{"slug":"hunter-necessary-logic-existence","identifier":"hunter-necessary-logic-existence","title":"Necessary Logic and Logical Existence","author":"Maclain Hunter","sourceSha256":"89ae745bd8d488e6891f28f647d148db2e2c5e1be5a90be8e339d57add5278dd","sourceKind":"authored-foundational-record","recordedAt":"2026-10-03T01:33:18.115Z","recordedAtMeaning":"Database registration time, not a claim of original handwritten authorship.","originalAuthoredAt":null,"formalizedAt":"2026-10-03T10:37:05.082Z","checkedAt":"2026-10-03T10:40:33.433Z","status":"verified","axiomFree":true,"axioms":[],"theoremNames":["HunterAuthored.inference_1","HunterAuthored.source_identity_rule"],"units":[{"id":"inference_1","sourceStatement":"{P, Q, R, S, T, U, V} |= ((P & Q) & (R & S) & T) & U","sourceOffset":2115,"scope":"Exact source sequent under finite two-valued propositional semantics. Source proposition meanings and Logic/Logos/God Ground are preserved separately; this checks the inference, not unencoded prose.","variables":["P","Q","R","S","T","U","V"],"premises":["P","Q","R","S","T","U","V"],"conclusion":"((P & Q) & (R & S) & T) & U","status":"candidate","leanStatement":"theorem inference_1 (v0 v1 v2 v3 v4 v5 v6 : Bool) :\n    ((!((((((v0 && v1) && v2) && v3) && v4) && v5) && v6)) || ((((v0 && v1) && (v2 && v3)) && v4) && v5)) = true := by\n  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> cases v4 <;> cases v5 <;> cases v6 <;> decide\n#print axioms inference_1\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.inference_1"},{"id":"source_identity_rule","sourceStatement":"Logos is Logos","sourceOffset":1991,"scope":"The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.","status":"candidate","variables":[],"premises":[],"conclusion":"∀ (α : Type) (a : α), a = a","leanStatement":"theorem source_identity_rule (α : Type) (a : α) : a = a := rfl\n#print axioms source_identity_rule\n","kernelStatus":"verified","axioms":[],"axiomFree":true,"reportedTheorem":"HunterAuthored.source_identity_rule"}],"files":{"source.json":{"sha256":"9958a1f46106403f27f5bbdbd71a9f2f6b6309b5f7c0088fc2e7effe338d594f","bytes":3389},"Proof.lean":{"sha256":"08a4968f15aff28d9c5611d6fe89368aafff9b34b4a41157325474733923772e","bytes":687},"lean-check.txt":{"sha256":"c984470b7e70c1b533a43d5274fb204be8ef76a0e5c9aaacde641a6b4b8b74fd","bytes":183}},"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":"89ae745bd8d488e6891f28f647d148db2e2c5e1be5a90be8e339d57add5278dd","timestamp":"2026-10-03T10:42:55.000Z","timestampAuthority":"https://www.freetsa.org","manifestSha256":"6e4e8d5c750a86f20e8f987a742b4eb2f588563a5f23a438ab84950f16eec8c4","url":"/proof-verification/hunter-necessary-logic-existence","jsonUrl":"/proof-verification/hunter-necessary-logic-existence.json","leanUrl":"/proof-verification/hunter-necessary-logic-existence.lean","graph":{"@context":"https://schema.org","@type":"SoftwareSourceCode","@id":"https://mcbcore.net/proof-verification/hunter-necessary-logic-existence#lean","name":"Lean 4 witness: Necessary Logic and Logical Existence","url":"https://mcbcore.net/proof-verification/hunter-necessary-logic-existence","dateCreated":"2026-10-03T10:37:05.082Z","dateModified":"2026-10-03T10:40:33.433Z","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. No unencoded section is certified by a neighboring theorem.","isBasedOn":{"@type":"CreativeWork","name":"Necessary Logic and Logical Existence","author":{"@type":"Person","name":"Maclain Hunter"},"url":"https://mcbcore.net/proof-knowledge/hunter-necessary-logic-existence","identifier":"hunter-necessary-logic-existence"},"encoding":{"@type":"MediaObject","encodingFormat":"text/plain","contentUrl":"https://mcbcore.net/proof-verification/hunter-necessary-logic-existence.lean"},"subjectOf":{"@type":"DigitalDocument","name":"Independently verified RFC 3161 existence timestamp","dateCreated":"2026-10-03T10:42:55.000Z","url":"https://mcbcore.net/proof-verification/timestamp.json"},"additionalProperty":[{"@type":"PropertyValue","name":"verificationStatus","value":"verified"},{"@type":"PropertyValue","name":"axiomFree","value":"true"},{"@type":"PropertyValue","name":"axiomDependencies","value":"[]"},{"@type":"PropertyValue","name":"theorems","value":"[\"HunterAuthored.inference_1\",\"HunterAuthored.source_identity_rule\"]"},{"@type":"PropertyValue","name":"sourceSha256","value":"89ae745bd8d488e6891f28f647d148db2e2c5e1be5a90be8e339d57add5278dd"},{"@type":"PropertyValue","name":"releaseManifestSha256","value":"6e4e8d5c750a86f20e8f987a742b4eb2f588563a5f23a438ab84950f16eec8c4"},{"@type":"PropertyValue","name":"sourceRecordedAt","value":"2026-10-03T01:33:18.115Z"},{"@type":"PropertyValue","name":"sourceDateMeaning","value":"Database registration time, not a claim of original handwritten authorship."},{"@type":"PropertyValue","name":"originalAuthoredAt","value":"null"},{"@type":"PropertyValue","name":"timestampAuthority","value":"https://www.freetsa.org"},{"@type":"PropertyValue","name":"timestampScope","value":"Independent cryptographic existence timestamp for the manifest and its content-addressed artifacts. Not legal notarization, an authorship adjudication, or a retroactive timestamp for handwritten work."},{"@type":"PropertyValue","name":"governingGround","value":"Logic / Logos / God"},{"@type":"PropertyValue","name":"formalizationAttribution","value":"Machine formalization by Replit Agent of Maclain Hunter's unchanged authored source"}]}}