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. Supplied metadata={"lean_version":"4.27.0","imports":["Mathlib","Module7"],"imports_declared":true,"environment_id":"","context_id":"ctx-7","source_sha256":"0000000000000000000000000000000000000000000000000000000000000007","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
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. Supplied metadata={"lean_version":"4.27.0","imports":["Mathlib","Module7"],"imports_declared":true,"environment_id":"","context_id":"ctx-7","source_sha256":"0000000000000000000000000000000000000000000000000000000000000007","core_type":"Prop","elaboration_status":"success"}. Give (version or missing, sorted distinct imports, imports declared?, environment or missing, context or missing, lexical lowercase 64-hex source-hash shape?, core type or missing, status or missing, missing-field reasons in protocol order, metadata complete?). Imports may be explicitly empty. Hash shape is not a verified source digest.
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.
Sort and deduplicate imports in the English locale.An explicitly empty list is allowed;declaration is a separate flag.No imports are actually executed.
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.