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R0012-06813 · q-20261010-advance-20261014-r02-real-number-0013
Use an exact finite rational-point slice embedded in R, without approximate decimals or a completeness claim. a=-12/2≤b=13/3. Give (midpoint, midpoint−a, b−midpoint). Use exact reduced fractions with positive denominators, retaining /1 for integers.
G001 — Use an exact finite rational-point slice embedded in R, without approximate decimals or a completeness claim. a=-12/2≤b=13/3. Give (midpoint, midpoint−a, b−midpoint). Use exact reduced fractions with positive denominators, retaining /1 for integers.Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
explicit rational points embedded in the real line
After
exact finite order and distance data,not real completeness or irrational classification
Conditions: none
Use exact rational values for this finite slice of the real line,without rounded decimals or claims about real completeness or classification of irrationals.
Rule: rational_real_slice_scope · Uses: G001
Before
endpoint sum := sum(-6, 13/3)
After
endpoint sum = -5/3
Conditions: none
Add the two ordered endpoints completely.
Rule: exact_rational_arithmetic · Uses: G001, S001
Before
ordered midpoint := div(-5/3, 2)
After
ordered midpoint = -5/6
Conditions: none
Divide by2 for the exact midpoint;equal endpoints are allowed.
Rule: exact_rational_arithmetic · Uses: G001, S002
Before
midpoint minus left endpoint := sub(-5/6, -6)
After
midpoint minus left endpoint = 31/6
Conditions: none
The left distance is midpoint minus the left endpoint.
Rule: exact_rational_arithmetic · Uses: G001, S003
Before
right endpoint minus midpoint := sub(13/3, -5/6)
After
right endpoint minus midpoint = 31/6
Conditions: none
The right distance is the right endpoint minus midpoint.
Rule: exact_rational_arithmetic · Uses: G001, S004
Before
a=-6≤midpoint=-5/6≤b=13/3
After
two nonnegative distances equal 31/6
Conditions: none
Endpoint order makes both differences nonnegative distances;when a=b both are0,so no degenerate-interval exclusion is needed.
Rule: ordered_midpoint_equidistance · Uses: G001, S005
S006 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S005 · premise_and_result_audit — Recompute right endpoint minus midpoint with exact rational arithmetic, not rounded decimals.S004 · premise_and_result_audit — Recompute midpoint minus left endpoint with exact rational arithmetic, not rounded decimals.S003 · premise_and_result_audit — Recompute ordered midpoint with exact rational arithmetic, not rounded decimals.S002 · premise_and_result_audit — Recompute endpoint sum with exact rational arithmetic, not rounded decimals.S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.(-5/6, 31/6, 31/6)
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: adfc2da32d49afff3abecbc7ff868683da32f4a3c98bbdc068e56d3e51c85b49candidate record SHA-256: e062bce520c294863c43635a795236b9f1f9b381fbe240ba808cd5996727284bsemantic review receipt SHA-256: 90dbc494b2d34ef51f412dcff63cfcc1a2215d038bff71f38f5dded4c64faf00question-first witness SHA-256: b72a3b8bcf10f584396e0dd5198c657b0934a71864e5a3fa6321d7a613aef9f9Lean: NOT_RUN · human review: NOT_PERFORMED