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: 2026-10-02T21:46:56.311Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:39:06.626Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 3a652e9950b283e4486a2b2b752a1c97b8ee66b68b736c662922b4f54c928d5f
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, Q, R} |= (P & R) <-> 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.
A is A
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
Knowledge and Application of Logic by Maclain Hunter
Premises:
P: Logic is the Principle of Reason underlying and manifest in the structure of coherent reasoning - at once God and the method we use to know Reality. Classical Logic posits three core rules, however, each is a restatement of identity in its own right. A cannot be not A is substantively the same as saying A is A. Likewise Truth cannot be falseness and the middle is excluded, but this is A is A applied to Truth - still. Truth cannot be its lack (which we call falseness but which is also simply “not A” when Truth is A).
Let P also have a numerical value of 1 for the purposes of showing that logically consistent Logic can handle both basic arithmetic and formal self-evidence, as well as formal proof of any articulable Truth claim.
Q: This proof is evidence I know Logic. This self-referential proof uses its own valid structure to rationally support the premises showing advanced mastery of Logic.
Let Q carry a numerical value of 2, for our propositional arithmetic.
R: Reality can’t be illogical w/o contradiction. Truth cannot exist outside logically consistent (or “highest order”) Logic, as Truth is superseded by Logic and Logical Existence (or “Reality and Reality’s Way of Being”). To say that logically consistent Logic and the Truth consistent with it cannot be formalized in a complete and consistent fashion is to deny the feasibility of genuine formal Logic itself - contradicting Logic’s own formal and metaphysical identity.
Let R also carry a numerical value of 1.
Formal Reasoning:
{P, Q, R} |= (P & R) <-> Q
Conclusion: {P, Q, R}:
The validity of the propositional structure of this proof, as written above, which can be and has been checked logically and empirically (ie - in an observable and logically retraceable manner), supports the Truth of premise Q, which exists in a biconditional relationship with the other premises and their encodings (P & R).
The complete/consistent Logic underlying the Universe (ie - the Logos that is Arche, Sophos, and Theos of the Cosmos in comparable Greek terms) is inherently complete. This proof demonstrates how formal LOGIC can remain complete while formally distilled and exhibited, without contradiction, all while retaining the capability of handling mathematical truths and arithmetic (basic or otherwise).
This gives formal example of what Gödel’s (flawed) results call impossible, refuting the common interpretation of Gödel’s incompleteness theorems with valid and non-contradictory counterexample - evidence in proof form of something that would be impossible if Gödel had not been mistaken (specifically by assuming that Logic is broken by paradox arising from self-defeating statements, when Logic simply knows these statements as invalid and logically meaningless).
This high level refutation of a result in Logic seen as groundbreaking, or even the pinnacle of human formal logical reasoning also serves as evidence of my specific level of mastery of Logic (ie - an extremely rare or even “unprecedented” grasp of Logic).
Truth Table Analysis:
PQR⎪P Q R╞(P&R)↔Q
TTT⎪T T T TTT TT
TTF⎪T T F TFF FT
TFT⎪T F T TTT FF
TFF⎪T F F TFF TF
FTT⎪F T T FFT FT
FTF⎪F T F FFF FT
FFT⎪F F T FFT TF
FFF⎪F F F FFF TF
Arithmetic:
P = 1
Q = 2
R = 1
(P & R) <-> Q :: 1 + 1 = 2
Meta-Logical Reasoning:
Applying the Rule of Logic (A is A), established as the Logical Standard by P:
Initial Test Results:
Does (section) contain contradiction of Logic’s A is A form?
P: No
Q: No
R: No
Formal Reasoning: No
Conclusion: No
Truth Table Analysis: No
Arithmetic: No
Meta-Logical Reasoning: No
Q.E.D.