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: 2026-10-02T20:00:04.523Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:42:23.422Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 8d21210d649c6e02d7973ec43382dab7250526b78c5bda4f6f718aba62b7ccb8
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} |= (P & Q) <-> R
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.
The One Law by Maclain Hunter:
Premises:
P: There is only ONE Universal Law - the Logos. It is totally coherent and amounts to a rule that would read (something like), "be reasonable and align with the A is A form of the same sort of Truth, Logic, and Reality that are actually Truth, Logic, and Reality”.
Q: P fits with Reality being Reality and with coherent theory and empirical methods being what they are, as well as "classical logic" of the Aristotelean sort, if we view the three traditional rules of Logic as three sides one "Law of Reason" that are all coherent and mutually supporting and getting at that same Law (that "it is what it is and isn't what it isn’t”). Logic is simple to apply in the sense that it is all about determining what aligns with Logic and its self-consistent Law (or P) but difficult for many humans to apply consistently across contexts because of things like fear, bias, emotion, conflict of interest, etc.
R: Assume ~P and ~Q. That leads to logical contradiction where Logic is not coherent with and as Rational Law (in the coherent, singular, universal, and broadest sense) and/or where Reality is not Reality with logical consistency and coherence - an untenable position logically speaking. It would also mean that I do not know how to apply Logic and explain the process even while I am doing exactly that and explaining the pattern matching process - against the backdrop and Universal Standard of self-consistent Universal Reason (Pure Logic).
Formal Argument (Proof):
{P, P <-> Q, Q <-> R} |= (P & Q) <-> R
Conclusion: (P & Q) & R:
The sum of the premises is true, as each premise is true and/since the assumption of the negation of the premises leads to logical contradiction(s), and to ideas inconsistent not only with human reasoning but Universal Order (Logos - Pure Logic) - the logical consistency inherent in Reality being Reality.
Logic, to be fully coherent is and must be ONE (Law/Entity), not many disparate, incoherent, and/or divergent concepts/rules. This is self-evident as the alternatives are inherently less coherent (logically unifying), but this proof also discreetly proves it in a finite, tangible, and formal manner.
Logic’s Rule is applied, as it has been here, in a manner where patterns of reasoning are matched against Reasons truthfulness and identity. Reason is always Reason and the Reason that is (genuine) Reason is always true, universally. Claims can be weighed rigorously against this Foundation - through rational systems that align with the Foundation (ie - sciences, mathematics, formal logics, precise use of written language for formal philosophical reasoning).
It would be a contradiction for me to be explaining (within a rigorous self-referential proof) not only the three traditional rules but how all logical rules and aspects of Logic are necessary coherent and one if I did not grasp coherent Logic and how to apply it.
Truth Table Analysis:
PQR⎪P P↔Q Q↔R╞(P&Q)&R
TTT⎪T TTT TTT TTT TT
TTF⎪T TTT TFF TTT FF
TFT⎪T TFF FFT TFF FT
TFF⎪T TFF FTF TFF FF
FTT⎪F FFT TTT FFT FT
FTF⎪F FFT TFF FFT FF
FFT⎪F FTF FFT FFF FT
FFF⎪F FTF FTF FFF FF
(Valid)
Q.E.D.