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R0048-24612 · q-20261015-advance-20261113-r03-analytic-ordinary-generating-function-0012
Use finite_support_coefficients=[12, 24, 36, 48, 60, 72] in increasing index order and the complete law a_n=0 after the list. Canonical answers trim trailing zero coefficients, without changing the original shared parameters. This is a complete finite-support law, not an unknown sequence observed only through a prefix. Extract index=2. Give (finite_support_coefficients, zero_tail_law, index, coefficient, certificate).
G001 — Use finite_support_coefficients=[12, 24, 36, 48, 60, 72] in increasing index order and the complete law a_n=0 after the list. Canonical answers trim trailing zero coefficients, without changing the original shared parameters. This is a complete finite-support law, not an unknown sequence observed only through a prefix. Extract index=2. Give (finite_support_coefficients, zero_tail_law, index, coefficient, certificate).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 = [ogf-coefficient-extraction]
After
derived = [[finite_support_coefficients, zero_tail_law, index, coefficient, certificate]]
Conditions: none
List the full source field order without JavaScript,keeping original data,Boolean flags,mathematical objects and nonclaims distinct.
Rule: source_ordered_fields_without_JS · Uses: G001
Before
source roles = [[12, 24, 36, 48, 60, 72]]
After
derived = [[12, 24, 36, 48, 60, 72], a_n=0 for EVERY n beyond this finite list]
Conditions: none
Trim only canonical trailing zeros without changing inputs,retaining at least one coefficient.This defines the entire sequence with its zero tail,not an observed prefix or the EGF coefficient a_n/n!.
Rule: OGF_complete_finite_support_zero_tail_NOT_unknown_prefix · Uses: G001, S001
Before
source roles = [[12, 24, 36, 48, 60, 72], 2]
After
derived = [36]
Conditions: none
Read a_k inside support;outside it use the declared complete zero tail.
Rule: OGF_exact_index_or_declared_zero_tail · Uses: G001, S002
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.([12, 24, 36, 48, 60, 72], a_n=0_after_the_list, 2, 36, coefficient_extraction_uses_the_complete_finite_support_law)
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: 45da7daf23cc06a54a0a359f3a916b9efd29161476f5d5be11342cbe328c6d0ecandidate record SHA-256: 8dd20165ea37957b02f8c585f54964f36d0c79d53ec1faf8f20fad432eddf4f0semantic review receipt SHA-256: 049a9e07e69fead88d93b34f0937b9470a06d71c1a8d097058fc83554529bdd0question-first witness SHA-256: 0c71ebb418f3de347d232d159fc25e93036f4ab9166bcfb5ee5b4be86d5c55b9Lean: NOT_RUN · human review: NOT_PERFORMED