Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
Axiom-free: true · 1 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: 2026-10-03T01:36:04.010Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:41:16.310Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 012772d374485448686e90e3e8659e7c16f74f77f683d5a7b08e02b156da8bd1
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
{P <-> Q, Q <-> R, R <-> S} |= (P & Q) <-> (R & S)
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.
Proven Facts by Maclain Hunter:
Terms:
Proof: Arguments or evidence establishing or helping to establish facts or Truth objectively.
Truth or/of Fact: A proposition or statement that accurately reflects reality and can be verified through observation or evidence.
Coherence or/of Logic: The property of logical reasoning that ensures internal consistency, meaning that the principles of Logic do not contradict each other.
Rational Consistency: The alignment of knowledge claims with logical reasoning and factual evidence, ensuring that they are not contradictory and can be justified rationally.
Genuine Knowledge: Information or beliefs that are true and justified, based on reliable evidence and reasoning.
Reality: The state of things as they actually exist, independent of perceptions or beliefs.
Tautological: A statement that is true by necessity or by virtue of its logical form, often self-evident and requiring no additional proof.
Proof by Contradiction: A method of demonstrating the truth of a proposition by assuming its negation and showing that this assumption leads to a logical contradiction.
Formal Argument (Logical Proof): A structured reasoning process that follows established logical principles to arrive at a (necessary) conclusion based on given premises.
Bi-conditional Relationship: A logical relationship indicating that two statements are equivalent; both must be true or both must be false.
Premises:
P: The “Truth of Fact” is necessarily true and factual.
Q: The “Coherence of Logic” is necessarily coherent and logical.
R: The rational consistency of genuine knowledge and Reality is tautological (self-evident) when analyzed coherently/properly with logical/rational consistency.
S: Assume that the Truth of Fact, the Coherence of Logic, and/or the rational consistency of genuine knowledge and Reality were incoherent and “not true”. We can see that would lead to logical contradiction. Therefore it’s logically untenable to hold that premises P, Q, and R are wrong/untrue. This means conclusions consistent with {P, Q, R} are necessarily and logically true. Proof and knowledge requires not only facts and Reality but Logic and Truth.
Proof (Formal Argument):
{P <-> Q, Q <-> R, R <-> S} |= (P & Q) <-> (R & S)
Conclusion: {P, Q, R, S}:
The “Truth of Fact” is logically equivalent to the “Coherence of Logic” which is itself coherent with and has a bi-conditional relationship with the rational consistency of true knowledge (logically consistent understanding) and Reality. This is proven through proof positive and the proof for contradiction in the premise S, incorporated into the (positive) proof.
Truth Table:
valid
↓ ↓ ↓ ↓
PQRS⎪P↔Q Q↔R R↔S╞(P&Q)↔(R&S)
―――――――――――――――――――――――――――――
TTTT⎪TTT TTT TTT TTT T TTT
TTTF⎪TTT TTT TFF TTT F TFF
TTFT⎪TTT TFF FFT TTT F FFT
TTFF⎪TTT TFF FTF TTT F FFF
TFTT⎪TFF FFT TTT TFF F TTT
TFTF⎪TFF FFT TFF TFF T TFF
TFFT⎪TFF FTF FFT TFF T FFT
TFFF⎪TFF FTF FTF TFF T FFF
FTTT⎪FFT TTT TTT FFT F TTT
FTTF⎪FFT TTT TFF FFT T TFF
FTFT⎪FFT TFF FFT FFT T FFT
FTFF⎪FFT TFF FTF FFT T FFF
FFTT⎪FTF FFT TTT FFF F TTT
FFTF⎪FTF FFT TFF FFF T TFF
FFFT⎪FTF FTF FFT FFF T FFT
FFFF⎪FTF FTF FTF FFF T FFF
Result: Validated
Q.E.D.