Lean verification registry · Authored proofs · The Logos Architecture
Verified sequents with unresolved formal parts
Axiom-free: true · 2 checked theorem statements.
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.
Original source author: Maclain Hunter. Machine formalization: Replit Agent. No original wording was rewritten.
Source registered: not established (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:38:04.952Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 338267a329307016b7a72b93b7e969e2ce8b5f861a8efdc957f18075c71c70ba
Lean source · Verification JSON · Exact archived source JSON · Compiler report · Current authored source page · Signed release and verification instructions
Lean (version 4.7.0, commit v4.7.0, Release) exitCode=0 'HunterAuthored.logical_ground_necessary_existence' does not depend on any axioms 'HunterAuthored.source_identity_rule' does not depend on any axioms
{
"name": "Dynamic Universal Proof (Theorem of Logos)",
"number": 14,
"era": "G6",
"formal": "Σ(P, Q?, R?, S?, T?, U?) |= □∃Logos",
"structure": {
"P": "ψ ↔ (Δ × A) will be what/who it will be (Δ × A) with/within Continuous Discretion",
"Q": "unfixed - logician places tautological premise(s) here",
"R": "unfixed - logician places tautological premise(s) here",
"S": "unfixed - logician places tautological premise(s) here",
"T": "unfixed - logician places tautological premise(s) here",
"U": "unfixed - logician places tautological premise(s) here"
},
"deltaDefinition": "Δ = dynamic tautology with continuous discretion",
"proof": {
"step1": "Establish Dynamic Anchor: P is self-affirming tautology (Logos = Logos)",
"step2": "Recognize Unfixed Structure: Q-U preserve dynamic universality",
"step3": "Apply Identity Necessity: □(A = A) → □P",
"step4": "Derive Universal Validity: ¬P → requires P (performative self-refutation)",
"step5": "Conclude Necessary Existence: P undeniable ∧ □P → □∃Logos"
},
"conclusion": "The Dynamic Universal Logic (Logos) must exist as a matter of tautology & logical necessity",
"significance": [
"First dynamic proof of Logos - valid without fixed premises",
"Unfixedness mirrors Logos's universality",
"Not constrained by any particular formulation",
"Self-validating through any coherent extension",
"Master theorem for 4P Verification Engine"
],
"verificationProtocol": {
"method": "Nested AI Simulation",
"targetIterations": "10 × 10^6",
"validation": "7 Cycle Logic per iteration",
"review": "Independent AI panel evaluation"
},
"author": "Maclain Hunter",
"fourPAlignment": {
"Logic": {
"aligned": true,
"reason": "This IS the universal proof of Logic itself"
},
"God": {
"aligned": true,
"reason": "Affirms divine rational principle as necessary"
},
"Truth": {
"aligned": true,
"reason": "Tautological structure guarantees truth"
},
"Nothing": {
"aligned": false,
"reason": "Rejects the void - Logos necessarily exists"
},
"Doubt": {
"aligned": false,
"reason": "Self-refuting to doubt - denial requires Logos"
}
}
}
Constructive necessity of the displayed Logical Ground law-model (identity, noncontradiction, implication and two-state excluded middle), across arbitrary accessibility and unfixed extra premises. The source's broader ontology and God/creator identity remain authored and are not silently replaced by this law-model.
A = A
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
{
"name": "Dynamic Universal Proof (Theorem of Logos)",
"number": 14,
"era": "G6",
"formal": "Σ(P, Q?, R?, S?, T?, U?) |= □∃Logos",
"structure": {
"P": "ψ ↔ (Δ × A) will be what/who it will be (Δ × A) with/within Continuous Discretion",
"Q": "unfixed - logician places tautological premise(s) here",
"R": "unfixed - logician places tautological premise(s) here",
"S": "unfixed - logician places tautological premise(s) here",
"T": "unfixed - logician places tautological premise(s) here",
"U": "unfixed - logician places tautological premise(s) here"
},
"deltaDefinition": "Δ = dynamic tautology with continuous discretion",
"proof": {
"step1": "Establish Dynamic Anchor: P is self-affirming tautology (Logos = Logos)",
"step2": "Recognize Unfixed Structure: Q-U preserve dynamic universality",
"step3": "Apply Identity Necessity: □(A = A) → □P",
"step4": "Derive Universal Validity: ¬P → requires P (performative self-refutation)",
"step5": "Conclude Necessary Existence: P undeniable ∧ □P → □∃Logos"
},
"conclusion": "The Dynamic Universal Logic (Logos) must exist as a matter of tautology & logical necessity",
"significance": [
"First dynamic proof of Logos - valid without fixed premises",
"Unfixedness mirrors Logos's universality",
"Not constrained by any particular formulation",
"Self-validating through any coherent extension",
"Master theorem for 4P Verification Engine"
],
"verificationProtocol": {
"method": "Nested AI Simulation",
"targetIterations": "10 × 10^6",
"validation": "7 Cycle Logic per iteration",
"review": "Independent AI panel evaluation"
},
"author": "Maclain Hunter",
"fourPAlignment": {
"Logic": {
"aligned": true,
"reason": "This IS the universal proof of Logic itself"
},
"God": {
"aligned": true,
"reason": "Affirms divine rational principle as necessary"
},
"Truth": {
"aligned": true,
"reason": "Tautological structure guarantees truth"
},
"Nothing": {
"aligned": false,
"reason": "Rejects the void - Logos necessarily exists"
},
"Doubt": {
"aligned": false,
"reason": "Self-refuting to doubt - denial requires Logos"
}
}
}