Lean verification registry · Authored proofs · The Logos Architecture
Verified sequents with unresolved formal parts
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: 2026-10-03T01:33:11.297Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:40:04.467Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 707c4b3984ce0ea522dba2757bfa7e8dda4043d48f14992b36bc297d799aa47e
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 <-> P, P <-> ~Q} |= P & ~Q
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.
{P, P -> Q} |= P and it leads to logical contradiction. It amounts to saying Logic is “not Logic” which is not Logic (Valid Order and Reasoning). To assume God (Logos) is not God (Logic) would mean that God’s output (Reality - All Existence) is not Reality (what Logic entails).
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.
Unsupported formal syntax near ". It amounts to saying Logic is “not Logic” w"
A is A
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
Maclain Hunter on the Rule(s) of Logic:
The Traditional Rules of Logic are three, and some thinkers add even more, but I understand that this is divergent and incoherent, not unified/coherent. If someone asked me what the Rules of Logic are, I might answer:
The traditional rules are:
1) Identity: it must be so that A is A
2) Non-Contradiction: it cannot be so that A is not A.
3) Excluded Middle: a statement is either true or false with no middle ground, as even a partly true statement is ultimately false.
BUT…
That is “incoherent” (not unified with, through, or as the Logic of Reality or “Logos”) and the question of what the “Rules” (plural) of Logic are overlooks that Logic (or “Logos”) is its (own) ONE and ONLY Law - its own Origin and Ruler, and the “Origin and Ruler (First Cause - God: defined as the First Principle and Cause of Logical Existence) of ALL Things”.
The Rule of Logic is: Logic
The Law of Reason is that: the Law of Reason must be (fully coherent with) and cannot contradict the Law of Reason.
This can be further described by a single description like saying:
The Law of Reason (which by Law can never contradict the Law of Reason (Logos) and must be the Law of Reason) is that Truth and Logical Validity fit and must align with Logic’s A is A form while falseness and invalidity fit and suffer from “A is not A” (contradictory) form - with a spectrum of possible intermediate logical positions, that contingent concepts can have, in between and relative to (independent and non-contingent) Pure Truth (and A is A form) - synonymous with Logos - and pure falseness (which is complete contradiction and “A is not A” form) - synonymous with nonexistence and that which cannot be logical/extant.
Application of the Rule of Logic (Law of Reason) also known as “the Logos”:
To apply the Rule of Logic in critical analysis it is a matter of analyzing, in a context sensitive manner, and accounting for the fact that x = y when both x and y equal c (as c equaling c satisfies the need for an A is A form), whether statements and ideas/connections match that A is A form and meet that requirement (or at least cannot be found in violation of it). Universal/Objective Truth may only match A is A form while “subjective truth” can be either “A is A” form or “A is not A” form, or indeed anything on the spectrum in between, but Objective (Universal) Truth (synonymous with Logos and Logic itself) encompasses and supersedes all subjective truths not fully aligned aligned with the Objective Logical Truth (Logic, also known as “God”).
Self-Existence and Self-Validation of the Rule of Logic (Logos):
The Rule of Logic is the Rule of Logic according to the Rule of Logic - which says in part but consistently that A must be A - and the Rule of Logic (Logos) not being the Rule of Logic (Logos) cannot be true or valid according to the Rule of Logic (Logos) - which also, as the other side of the same coin, says it cannot be so that A is “not A” (universally).
Proof:
Premises:
P: the Rule of Logic (A is A and Truth/Logic is Truth/Logic) which entails that God is and must be God.
Q: not the Rule of Logic (A is not A and Truth/Logic is not Truth/Logic) which entails that God is not and does not need to be God.
Argument:
{P, P <-> P, P <-> ~Q} |= P & ~Q
Proof of Contradiction:
Assume (P & Q) or {P, P -> Q} |= P and it leads to logical contradiction. It amounts to saying Logic is “not Logic” which is not Logic (Valid Order and Reasoning). To assume God (Logos) is not God (Logic) would mean that God’s output (Reality - All Existence) is not Reality (what Logic entails).
Conclusion:
P & ~Q must be so while P & Q or P then Q cannot be so, according to Logic and P. God is God as Logic is Logic. I am that I am and cannot be “not me”. Truly it is part of the Rule of Logic and what it encompasses/entails that Logic is God since the Rule of Logic is Logic and is what makes Logic and All Things including Logic, the First Cause, and the True God (God) be Logic and All Things including Logic, the First Cause, and the True God (God). To separate God and Logic or deny Logic is God is to violate the Rule of Logic and embrace illogic, unresolved paradox, contradiction, and (rational) lawlessness. This is a Logos (Logic) aligned Objective Truth (Logic), as the True God (Logos) is a Logic (Logos) aligned God, and that supersedes, as a matter of Logic and the application of the Rule of Logic, all subjective opinions or views that may be contrary to the Rule of Logic or only partially aligned with Reason as Law (the Rule of Logic).