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: 2026-10-03T01:33:04.237Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:38:54.570Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: d5d605ddc507120a8697c591af1ae2d6c03ad84b39a8415dc01c3548cac69754
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
{Q <-> P, ~P, ~P -> 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.
A is A
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
If, Then, But, Since by Maclain Hunter:
P: IF: Logic is only a mental process in the minds of humans
Q: THEN: it’s a product of the mind’s imagination and would be arbitrary (not grounded in the Coherence and Logic inherent in Reality being Reality - the Logic of Reality or “Logos” - as True Logic is and as truly coherent things like Logic must be) and imaginary.
R: BUT: That cannot be the case that Logic is limited to human reasoning (that is itself limited and contingent upon higher forms and orders of Order, Logic, and Reason, such as the Logos - the Highest Order of Logic).
S: SINCE: Logic is not arbitrary and Reason is observed in animals and in the Order of the Universe which itself displays a profound coherence and unity at the highest most macroscopic level. This is supported by the entire body of logically coherent scientific evidence which itself relies on this Logos to be valid and coherent and which shows fine tuning and systems beyond man in Reality that exhibit an otherwise impossible (if not logically grounded) mix of coherence and complexity - which is consistent with Logic and Logic’s fundamental demand that A is A and all must be and (universally, and at least in some particular sense/context) equal all.
Formal Argument (Logical Proof):
{Q <-> P, ~P, ~P -> R, R <-> S} |= (~P & ~Q) & (R & S)
Conclusion: The conclusion of not P and not Q but rather R and S holds true because it is not tenable that Logic is arbitrary and imaginary and only valid in the minds of humans. That would lead to logical contradiction and defies Logic. Logic is universal and universally comprehensive, as the Logical Foundation of Truth.
Truth Table:
valid
↓ ↓ ↓ ↓ ↓
PQRS⎪Q↔P ¬P ¬P→R R↔S╞(¬P&¬Q)&(R&S)
―――――――――――――――――――――――――――――――――――
TTTT⎪TTT FT FTTT TTT FTFFT F TTT
TTTF⎪TTT FT FTTT TFF FTFFT F TFF
TTFT⎪TTT FT FTTF FFT FTFFT F FFT
TTFF⎪TTT FT FTTF FTF FTFFT F FFF
TFTT⎪FFT FT FTTT TTT FTFTF F TTT
TFTF⎪FFT FT FTTT TFF FTFTF F TFF
TFFT⎪FFT FT FTTF FFT FTFTF F FFT
TFFF⎪FFT FT FTTF FTF FTFTF F FFF
FTTT⎪TFF TF TFTT TTT TFFFT F TTT
FTTF⎪TFF TF TFTT TFF TFFFT F TFF
FTFT⎪TFF TF TFFF FFT TFFFT F FFT
FTFF⎪TFF TF TFFF FTF TFFFT F FFF
FFTT⎪FTF TF TFTT TTT TFTTF T TTT
FFTF⎪FTF TF TFTT TFF TFTTF F TFF
FFFT⎪FTF TF TFFF FFT TFTTF F FFT
FFFF⎪FTF TF TFFF FTF TFTTF F FFF