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: 2026-10-03T01:36:08.053Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:41:09.781Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: a039265504533a8ab66bfd6e3a625cbd33993c9c78990f8f28cc6b388f44f6af
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, Q -> R, R -> S, S -> T} |= (P & Q) & (R & S) & T
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.
Logic is Logic
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
Proof of Reason Demanding Reasoning and the Realization of Emergent Properties and Reality by Maclain Hunter:
Premises:
P: Logic is Logic and is the Standard of Logic, defined by consistency with its own Law of A is A.
Q: Reasoning is the application of Logic and reasoning is coherent with Logic when coherent and encompassed by Logic (and the Logical Reality) even when incoherent.
R: Logic is intrinsic to Reality and allows for reasoning and emergent concepts.
S: Reason demands that reasoning begin (and continue) according to the Standard of Logic in Reality (or in a given system of Logic that is finite and within the broader Reality/Framework), which is Reason itself. The emergent properties latent within that system then begin to emerge, including notions of spacetime and temporally bound concepts, as a result of what the “Axiom of the System” (Logic - First Cause) entails.
T: Assume ~{P, Q, R, S}. That assumption leads to logical contradiction and an inability to explain the Foundation of the Universe (Logos - Universal Logic), finite logical systems within the Universe, and emergent properties in logical systems of all kinds (or any kind).
Formal Argument (Proof):
{P, P -> Q, Q -> R, R -> S, S -> T} |= (P & Q) & (R & S) & T
Conclusion: (P & Q) & (R & S) & T
Logic being Logic allows for coherent Reason and reasoning to exist and begin manifesting/realizing (reasoning into Reality) emergent properties and concepts of and within Logic itself, according to Logic and A is A form as the Axiom and Law of Reasoning that leads to all logical systems up to and including the Universe (but also including finite instances of Logic and reasoning like my own existence and mental faculties that allowed this proof to emerge).
Truth Table:
valid
↓ ↓ ↓ ↓ ↓ ↓
PQRST⎪P P→Q Q→R R→S S→T╞(P&Q)&(R&S)&T
――――――――――――――――――――――――――――――――――――――
TTTTT⎪T TTT TTT TTT TTT TTT T TTT TT
TTTTF⎪T TTT TTT TTT TFF TTT T TTT FF
TTTFT⎪T TTT TTT TFF FTT TTT F TFF FT
TTTFF⎪T TTT TTT TFF FTF TTT F TFF FF
TTFTT⎪T TTT TFF FTT TTT TTT F FFT FT
TTFTF⎪T TTT TFF FTT TFF TTT F FFT FF
TTFFT⎪T TTT TFF FTF FTT TTT F FFF FT
TTFFF⎪T TTT TFF FTF FTF TTT F FFF FF
TFTTT⎪T TFF FTT TTT TTT TFF F TTT TT
TFTTF⎪T TFF FTT TTT TFF TFF F TTT FF
TFTFT⎪T TFF FTT TFF FTT TFF F TFF FT
TFTFF⎪T TFF FTT TFF FTF TFF F TFF FF
TFFTT⎪T TFF FTF FTT TTT TFF F FFT FT
TFFTF⎪T TFF FTF FTT TFF TFF F FFT FF
TFFFT⎪T TFF FTF FTF FTT TFF F FFF FT
TFFFF⎪T TFF FTF FTF FTF TFF F FFF FF
FTTTT⎪F FTT TTT TTT TTT FFT F TTT TT
FTTTF⎪F FTT TTT TTT TFF FFT F TTT FF
FTTFT⎪F FTT TTT TFF FTT FFT F TFF FT
FTTFF⎪F FTT TTT TFF FTF FFT F TFF FF
FTFTT⎪F FTT TFF FTT TTT FFT F FFT FT
FTFTF⎪F FTT TFF FTT TFF FFT F FFT FF
FTFFT⎪F FTT TFF FTF FTT FFT F FFF FT
FTFFF⎪F FTT TFF FTF FTF FFT F FFF FF
FFTTT⎪F FTF FTT TTT TTT FFF F TTT TT
FFTTF⎪F FTF FTT TTT TFF FFF F TTT FF
FFTFT⎪F FTF FTT TFF FTT FFF F TFF FT
FFTFF⎪F FTF FTT TFF FTF FFF F TFF FF
FFFTT⎪F FTF FTF FTT TTT FFF F FFT FT
FFFTF⎪F FTF FTF FTT TFF FFF F FFT FF
FFFFT⎪F FTF FTF FTF FTT FFF F FFF FT
FFFFF⎪F FTF FTF FTF FTF FFF F FFF FF