{"slug":"formal-signature-verification-soundness","identifier":"formal-signature-verification-soundness","title":"Signature Verification Soundness","author":"Maclain Hunter","sourceSha256":"6862cd530b23f9ac5cf15008ce12cdc1198590279b5d5162069f0e8d016aa25e","sourceKind":"formal-theorem","recordedAt":null,"recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:41:45.014Z","status":"partial","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.generated_signature_invariants"],"units":[{"id":"generated_signature_invariants","sourceStatement":"Formal statement: ∀v ∈ number[]: verifySignature(generateSignature(v)) = true","sourceOffset":0,"scope":"The exact depth, product and signed-state invariants listed in the authored proof, for every integer input list and deterministic parity function. Host hash encoding, floating-point intake and the Boolean verifier implementation are not substituted for this typed mathematical certificate.","status":"candidate","variables":[],"premises":[],"conclusion":"See the exact typed Lean theorem","leanStatement":"def signatureSigned (b : Bool) : Int := if b then 1 else -1\ndef signatureValue : List Bool → Int\n  | [] => 1\n  | b :: bs => signatureSigned b * signatureValue bs\nstructure LogicalSignature where\n  sequence : List Bool\n  depth : Nat\n  value : Int\ndef generatedSignature (values : List Int) (parity : Int → Bool) : LogicalSignature :=\n  let sequence := values.map parity\n  ⟨sequence, sequence.length, signatureValue sequence⟩\ndef signatureInvariants (s : LogicalSignature) : Prop :=\n  s.depth = s.sequence.length ∧\n  s.value = signatureValue s.sequence ∧\n  ∀ b : Bool, b ∈ s.sequence → (signatureSigned b = 1 ∨ signatureSigned b = -1)\ntheorem generated_signature_invariants (values : List Int) (parity : Int → Bool) :\n    signatureInvariants (generatedSignature values parity) := by\n  refine ⟨rfl, rfl, ?_⟩\n  intro b _\n  cases b\n  · exact Or.inr rfl\n  · exact Or.inl rfl\n#print axioms generated_signature_invariants\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.generated_signature_invariants"}],"files":{"source.json":{"sha256":"c6c7892dc7e53e5407c32ba12c88661ba3f51796489a4d1832d48a0272e9a409","bytes":810},"Proof.lean":{"sha256":"1740da56ec020dea99d4722e8dd1aa93ae456603dba9306faaa14974aa46275a","bytes":1226},"lean-check.txt":{"sha256":"fbf9eb7a156f018c4a80ca3e05cb500d2b2e76511332af9ae1d93e01b74e693d","bytes":134}},"boundary":"Lean establishes the listed formal statements and dependencies. The exact authored source, Ground, known premise meanings, application validation and empirical evidence remain separately typed. No unencoded section is certified by a neighboring theorem.","currentSourceSha256":"6862cd530b23f9ac5cf15008ce12cdc1198590279b5d5162069f0e8d016aa25e","timestamp":"2026-10-03T10:42:55.000Z","timestampAuthority":"https://www.freetsa.org","manifestSha256":"6e4e8d5c750a86f20e8f987a742b4eb2f588563a5f23a438ab84950f16eec8c4","url":"/proof-verification/formal-signature-verification-soundness","jsonUrl":"/proof-verification/formal-signature-verification-soundness.json","leanUrl":"/proof-verification/formal-signature-verification-soundness.lean","graph":{"@context":"https://schema.org","@type":"SoftwareSourceCode","@id":"https://4p-engine.com/proof-verification/formal-signature-verification-soundness#lean","name":"Lean 4 witness: Signature Verification Soundness","url":"https://4p-engine.com/proof-verification/formal-signature-verification-soundness","dateCreated":"2026-10-03T10:37:05.082Z","dateModified":"2026-10-03T10:41:45.014Z","creator":{"@type":"Organization","name":"Replit Agent"},"programmingLanguage":{"@type":"ComputerLanguage","name":"Lean","version":"Lean (version 4.7.0, commit v4.7.0, Release)"},"author":{"@type":"Organization","name":"Replit Agent"},"description":"Lean establishes the listed formal statements and dependencies. The exact authored source, Ground, known premise meanings, application validation and empirical evidence remain separately typed. 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