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R0070-35524 · q-20260914-basic-counting-principle-0004
A process has 5 first-stage choices, but the number of second-stage options depends on the first choice and can be 4 or 5. May one fixed product be used unconditionally?
G001 — A process has 5 first-stage choices, but the number of second-stage options depends on the first choice and can be 4 or 5. May one fixed product be used unconditionally?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 = [qf-basic-counting-principle, [branch_counts, conditional_stage_witness, mode, overlap_witness, stages]]
After
derived = [counting, null, null]
Conditions: none
Use THIS bank’s actual fields,operation/domain and types.BASE retains permissible extra metadata.Do not import LDL SAFE/set limits or a different bank’s deduplication rules.
Rule: R70_SOURCE_bank_specific_interface · Uses: G001
Before
source roles = [5, 4, 5]
After
derived = [cannot multiply unconditionally]
Conditions: none
Two GIVEN conditional continuation counts differ,u≠v,so there is no common fixed b for an unconditional a·b total.A full total requires every first choice’s continuation count and summation.Unused stage metadata is not an extra premise.
Rule: Counting_CONDITIONAL_different_continuations_no_fixed_product · Uses: G001, S001
S002 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.S001 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.Cannot multiply unconditionally
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: 509e82b156472f019afd07c3f097715fda89fd4b4e27161bb69ce8b98f5785c1candidate record SHA-256: 7b2e0f5350d16f6fe94f1295084ae1db395961b708892f37590eccb97ae5f001semantic review receipt SHA-256: 9820ac6529139bd53d516c8bfdfdd41184b0cd52dad69fa433344010db37af80question-first witness SHA-256: c9c939762bbd4d3ea3403084c8e95541dc2c7e56eb82fc74eaba8c80a4517dabLean: NOT_RUN · human review: NOT_PERFORMED