# Question 8955: Synthetic Statement, Proof-Term, and Kernel Flags

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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.

R0016-08955 · q-20261013-advance-20261018-r07-lean-formal-statement-0055



## 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-4", statement_elaborated_prop=false, proof_term_present=true, 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-4", statement_elaborated_prop=false, proof_term_present=true, 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.


- [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

statement=No;proof term present=Yes;kernel flag=No

After

proof implies statement=No;kernel implies proof=Yes

Conditions: none

Separate the statement,proof-term presence and kernel flag,checking their prerequisite chain.A later flag cannot bypass an earlier requirement.

Step identifiers and dependenciesRule: formal_statement_proof_kernel_prerequisites · Uses: G001, S001





S003 · impliesBefore

environment=env-4;coherent=No

After

synthetic statement/proof state=incoherent receipt

Conditions: none

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.

Step identifiers and dependenciesRule: synthetic_kernel_flag_not_real_receipt · Uses: G001, S002









## 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

(env-4, No, Yes, No, No, inconsistent-receipt)

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: 25ae0832545564ebccb9a1d46a593214e5592182f8133b8635093a966a4fcf26
- candidate record SHA-256: bb26d0594f44c49720ad6b5da2cb733f9ad3af52bba6f7a02a4037b2e64a59b6
- 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-0055.json)