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R0001-01351 · q-20261007-advance-20261008-r06-antiderivative-0051
On all R, f has ascending coefficients [0], starting with its constant term. The candidate F has ascending rational coefficient pairs [[7, 1]], with positive denominators. Is F′=f as a coefficient identity?
G001 — On all R, f has ascending coefficients [0], starting with its constant term. The candidate F has ascending rational coefficient pairs [[7, 1]], with positive denominators. Is F′=f as a coefficient identity?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
domain=R; coefficient lists are in ascending powers
After
constant term first; rational pairs=[numerator,denominator]
Conditions: none
Fix coefficient order;do not read ascending coefficients as descending or swap numerator and denominator.
Rule: polynomial_representation · Uses: G001
Before
candidate F coefficients=[7]
After
target f coefficients=[0]
Conditions: none
A candidate may contain any constant,which disappears under differentiation.
Rule: candidate_vs_target · Uses: G001, S001
Before
differentiate all positive-degree terms
After
F′ coefficients=[0]
Conditions: none
For a constant polynomial,normalize the derivative list to one zero coefficient.
Rule: constant_derivative_zero · Uses: G001, S002
Before
F′ coefficients=[0]; f coefficients=[0]
After
F′=f identically: Yes
Conditions: none
Positive cases use full coefficient identity;negative cases also have an explicit counterexample point.
Rule: primitive_candidate_verdict · Uses: G001, S003
S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.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.Yes
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: e86559741f76e43bde2db6b00344014ee50fd1a01190cb442fcf6ed3f47fb960candidate record SHA-256: db731b16f279788991952387f772258c6b653ff62f64d297958519e95475dafbsemantic review receipt SHA-256: c3b44ce8ed60ada6902fb206627537d5f90ba2a867eaba43a36f903280c496ccquestion-first witness SHA-256: 3e91602adc7f81a2671a2a3ffaf6a447028b56abc5853e8271673d76f30cd7adLean: NOT_RUN · human review: NOT_PERFORMED