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R0009-05496 · q-20261008-advance-20261012-r01-mathematical-induction-0021
N is indexed from 0; this is an explicitly finite induction protocol, not a universal proof. n=20. Give (index n of hypothesis P, index n+1 of the successor target), without claiming P holds.
G001 — N is indexed from 0; this is an explicitly finite induction protocol, not a universal proof. n=20. Give (index n of hypothesis P, index n+1 of the successor target), without claiming P holds.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
natural indices start at0;finite induction protocol
After
index bookkeeping and finite values are not proofs of all P(n)
Conditions: none
Natural indices do not require nonnegative sequence values.Checking a finite range or a successor index does not supply proposition truth or an induction proof over all naturals.
Rule: finite_induction_claim_boundary · Uses: G001
Before
successor target index := sum(20, 1)
After
successor target index = 21
Conditions: none
Add1 to the current natural index to obtain the successor target.
Rule: exact_rational_arithmetic · Uses: G001, S001
Before
hypothesis index=20
After
target index=21
Conditions: none
P(n) marks the induction hypothesis and P(n+1) the target;listing their indices does not assert either proposition.
Rule: hypothesis_vs_successor_target · 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 — Recompute successor target index 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.(20, 21)
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: 2f5efdbf997372425a072f351a7861d230bddcfb69cc5128d39c19c27857b12ecandidate record SHA-256: 942291a67b1d4ef69fdb16475253e1424cf91fa1409a19fb73189f05c008e0e0semantic review receipt SHA-256: 71e7db519df31f3a164533e472e293cb64f001b475a8d002b4a5c2740a237b56question-first witness SHA-256: 5a43f4f81b6256281f8d139a4010bbde127be803c528e5878857269c8f854462Lean: NOT_RUN · human review: NOT_PERFORMED