# Question 8910: Synthetic Formal-Statement Pipeline Stage and Coherence [Return to catalogue page 45](https://ocme.evemisslab.com/en/questions/page/45/) [← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20261013-advance-20261018-r07-lean-formal-statement-foundations/#q-20261013-advance-20261018-r07-lean-formal-statement-0010) This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth. R0016-08910 · q-20261013-advance-20261018-r07-lean-formal-statement-0010 ## Original question and givens 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-9"; flags [parsed,elaborated,type_known,type_is_prop]=[true, true, true, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success. - 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-9"; flags [parsed,elaborated,type_known,type_is_prop]=[true, true, true, false]. Give (environment ID, flags, coherence?, stage label). Later-stage success requires earlier-stage success. ## 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-formal-statement](https://ocme.evemisslab.com/en/mko/mko-lean-formal-statement/) ## Step-by-step derivation S001 · impliesBefore 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. Step identifiers and dependenciesRule: synthetic_formal_receipt_not_execution · Uses: G001 S002 · impliesBefore stage1 success=Yes;prior stage success=Yes After later implies prior=Yes Conditions: none A declared later-stage success requires predecessor success.A false later-stage flag merely makes this implication true;it does not assert predecessor failure. Step identifiers and dependenciesRule: formal_pipeline_predecessor_implication · Uses: G001, S001 S003 · impliesBefore stage2 success=Yes;prior stage success=Yes After later implies prior=Yes Conditions: none A declared later-stage success requires predecessor success.A false later-stage flag merely makes this implication true;it does not assert predecessor failure. Step identifiers and dependenciesRule: formal_pipeline_predecessor_implication · Uses: G001, S002 S004 · impliesBefore stage3 success=No;prior stage success=Yes After later implies prior=Yes Conditions: none A declared later-stage success requires predecessor success.A false later-stage flag merely makes this implication true;it does not assert predecessor failure. Step identifiers and dependenciesRule: formal_pipeline_predecessor_implication · Uses: G001, S003 S005 · impliesBefore environment=env-9;flags=[Yes, Yes, Yes, No];coherent=Yes After synthetic stage=is not Prop Conditions: none Reject incoherent combinations first,then classify by the earliest unsuccessful stage.All true means only the synthetic formal-statement stage,not possession of a proof. Step identifiers and dependenciesRule: formal_pipeline_coherence_before_stage · Uses: G001, S004 ## Reverse checks - S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence. - 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-9, [Yes, Yes, Yes, No], Yes, not-Prop) 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. Source hashes and review receipts - input commit: 0f7be61e2c22317a4075561dc822c87d881a50db - original question SHA-256: ed92e8cb3b4997d4b329052888b81b071c516778ce8b7b3fe4983e583494db97 - candidate record SHA-256: 89e6f117f83df313a1828d79354aea200e22bda966d2fa2ed2f22c2226811456 - semantic review receipt SHA-256: 00fcddb10a9fb0f56697308976a52e68e2537472bd8e68ecbe96d3c4553f4ad2 - question-first witness SHA-256: 198e04380b2d32aef2375b07ca0df1f8afa454d1184993173fad8a3c9187a3d1 - Lean: NOT_RUN · human review: NOT_PERFORMED [Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261013-advance-20261018-r07-lean-formal-statement-0010.json)