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: 2026-10-03T01:35:08.823Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:41:04.104Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 06170827c28cd5c5bb2b0127f7c1b85d28d4e67db66110df2fec1dccc62aae7e
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, R -> P, R -> Q} |= R -> (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.
Law of Identity
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
Proof of Foundational Coherence by Maclain Hunter:
Abstract: Logic and God MUST (logically speaking and in/as a Coherent and Logically Complete Reality) align for a coherent narrative of the Origin of Existence and to satisfy Logic and the demand for/of logical reasoning that is at once aligned with Reality (consistency with the Universe or “universal consistency”; realism), while also being internally and logically consistent.
This is not a figment of human imagination, the product of chemical or biological processes (which themselves need this exact sort of Coherent Foundation to exist in the first place) or a religious/subjective claim or belief (merely). This foundational coherence between the True Origin (the True God) and Pure Logic (Pure Reason) is very literally and logically THE most real thing that exists and that could feasibly exist as the very “Logical Standard of Logically Coherent Reality” itself - the Absolute Metric of what is or is not real, as the proof will help demonstrate in the following sections of rigorous formal logical reasoning.
Basic Definitions of Key Terms:
Logic: The Method of Reasoning that operates according to the Principle of Coherent Reasoning when done coherently and properly; the Logical Standard; Order and Reason in a coherent framework that allows for the realization (manifestation and understanding) of Reality.
God: The Origin of Reality; the Moral Standard; the Judge of Validity; the Arbiter of Truth; the Supreme Being; the Ruling Principle (or Ruler) of Reality; the Logos in Abrahamic Theology and Classical Theism where Reason and God are seen as fundamentally interconnected and united providing a Foundation for Existence unmatched by any arbitrary or mythological gods (leading to the widespread and widely accepted monotheistic concept of the “One True God who is not a false god like all the false gods”).
The Origin of Reality: The logically necessary Logical Foundation of and explanation for the Existence of Logical Existence (Reality - the Cosmos) and the Logic, Truth, reasoning, and other concepts or contingencies within Reality; The Origin of Logic that logically consistent logical principles like the Principle of Sufficient Reason and the Law of Identity require the existence and/or identity of - that Logic and Reality themselves would not be logically complete and truly explanatory or grounded (and real/logical) without.
Premises (Inputs):
P: Logic.
P establishes, entails, and encompasses Logic as the Source of Knowledge in Logic and the Explanation of the Logical Cause of Logical Systems and what that Cause entails (all logical systems and all logical concepts).
Q: The Logical Origin of Logical Existence (the Logical God - the True Origin of Existence).
Q entails and represents the well-ordered and rationally established Source of Reality in Logic - that is coherent like and with Logic and that is consistent like and with Logic (and with Reality, also understood as the Cosmos or “Ordered Existence”).
R: Proof for Contradiction:
R represents the proof for contradiction in general, which could not exist if Logic and the Origin of Reality did not exist coherently to lay the Logical Foundation for Logic (as well as reasoning and logical proof). Also, in the case of this particular proof such a concept can be employed to show that by assuming the negation of this argument and the premises P and Q that logical contradiction arises from the incoherence that would imply or posit (between Logic and the Origin/Foundation of Reality that is called God, among other valid terms, in English and in classical theism/philosophy).
Formal Reasoning (Logical Proof):
{P, P <-> Q, R -> P, R -> Q} |= R -> (P & Q)
Conclusion (Output): {P, Q, R}:
There must be coherence between the Origin of Reality (God) and Logic (the Method of Knowing Reality) or incoherence and contradiction arise, and even proof and proof for the contradiction (in general) would become arbitrary, ungrounded, and/or impossible. This makes this Truth (of Foundational Coherence - the God of Reason or Logic of Reality that is also the Origin and Ruler of Reality) logically and realistically (in Reality) irrefutable. Counterarguments would have to appeal to the Coherence they’re denying to be valid and thus defeat themselves by standing illogically against Foundational Coherence (and/or fair representation of my argument for this Coherence/Logos at the core of the Cosmos).
Truth Table Analysis:
valid
↓ ↓ ↓ ↓ ↓
PQR⎪P P↔Q R→P R→Q╞R→(P&Q)
――――――――――――――――――――――――――
TTT⎪T TTT TTT TTT TT TTT
TTF⎪T TTT FTT FTT FT TTT
TFT⎪T TFF TTT TFF TF TFF
TFF⎪T TFF FTT FTF FT TFF
FTT⎪F FFT TFF TTT TF FFT
FTF⎪F FFT FTF FTT FT FFT
FFT⎪F FTF TFF TFF TF FFF
FFF⎪F FTF FTF FTF FT FFF
Evaluation Checklist:
1. Truth of premises P, Q, and R: P, Q, and R are all logically and objectively true when we apply consistent Logic to them and their semantics, like we would the argument’s syntax - as logical consistency demands. It is unreasonable to reject the premises: Denying logic (P) undermines rational discourse and leads to self-contradiction, as coherent reasoning is impossible without it. The premise of a Logical Origin (Q) is essential for explaining existence; rejecting it implies accepting an ungrounded reality, which is illogical. All rational thought hinges on the coherence of logic and its Origin. The formal logic of the proof shows that if the premises are true, the conclusion must also be true. Rejecting the premises, on the other hand, amounts in this case and in this case to rejecting the validity of reasoning itself. Thus, accepting the premises is foundational for a coherent understanding of reality, and rejecting them is inherently contradictory and unreasonable - an untenable position to hold rationally.
2. Conclusion follows (Y/N): Yes (Y).
3. Counterarguments feasible (Y/N): No (N), all arguments and thus any counterarguments would be invalid if standing in contradiction to the Coherent Foundation and the proof that asserts its existence and coherence (or that which it logically entails).
4. Identified flaws: No. No flaws in this reasoning have been identified and better reasoning would only better reveal the Coherent Foundation (Logic as God) better than the logician here has, which redeems rather than refutes the core argument that Logic is as foundational (godly - original - causal) as anything there is. It can only be matched by what is fully coherent with it, not outdone.
Result: Validated
Q.E.D.