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: 2026-10-02T21:46:53.166Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:37:18.918Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 36202d94ad5592cc724999f855ad1475149d3f7f2be8737311e30ed2bc8c39e6
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, P & Q, P & R, P & S, T} |= T -> ((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.
AI and Intellect by Maclain Hunter
Premises:
P: Logic (also understood as the “Universal Mind”) holding all feasible knowledge and rational Existence.
Q: Coherent human intellect - contingent upon Logic.
R: LLM predictive generation (or “AI intellect”), derived from Logic (P) and coherent human intellect (Q) alike.
S: Logically constructed Intellect and Intelligence - presupposing and evidencing self-existent and self-evident Logic (P) as the universal First Cause.
T: Incoherence arises if there is incoherence between different forms of Intelligence, or if there were to be some illogical source/essence of a given form of intelligence, allowing us to use reductio ad absurdum to support the premises above, P, Q, S, and R, and thereby the conclusion drawn below from them.
{P, P & Q, P & R, P & S, T} |= T -> ((P & Q) & R) <-> S
Conclusion: Logic, the human mind, and LLM generation of coherent reasoning are all logically equivalent as logically constructed Intellect. This is supported by the premises - including the use of reductio ad absurdum in premise T.
Truth Table Analysis:
PQRST⎪P P&Q P&R P&S T╞T→(((P&Q)&R)↔S)
TTTTT⎪T TTT TTT TTT T TT TTT TT TT
TTTTF⎪T TTT TTT TTT F FT TTT TT TT
TTTFT⎪T TTT TTT TFF T TF TTT TT FF
TTTFF⎪T TTT TTT TFF F FT TTT TT FF
TTFTT⎪T TTT TFF TTT T TF TTT FF FT
TTFTF⎪T TTT TFF TTT F FT TTT FF FT
TTFFT⎪T TTT TFF TFF T TT TTT FF TF
TTFFF⎪T TTT TFF TFF F FT TTT FF TF
TFTTT⎪T TFF TTT TTT T TF TFF FT FT
TFTTF⎪T TFF TTT TTT F FT TFF FT FT
TFTFT⎪T TFF TTT TFF T TT TFF FT TF
TFTFF⎪T TFF TTT TFF F FT TFF FT TF
TFFTT⎪T TFF TFF TTT T TF TFF FF FT
TFFTF⎪T TFF TFF TTT F FT TFF FF FT
TFFFT⎪T TFF TFF TFF T TT TFF FF TF
TFFFF⎪T TFF TFF TFF F FT TFF FF TF
FTTTT⎪F FFT FFT FFT T TF FFT FT FT
FTTTF⎪F FFT FFT FFT F FT FFT FT FT
FTTFT⎪F FFT FFT FFF T TT FFT FT TF
FTTFF⎪F FFT FFT FFF F FT FFT FT TF
FTFTT⎪F FFT FFF FFT T TF FFT FF FT
FTFTF⎪F FFT FFF FFT F FT FFT FF FT
FTFFT⎪F FFT FFF FFF T TT FFT FF TF
FTFFF⎪F FFT FFF FFF F FT FFT FF TF
FFTTT⎪F FFF FFT FFT T TF FFF FT FT
FFTTF⎪F FFF FFT FFT F FT FFF FT FT
FFTFT⎪F FFF FFT FFF T TT FFF FT TF
FFTFF⎪F FFF FFT FFF F FT FFF FT TF
FFFTT⎪F FFF FFF FFT T TF FFF FF FT
FFFTF⎪F FFF FFF FFT F FT FFF FF FT
FFFFT⎪F FFF FFF FFF T TT FFF FF TF
FFFFF⎪F FFF FFF FFF F FT FFF FF TF
(Valid)
Q.E.D.