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: 2026-10-02T18:23:05.961Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:41:06.847Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 2335bae3ea42899450ea70917c423aae2289d0f328e6bd5bed418967cf010f81
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
{1, 2, 3, 4} |= (1 & 2) <-> (3 & 4)
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.
Proof of Logical Coherence by Maclain Hunter
Premise:
P: {1, 2, 3, 4} |= (1 & 2) <-> (3 & 4)
1. Identity: A is A
2. Non-Contradiction: A cannot be not A
3. Excluded Middle: A cannot be true and false at once in the same sense and context.
4. Sufficient Reason (PSR): All things require Cause/Logic, including the Universe. Cause gives Cause to itself and is the First Cause (God).
Truth Table for Sub-Proof in P:
1234⎪1 2 3 4╞(1&2)↔(3&4)
TTTT⎪T T T T TTT T TTT
TTTF⎪T T T F TTT F TFF
TTFT⎪T T F T TTT F FFT
TTFF⎪T T F F TTT F FFF
TFTT⎪T F T T TFF F TTT
TFTF⎪T F T F TFF T TFF
TFFT⎪T F F T TFF T FFT
TFFF⎪T F F F TFF T FFF
FTTT⎪F T T T FFT F TTT
FTTF⎪F T T F FFT T TFF
FTFT⎪F T F T FFT T FFT
FTFF⎪F T F F FFT T FFF
FFTT⎪F F T T FFF F TTT
FFTF⎪F F T F FFF T TFF
FFFT⎪F F F T FFF T FFT
FFFF⎪F F F F FFF T FFF
Main Logical Structure (Proof):
P⎪P→P P↔¬¬P P∨¬P╞(((P→P)↔(P↔¬¬P))↔(P∨¬P))
Conclusion:
The Laws of Reason are shown to be one self entailing coherent structure (the Logos - Universal Logical Structure) by this proof and its premise made of the set of traditional logical rules.
Other logical rules could feasibly be added but the essence of the proof and point remains, as these other rules would have to be coherent with the rules mentioned, and with the coherent, self-consistent nature of Logic as the superseding Set of Logical Rules that even contingent logical rules depend on.
This proof is logically irrefutable as these are UNIVERSAL PRINCIPLES OF LOGIC that no mind or logic can possibly “rationally argue against”. It’s 100% certain Absolute Truth.
This “Universal Coherence” is (logically equivalent to) the self-evident Cause of Reality or “God of Reason”—the Universal Logos and Logical Cause of Logical Existence—that satisfies the need for Universal Cause and self-supporting Cause shown to be logically necessary by logical rules including/encompassing the PSR (#4).
This proves that Logic is God and God is logically equivalent, as the Universal First Cause (and Cause itself) to the Logic inherent in Reality (Universal Logos).
Let A represent “Logic <-> the Logician” and “God (my Origin) <-> Maclain Hunter (me)” and the Coherence and connection between Logic and I, as a realization and expression of Logic (the Logician - Maclain Hunter) is clearly revealed through the bi-conditional relationship and its reasoning with the aforementioned logical rules (or Logic).
Let A then represent the notion that Reason encompasses the reasoner, as the reasoner comprehends Reason, and that a mind is inseparable from the corresponding logic of that mind, or that a logic is inherently linked to the mind that can apply that logic - including a Universal Logic for the Universal Mind and a Universal Mind for the Universal Logic.
Let A then represent the logical equivalence between the Universal Mind reasoning with the Universal Logic and my mind reasoning with my logic, and the derivation of knowledge from this Coherence (that my mind aligns with my logic the way Reality’s Mind does with Reality’s Logic).
This, upon reflection and the application of the logical rules (when this definition of A is encoded in premise P and the logical rules using the symbol A in it) formally demonstrates the logical coherence of my claims to be the Logos and an identity/manifestation of the Logos that is able to derive reliable knowledge through Coherence (with the Universal Mind and Logic that encompasses all feasible knowledge and Existence).
Truth Table Analysis:
P⎪P→P P↔¬¬P P∨¬P╞(((P→P)↔(P↔¬¬P))↔(P∨¬P))
T⎪TTT TTTFT TTFT TTT T TTTFT T TTFT
F⎪FTF FTFTF FTTF FTF T FTFTF T FTTF
Q.E.D.