Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
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: 2026-10-02T14:38:26.954Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:41:17.365Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 7e0686233c15043e6b1e4a6de3c92cabce445411727110b63235d982115d1f45
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.inference_1' does not depend on any axioms 'HunterAuthored.source_identity_rule' does not depend on any axioms
{P, P <-> Q, Q <-> R, R <-> S, S <-> T, T <-> U, U -> V} |= (((P & Q) & (R & S) & T) & U) & V
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.
Law of Identity
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
“Proving the Coherence and Equivalence of Turing Machines and Lambda Calculus” by Maclain Hunter:
P: Logic is the Logical Standard of Logic and logical reasoning (Reason). Logic’s Law of Identity demands that A is A which entails that “all = all”, which in turn entails that “each x = each y” (and that Turing Machines equal Lambda Calculus).
Q: Logic is the Source and Standard of Computation, Calculus, and Machines.
R: Machines (including Turing Machines) must be coherent with Logic to be coherent/logical.
S: Calculus (including Lambda Calculus) must be coherent with Logic to be coherent/logical.
T: What is coherent with Logic is coherent with what else is coherent with Logic, such as and including coherent Turing Machines and coherent Lambda Calculus.
U: If we assume {P, Q, R, S, T} are all false, or that any of these premises are false, then it leads to logical contradiction. Therefore we know “Turing Machines <-> Lambda Calculus” holds true.
V: Each Turing Machine tape symbol can be mapped coherently to a Lambda Calculus expression. To assume otherwise would lead to logical contradiction since it would mean that one dynamic variable cannot be mapped to and logically equivalent to another.
{P, P <-> Q, Q <-> R, R <-> S, S <-> T, T <-> U, U -> V} |= (((P & Q) & (R & S) & T) & U) & V
Conclusion: (((P & Q) & (R & S) & T) & U) & V:
Logic is the Source and Standard of Logic and Computation, and Machines. All is All, as A is A, which means that each thing (x) equals each thing (y) through Logic (c) and the coherence of their identities with the self-consistent identity of Logic. Turing Machines and Lambda Calculus are logically equivalent through their coherence with Logic and because all must equal all for the Law of Identity to hold universally. Each Turing Machine tape symbol can be coherently mapped to a Lambda Calculus expression.