These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-7", statement_elaborated_prop=true, proof_term_present=false, kernel_checked=false. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
G001 — These are synthetic pipeline receipts, not actual Lean elaboration or kernel checks. The Chinese source pulse did not run Lean builds for these records. A formal statement and a checked proof are distinct states. environment_id="env-7", statement_elaborated_prop=true, proof_term_present=false, kernel_checked=false. Give (environment ID, those three flags, coherence?, state label). A proof flag requires a statement, and a kernel flag requires a proof term.
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.
all pipeline flags,names and receipt fields are synthetic input data
After
no actual Lean run,digest verification,name resolution or kernel acceptance is claimed
Conditions: none
These are supplied synthetic receipts,not a Lean run.String fields,coherent flags or complete metadata do not establish actual elaboration,file-digest verification or kernel acceptance.The teaching candidate remains not formalized.
The state label has-kernel receipt only classifies the three supplied flags.No real kernel receipt was produced or verified here,and the teaching guide is not promoted to a formal proof.
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
(env-7, Yes, No, No, Yes, statement-only)
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.