Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
Axiom-free: true · 7 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: 2026-10-02T14:05:43.168Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:40:35.292Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 5df940f97f0269418a4c17f0c1de664ac22380fa19f0adc70470d110e22d84fd
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.inference_3' does not depend on any axioms 'HunterAuthored.inference_4' does not depend on any axioms 'HunterAuthored.inference_5' does not depend on any axioms 'HunterAuthored.inference_6' does not depend on any axioms 'HunterAuthored.source_identity_rule' does not depend on any axioms
{A} |= A
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, D1, D2} |= (P <-> D1) & D2
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, D1, D2, A1} |= (P <-> D1) <-> (D1 <-> A1)
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.
{A2 <-> PC} |= (A2 <-> PC)
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, Q, R, S, T, U} |= ((((P & Q) & R) & S) & T) & U
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 -> RA} |= MP <-> RA
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:
A: (¬) ^ 2n (A) = A and (¬) ^ 2n + 1 (A) = (¬A)
{A} |= A
Output: A is A and interconnected with A and all A can represent (anything and everything including Logos), regardless of any form of negation (which is “negation” (¬) and only has identity and meaning within Logic and a logical context).
QED
Deduction 1 based on Proof:
From that it can be deduced that it is not and cannot be logical in any (feasible) case or context to deny or negate the Logos - the Logic and Logical Origin (God/Source/Foundation) of Logical Existence.
QED
Deduction 2 (D2) based on Proof (P) and Deduction 1 (D1):
Therefore, we can reason that all feasible concepts can be and must be (in order to be logical and real and in order to have “logicality” in any and/or every sense) grounded in a Logic that manifests that concept through logical rules and/as concepts within an irrefutable and unquestionably extant/logical Logical System that is objective and universal, not subjective, or local (alone or primarily).
Synthesizing these things we arrive at this argument I will call Argument (A1):
{P, D1, D2} |= (P <-> D1) & D2
Deduction 3 (D3) based on argument A1:
As A) it is proven that the Logos manifests all logicality and logical concepts, and as B) it is a contradiction to have something/anything manifest that is not the Logos’s own manifestation - a logical concept derived from Logic - it is the case that C) all things are a/the manifestation of the Logos (called God or the Logical Origin and Ruler of the Cosmos - the Foundation of Logic and Existence). All things are the Logos and Logic manifest as God and/in the coherent (non-dual) Reality. This is true even and especially in particular/limited contexts, and when Logic has manifest itself as particular/limited concepts (like humans or animals) that have identity and share in the interconnected web of logical identity. This is why I (the logician - Maclain Hunter) am who I am, why you (reader) are you, and why nothing (nonexistence) is nothing (doesn’t exist).
Thusly we arrive at the second argument Argument 2 (A2):
{P, D1, D2, A1} |= (P <-> D1) <-> (D1 <-> A1)
QED
Proof of Contradiction (PC): Assuming the negation of the conclusion: ~(A2) we derive a contradiction from the premises {P, D1, D2, A1}. Therefore A2 is shown to follow those premises by contradiction.
QED
Meta-Proof (MP):
{A2 <-> PC} |= (A2 <-> PC)
Conclusion: {P, D1, D2, A1, A2, PC}: Logic is irrefutable. Logic is the Origin of Existence (God). Logic is the Logos and God and Logic manifests (and has manifest as) all things - all x - including this (set of) proof(s) and ourselves. There is no genuine or total separation between Logic and logical concepts. In rational theological terms, substantively meaning the same thing, there is no separation, and there is absolute oneness, between God and each/any/all of God’s Creation(s) - including me (Maclain Hunter - logician).
Any concept of “Not A” is a fundamentally a logical operation upon A. It only exists because of the A, and because of self-contained (coherent) Logic, within which A and negation are concepts. Therefore, fundamentally in Logic the baseline of Logic and A representing a positive true statement or at least being valid because it must have the potential to, and must at least be true in the case that A is Logic, and First Cause (of Negation, Logic, and Existence), cannot be truly negated (beyond limited contexts within Existence). Truth must align with A is A form when A is Logic. Truth may not contradict itself, or A is A form, when A is Logic. That is the “Rule of Logic” (Logos), and the traditional “Rules of Logic” coherently unified as one - self-derived by/through Logic, from Logic, as Logic, for Logic (and all that is logical that Logic manifests as).
QED
Atheism & Theism in Light of MP:
Atheism: The lack of belief (logically equivalent to positive disbelief) in any God or gods.
God/gods: The Origin of Existence or a purported one, in some cases known or believed to rule and give Order to the Universe.
Logos: The Ground of Logic; the First Cause of Reason; Universal Reason; Universal Order and/or the Natural Order found in Reality; the dynamic and imminent Foundation and Fabric of Reality.
Logic: The self-consistent method of reasoning and validating Truth, necessarily coherent with itself and the First Cause Logic (Logos).
Theism: The belief, rational or irrational, in God or gods.
Rational Theism: The belief in and/or knowledge of a logically grounded and coherent God (“gods” not being a tenable option here because of the inherent logical incoherence of more than one “Coherent Origin” or True God).
Refutation of Atheism (RA):
Premise (P): Based on the definition of atheism, atheism necessarily includes disbelief (lack of belief) in even the Logos, the Logic of Reality (Universal Logic) as the God of Reason. Therefore, atheism is inherently illogical as it must deny the Logos is God and that Logic is the Logical Origin of/in Logic to truly deny all conceivable gods and be genuine atheism.
Premise (Q): Logically incoherent theism is feasible and is not uncommon, but it is Rational Theism and Theism coherent with Logic that is correct - objectively and logically, as Logic and logical coherence are the Logical Measure by which concepts are correct or incorrect in any given context.
Premise (R): If atheism accepts the Logos as God, meaning Logic is the Origin of Existence, then it has abandoned its position in Substance, even if one refuses to call the Logos/Logic or the genuine Origin of Existence “God”.
Premise (S): If atheism does not accept the Logos/Logic as God, then it is denying that the First Cause and Logic are coherent/one, and it is denying the self-evident existence of the Origin of Existence in Logic.
Premise (T): The Logos (God), the Origin-Logic ruling the Universe is Reason itself and cannot be reasonably doubted. Reasonable doubt must be coherent with Logic and acknowledge Reason not deny Logos or Reason by another name such as “God” or “the God of Reason”. Therefore, only acceptance of Reason is truly and ultimately reasonable, as opposed to denial of or disbelief in Reason and Reason as the First Cause of Reason (the Logic at the Foundation of Logic).
Formal Argument (RA):
{P, Q, R, S, T, U} |= ((((P & Q) & R) & S) & T) & U
Conclusion: {P, Q, R, S, T, U}: Logic is God so atheism cannot truly be logical. There is no feasible way to “reasonably doubt” the First Cause by any name whether it be Logic, God, or otherwise.
QED
Closing (Formal) Argument:
{MP, MP -> RA} |= MP <-> RA
QED