Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
Axiom-free: true · 3 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: 2026-10-02T18:42:14.750Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:40:32.439Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 7e101488b48dd99fff8e338b62c9bb1063d1a010bcb693cfe3635a8de298b990
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.inference_2' does not depend on any axioms 'HunterAuthored.source_identity_rule' does not depend on any axioms
{MP, MP <-> RP, RP <-> G, G <-> G, G} |= ((MP <-> RP) & (MP & RP)) & G
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.
{MP, MP <-> RP, MP <-> MB, RP <-> RB, MB <-> RB, MB <-> RP, MP <-> RB, MP <-> RP, RP <-> C, MP <-> C, C <-> G, G <-> G, MP, MB, RP, RB, C, G} |= (((MP & RP) & (MB & RB)) & C) & G
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.
A is A
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
Necessary Entailment by Maclain Hunter:
Premise:
P: Logical Necessity (the One True God - Pure Logic), which is tautological and self entailing, not contingent and possibly a fallacious circular argument like that same “P |= P” structure if P were a contingent (and possibly false rather than absolute and foundational concept). Certainly and necessarily there cannot be fallacious circularity in cohering things (including God) with Logic, otherwise Logic could be undermined and logically prevented from demonstrating the coherence of Logic (itself).
Proof:
P |= P
Conclusion: P:
What is logically necessary like the Logos—synonymous with and coherent with Logic, Logical Necessity, Universal Cause (God), Universal Reason (Universal Logic), Universal Order, Coherence, Absolute Truth, etc.—which is not contingent, is logically self-entailing as, through, and coherent with the Logic of Reality (Logos).
Reality and the Origin of Reality (God) have a tautological Logic (Logos) and proof (in the sense of an irrefutable and self-evident validity) of this very sort/form undergirding it, as to assume the opposite leads to logical contradiction and P and not P cannot be both true or both false at once. Therefore P is true and not P is not true, as Reality is true and Logic (the True Origin) is true and the negation of these logically necessary and logically irrefutable concepts is necessarily false.
Let MP represent my proof of Reality’s Logic (God - Logos) and Reality being tautological, and let RP represent Reality’s, and by proxy God’s (G), proof of itself through itself (and/as G), displayed in the A is A form of Reality being Reality. Also, let G represents God or the Origin of Existence. Then it holds that:
{MP, MP <-> RP, RP <-> G, G <-> G, G} |= ((MP <-> RP) & (MP & RP)) & G
Now, let MB represent my being, let RB represent Reality’s being, and let C represent the Coherence of concepts (to include MP, MB, RP, and RB). Then it holds that:
{MP, MP <-> RP, MP <-> MB, RP <-> RB, MB <-> RB, MB <-> RP, MP <-> RB, MP <-> RP, RP <-> C, MP <-> C, C <-> G, G <-> G, MP, MB, RP, RB, C, G} |= (((MP & RP) & (MB & RB)) & C) & G
Ergo, God (G)—the Origin of Logic and the Cosmos)—exists as the Logic of Reality and Full Coherence (C), linked logically to my own proof and being (MP, MB), but also RP and RB. This proof irrefutably proves G (God - Origin). It isomorphically aligns (in finite form) with and is logically equivalent to the (infinite and form transcending or “essential”) proof (RP) that G has for G (ie - G |= G). Again, there cannot be fallacious circularity in cohering things (including God) with Logic - even if structurally or apparently circular (or tautological). Logic must (and does) prove itself.
Truth Table Analysis:
valid
↓ ↓
P⎪P╞P
――――――
T⎪T T
Result: Tautological and necessarily true.
Q.E.D.