Question 9944: Synthetic Kernel Metadata Qualification and Axiom Inventory Flag

Original question and givens

Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"","statement_id":"thm-18","term_sha256":"0000000000000000000000000000000000000000000000000000000000000012","type_sha256":"bad","kernel_checked":true,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.

• G001 — Use the synthetic small propositional calculus or synthetic receipt specified here, not actual Lean execution. The original source pulse did not run Lean builds for these questions. A statement, tactic log and kernel-checked proof are different obligations. Supplied metadata={"environment_id":"","statement_id":"thm-18","term_sha256":"0000000000000000000000000000000000000000000000000000000000000012","type_sha256":"bad","kernel_checked":true,"axioms_recorded":true}. Give (environment or missing, statement or missing, term-hash lexical shape?, type-hash lexical shape?, kernel flag, axioms-recorded flag, nonempty IDs plus both shapes plus kernel flag qualify?, synthetic receipt fields complete/still incomplete). Completeness additionally requires the axiom-recorded flag; no digest or kernel run is independently verified here.

Definition and scope

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.

• mko-lean-proof-term

Step-by-step derivation

synthetic proposition/term calculus or supplied synthetic receipt

no actual Lean build,source-digest check or kernel acceptance

environment ID="";statement ID="thm-18";term hash text="0000000000000000000000000000000000000000000000000000000000000012";type hash text="bad"

IDs nonempty=No;term lexical shape=Yes;type lexical shape=No

IDs and shapes qualified=No;supplied kernel flag=Yes;axioms recorded=Yes

synthetic qualified=No;status=composition receipt still incomplete

Reverse checks

• 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.

Result

(missing, thm-18, Yes, No, Yes, Yes, No, synthetic-receipt-still-incomplete)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

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.