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R0047-24049 · q-20261014-advance-20261112-r02-taylor-polynomial-0099
Use mode=remainder_claim, supplied derivatives=[24, 48, 72], center=11, order=2, alternate_center=12. Give (mode, order, derivatives, center, alternate_center, unsupported_definition_or_remainder_claim, boundary).
G001 — Use mode=remainder_claim, supplied derivatives=[24, 48, 72], center=11, order=2, alternate_center=12. Give (mode, order, derivatives, center, alternate_center, unsupported_definition_or_remainder_claim, boundary).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
source roles = [taylor-definition-boundary]
After
derived = [[mode, order, derivatives, center, alternate_center, unsupported_definition_or_remainder_claim, boundary]]
Conditions: none
List the source field order without JavaScript.Gradient boundary uses its original mode to choose6,8 or7 fields;no padding or answer-derived mode.
Rule: source_ordered_fields_without_JS · Uses: G001
Before
source roles = [remainder_claim, 2, [24, 48, 72], 11, 12]
After
derived = [[0, 1, 2], 3, No, a_Taylor_polynomial_alone_gives_no_remainder_or_series_equality]
Conditions: none
Missing data means every derivative order0..n,including f(a),not that values must vanish.A center-bound jet cannot simply be shifted,even if a constant special case agrees.Division by k! is required despite accidental low-order equality.A polynomial alone supplies neither a remainder bound nor analyticity;No does not deny special equality.
Rule: Taylor_definition_boundary_keeps_actual_jet_and_center · Uses: G001, S001
S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.(remainder_claim, 2, [24, 48, 72], 11, 12, No, a_Taylor_polynomial_alone_gives_no_remainder_or_series_equality)
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: 52eb12926024740f9f071fbd5ff649ea571009896bdd8ce801e429476d4e84b5candidate record SHA-256: c2b532261ef9a2582ae62811fc33e0be6e214665b91569f337cad61406136b76semantic review receipt SHA-256: 9b43b9823e9bd2478d6caa5b57ffed161c2c8956af86974e901d5662ad994386question-first witness SHA-256: eb97596068e2d5648033bab2b8f6ca9b653bbe8cb77c0f8e1d16d0c40e46f50bLean: NOT_RUN · human review: NOT_PERFORMED