{"slug":"archived-q1061-d17a3726a953","identifier":"archived-q1061-d17a3726a953","title":"Conditional Determinism","author":"Maclain Hunter","sourceSha256":"d17a3726a9531ad56a817bc94a22f0200baa806232abd05e31238c3b3d0fb2c9","sourceKind":"archived-authored-source","recordedAt":null,"recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:37:55.105Z","status":"partial","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.conditional_returns_declared_branch"],"units":[{"id":"conditional_returns_declared_branch","sourceStatement":"{\n  \"name\": \"Conditional Determinism\",\n  \"formal\": \"∀c,t,e: mcbConditional(c,t,e) ∈ {t, e}\",\n  \"proof\": \"c.state ∈ {+1, -1} maps deterministically to branches\",\n  \"implementation\": \"mcbConditional(condition, thenBranch, elseBranch): MCBComputationUnit\"\n}","sourceOffset":0,"scope":"Universal branch membership for the declared deterministic conditional, over arbitrary result types.","status":"candidate","variables":[],"premises":[],"conclusion":"See the exact typed Lean theorem","leanStatement":"theorem conditional_returns_declared_branch {α : Type} (condition : Bool) (t e : α) :\n    (if condition then t else e) = t ∨ (if condition then t else e) = e := by\n  cases condition\n  · exact Or.inr rfl\n  · exact Or.inl rfl\n#print axioms conditional_returns_declared_branch\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.conditional_returns_declared_branch"}],"files":{"source.json":{"sha256":"81682f6b75ffea3b7d7903f93d57be553bbe03018251d5ba716b1e23c79aadad","bytes":815},"Proof.lean":{"sha256":"774070b9ebde01421c252a4284a2f003e2b762b15881bce844703d156c1ebe49","bytes":555},"lean-check.txt":{"sha256":"a54bde994b92162852a8caaf91ab837249a7827346df70328312c165b96a640c","bytes":139}},"boundary":"Lean establishes the listed formal statements and dependencies. 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