-1\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[-3, 1], [0, 0]], [[0, 9], [0, 0]], [[-1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[-3, 1], [0, 9], [-1, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[-3, 1], [0, 9], [-1, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0086","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"51b0982401a4ef65cf096f7fa3b092552af24815cd083a8c4974cbe9cbb0e612","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157086,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"-2\",\"1\"],[\"0\",\"10\"],[\"0\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[-2, 1], [0, 0]], [[0, 10], [0, 0]], [[0, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[-2, 1], [0, 10], [0, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[-2, 1], [0, 10], [0, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0087","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fc3d3f3cd40dbaa16fbf19a184c12a09ef320ae977fee5bfcb8004aced4ecdc4","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157087,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"-1\",\"1\"],[\"0\",\"11\"],[\"1\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[-1, 1], [0, 0]], [[0, 11], [0, 0]], [[1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[-1, 1], [0, 11], [1, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[-1, 1], [0, 11], [1, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0088","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9299499fd1104021efce2201455d0ea335ac7544b76ea63613028f4bfb7cce69","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157088,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"0\",\"1\"],[\"0\",\"12\"],[\"-1\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[0, 1], [0, 0]], [[0, 12], [0, 0]], [[-1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[0, 1], [0, 12], [-1, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[0, 1], [0, 12], [-1, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0089","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2b4e07603dc5568bf999a3349e9ad5e34340005a1a22497b82c4e0475ea74f64","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157089,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"1\",\"1\"],[\"0\",\"13\"],[\"0\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[1, 1], [0, 0]], [[0, 13], [0, 0]], [[0, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[1, 1], [0, 13], [0, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[1, 1], [0, 13], [0, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0090","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0e6fc096bb373f583644cf43aa4c949c2eb5411af4baaa2b0f22be5ea4fe2abd","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157090,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"2\",\"1\"],[\"0\",\"14\"],[\"1\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[2, 1], [0, 0]], [[0, 14], [0, 0]], [[1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[2, 1], [0, 14], [1, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[2, 1], [0, 14], [1, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0091","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e55f7d10d91b42b98b6d0838c95d980d9a4c3eea3bd27ffa61f447c44966469b","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157091,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"3\",\"1\"],[\"0\",\"15\"],[\"-1\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[3, 1], [0, 0]], [[0, 15], [0, 0]], [[-1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[3, 1], [0, 15], [-1, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[3, 1], [0, 15], [-1, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0092","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5bd8bf482dd98f890697933742433b5d07bc665492498739d50d73edb7f64d84","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157092,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"4\",\"1\"],[\"0\",\"16\"],[\"0\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[4, 1], [0, 0]], [[0, 16], [0, 0]], [[0, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[4, 1], [0, 16], [0, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[4, 1], [0, 16], [0, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0093","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"89ef5951cacfb096b76d2c35805739bb6a4cabc2a680de10a676b25145344913","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157093,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"5\",\"1\"],[\"0\",\"17\"],[\"1\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[5, 1], [0, 0]], [[0, 17], [0, 0]], [[1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[5, 1], [0, 17], [1, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[5, 1], [0, 17], [1, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0094","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c5f3d0b9a73461740e1552f0f0cee108f7fcf6388ebede64b44c12d8a3d5308f","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157094,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"6\",\"1\"],[\"0\",\"18\"],[\"-1\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[6, 1], [0, 0]], [[0, 18], [0, 0]], [[-1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[6, 1], [0, 18], [-1, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[6, 1], [0, 18], [-1, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0095","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c684f5878d12c316e276b886eb2d499e9da0f10f5143079f0cbcc4b7ba7c02de","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157095,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"7\",\"1\"],[\"0\",\"19\"],[\"0\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[7, 1], [0, 0]], [[0, 19], [0, 0]], [[0, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[7, 1], [0, 19], [0, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[7, 1], [0, 19], [0, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0096","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fe87f59235ff120bf1ee482c31df9d11ff01be0c8566980bdf2055411c92a6a5","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157096,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"8\",\"1\"],[\"0\",\"20\"],[\"1\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[8, 1], [0, 0]], [[0, 20], [0, 0]], [[1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[8, 1], [0, 20], [1, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[8, 1], [0, 20], [1, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0097","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"590f008255e87589f928b713b37f8d06b1e2a49a37bd3f67801db254d460a82b","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157097,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"9\",\"1\"],[\"0\",\"21\"],[\"-1\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[9, 1], [0, 0]], [[0, 21], [0, 0]], [[-1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[9, 1], [0, 21], [-1, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[9, 1], [0, 21], [-1, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0098","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b7b835e71967cdb49f0e1a345bfc9b20a59e98ebb7065ace43e1dc992b67f362","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157098,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"10\",\"1\"],[\"0\",\"22\"],[\"0\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[10, 1], [0, 0]], [[0, 22], [0, 0]], [[0, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[10, 1], [0, 22], [0, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[10, 1], [0, 22], [0, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0099","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c29a63733724f6bf6cb1322f54310f8ea713c9efa4b6b71b51f7fcd83145162","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157099,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"11\",\"1\"],[\"0\",\"23\"],[\"1\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[11, 1], [0, 0]], [[0, 23], [0, 0]], [[1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[11, 1], [0, 23], [1, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[11, 1], [0, 23], [1, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20261011-advance-20261015-r07-coordinate-plane-0100","batch_id":"batch-20261011-advance-20261015-r07-coordinate-plane-foundations","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0e333b11468d54d0f7f40dec98fc09483c2fcbea5717689189c773bafe562926","family_id":"qf-density15-coordinate-first-mismatch-index","seed":202610157100,"semantic_template":"qf-density15-coordinate-first-mismatch-index/[[\"12\",\"1\"],[\"0\",\"24\"],[\"-1\",\"-1\"]]"},"fields":{"title":"Three Ordered Coordinate Comparisons and First Mismatch","stem":"Use ordered integer pairs in the same orthogonal directed xy frame. The origin lies on both axes; axis points are not in quadrants. Three ordered [P,Q] pairs=[[[12, 1], [0, 0]], [[0, 24], [0, 0]], [[-1, -1], [0, 0]]]. Give (each P−Q component residual pair, pair-equality mask, first unequal zero-based index or none).","answer":{"kind":"expression","value":"([[12, 1], [0, 24], [-1, -1]], [No, No, No], 0)","explanation":"Check both components in each pair and take the first actual mismatch in original order; all equal gives none, and components are not distances. The exact result, retaining the requested order, is ([[12, 1], [0, 24], [-1, -1]], [No, No, No], 0)."},"skills":["Three Ordered Coordinate Comparisons and First Mismatch"],"verification_warning":"This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."}}