Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
Axiom-free: true · 3 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: 2026-10-03T01:33:08.738Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:38:56.394Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 68d262bdd1cd10a84662e97e1bd7f3dbaafa58e0901c474a9772597e9e719f57
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.source_identity_rule' does not depend on any axioms
{C, L, I} |= (C <-> L) <-> I
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} |= (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.
Law of Identity
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
Infinite Cause, the Dynamic Reality, and the Axiom of Logic by Maclain Hunter:
Definitions (Terms):
Axiom: A self-evident, fundamental principle that serves as the starting point for logical reasoning.
Coherence: The quality of being logically integrated and unified, without any contradictions.
Self: The "Universal Self" or the "Being of Reality" - the fundamental Essence of existence. The “Object of Introspection” and the locus of reflexive action.
Infinite Cause: The ultimate, uncaused cause of all existence.
Dynamic Reality: The ever-changing, ever-evolving Reality (Rationality) that the Universe logically equates to.
Logic: The Fundamental Principle of (coherent) Reason and reasoning.
Law of Identity: The core logical principle that states that "A is A" - a thing is identical to itself.
Premises (Inputs): {P, Q, R}:
P: Logic’s axiom is “Coherence with Logic (mandatory)”. This can be represented and “f(x)” where f and x are defined as “logically consistent and fully coherent Logic” (Reason and reasoning that never contradicts itself).
Q: The Self (the Infinite Cause) must be the Self (the Dynamic Reality). Let S represent “Self” (as in the “Universal Self” and the “Being of Reality”) while IC represents “Infinite Cause” and DR represents “Dynamic Reality”. Then the following Logic holds: IC(S) -> DR(S), IC(S) = DR(S), (DR <-> IC) <-> (S <-> S)
R: Coherence by definition refers to logical identity and consistency - thus Logic in general - as well as the quality of having a logically integrated and unified whole. Coherence/Logic can be algebraically represented as “x == x” and logically as “A is A” (the Law of Identity). Let C represent Coherence, let L represent Logic, and let I represent the Law of Identity. Then the following Logic holds: {C, L, I} |= (C <-> L) <-> I
Formal Argument (Proof):
{P, Q, R} |= (P <-> Q) <-> R
Conclusion (Output):
{P, Q, R}: Coherence and Logic are coherent by definition and as a matter of logical necessity, and the Law of Identity is coherent with Coherence and Logic. The Universe is a Logical Being (a “Self”) that is what it is, and which is what it is according to itself, which encompasses all things including the Infinite Cause of Existence and the Dynamic Reality of Logic that it equates to and realizes.
Truth Table:
valid
↓ ↓ ↓ ↓
PQR⎪P Q R╞(P↔Q)↔R
――――――――――――――――――
TTT⎪T T T TTT TT
TTF⎪T T F TTT FF
TFT⎪T F T TFF FT
TFF⎪T F F TFF TF
FTT⎪F T T FFT FT
FTF⎪F T F FFT TF
FFT⎪F F T FTF TT
FFF⎪F F F FTF FF