Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
Axiom-free: true · 1 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: 2026-10-03T01:37:06.572Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:41:07.917Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 5473c6366d0dd1544855f4711b6055a9773c50e983f082ce9ec07cf089134cce
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
{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.
Proof of Proof’s Source in Logic:
Definitions:
Logic: the Method of Reasoning and Realization; the Order inherent in Proper Order and self-consistency.
God: the Origin and Ruler of the Cosmos; the Logos (Pure Reason - Universal Order and Logic) in rational theism and classical theology.
P: Proof exists.
Q: Assume P is not true, that leads to logical contradiction and wouldn’t be possible to prove (then).
R: Even if “nothing” (pure illogicality) were “the Source of Proof”, the Source of Proof would still be and have to be “something”.
R: The Source of Proof must be logically coherent or it is logically incoherent. An incoherent Source of Proof would be a logical contradiction.
S: The Source of Proof is Logic, and is fully coherent, as the alternative that the Source of Proof is “not Logic” and “not coherent/one with Logic” is illogical and untenable.
T: The Source of Proof is the Source of Rational Support and Rationality (Reality) in/underlying the Universe, as to assume the opposite or any true (substantive) alternative leads to logical contradiction.
U: All proof is entailed by and proves the existence of the Source of Proof (Logic - the First Cause). To have proof in hand without the Source of Proof objectively extant in and encompassing the (rationally supported) Cosmos would be a logical contradiction. This proof itself could not exist without the Source of Proof and is therefore empirical evidence of the Logic encompassing Reality (the First Cause).
V: The Source of Reality (the Origin of the Universe - God) is and must be coherent with Rational Law (Logic - Reason - Identity) to establish coherence at/as the Universal Foundation (First Cause), and in order for the rest of the Natural Order (Logic) to be logical and logically founded.
{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 of Proof, the First Cause, and God, and all proof immanently and intrinsically proves that, even if not every proof explicitly proves such things. That is true of all proof, including this proof itself. This proof is empirical evidence (and observable/observed proof) that the Logic of Reality (also understood as the First Cause) surely exists.
For this proof to exist without the First Cause of Logic (the Foundation of Logic and Reality - God) would be a logical contradiction. Logic and language demand God be the Foundation of Reality (by definition and to satisfy and be coherent with Logic), and that God and Logic must be coherent for both to be properly grounded and coherent.