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R0055-28225 · q-20261003-r01-power-root-0025
For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (12)^0 exactly.
G001 — For real bases and natural-number exponents, use the empty-product convention a^0=1, including 0^0=1 in this algebraic setting. Compute (12)^0 exactly.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-natural-power-exact, natural_power]
After
derived = [[exact_integer_power]]
Conditions: none
List this scalar/label/set/point answer role or mode-specific ordered fields,not an imposed universal tuple.Retain legacy domain/underscore operation and integer fractions with/1;original bilingual snapshots stay unchanged.
Rule: source_answer_roles_or_ordered_fields_without_JS · Uses: G001
Before
source roles = [12, 0, empty_product]
After
derived = [1, positive]
Conditions: none
The n0 empty product is1,including0^0=1 in THIS algebraic setting,not a limit rule.For n>0 a zero base gives0;otherwise sign follows base sign and exponent parity.All BigInt results remain exact without derived SAFE/1e8 clipping.
Rule: Legacy_power_ALL_n_products_EMPTYproduct_n0_and_sign_parity · Uses: G001, S001
S002 · premise_and_result_audit — Reverse-check complete original data,operands and premises;finite checks,conditional reasoning,formal proof and publication authority remain distinct.S001 · premise_and_result_audit — Reverse-check complete original data,operands and premises;finite checks,conditional reasoning,formal proof and publication authority remain distinct.1
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: 56ea32f4671e149019ed27263517f78eb576d72e79bfe9b7142624dc7bd04cd7candidate record SHA-256: 9988f569405f2f2fbafed727087d957e30a4737cbd89880d544a78b9812fd6e7semantic review receipt SHA-256: 6af367dae24a584f3596525c4953bbc2115343efd68cc9083693eb5c1ef2e683question-first witness SHA-256: 611eb69f3716404b968296a8b0d7d8c61b5ca18129d406f1ff9c7c11e10ffb4eLean: NOT_RUN · human review: NOT_PERFORMED