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R0009-05326 · q-20261008-advance-20261012-r02-counting-principle-0001
Mutually exclusive tagged categories have ordered sizes=[]. Give (total choices, each prefix’s total), retaining an empty list.
G001 — Mutually exclusive tagged categories have ordered sizes=[]. Give (total choices, each prefix’s total), retaining an empty list.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
declared finite tagged choices or full-product protocol
After
combinatorial counts,not probabilities or independence
Conditions: none
Addition uses disjoint tags and multiplication uses the declared full cross-stage protocol;neither is a probability-independence assumption.
Rule: finite_counting_protocol_scope · Uses: G001
Before
ordered sizes=[]
After
initial accumulator=0
Conditions: none
The empty disjoint sum is0;the empty full product is1,representing one empty choice sequence.
Rule: counting_prefix_initial · 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.(0, [])
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: 87b2933ba3a2d351ed36afaff8e6fa475d0ebee7fbb4e80ef7d9fb49d3bac891candidate record SHA-256: 1d6b5f793ef84d50f02b81f83de07aa0dbb5936c6ffcb73af237a0890ae1de16semantic review receipt SHA-256: 71e7db519df31f3a164533e472e293cb64f001b475a8d002b4a5c2740a237b56question-first witness SHA-256: 5a43f4f81b6256281f8d139a4010bbde127be803c528e5878857269c8f854462Lean: NOT_RUN · human review: NOT_PERFORMED