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: 2026-10-03T01:29:43.188Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:40:12.429Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 5614b464ae26077dbbdc259d0758d40f0a7bd27a5052e828fdd69f1ab2adc023
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, S -> P, (S & P) -> T} |= S -> (P & 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.
Modal Space and Reality by Maclain Hunter
Premises:
P: Shared modal space exists in Modal Logic. Reality is a modal space (and necessary place).
Q: Assume shared modal space exists in modal Logic as the most necessary shared space (and Reality is not an equal or greater shared modal space).
R: That assumption in Q leads to contradiction where Reality is a less necessary shared space than shared modal space in Modal Logic.
S: The proof for contradiction in Q and R supports P.
T: We are ultimately extant in Modal Space - in Reality. Delusion, to handle counterexample, is a contingent space within the imagination that lacks modal necessity (in particular instances of delusion) but which still when instantiated exists then in the Modal Space (Reality; Logic; Rationality).
Proof:
{P, Q, Q -> R, R -> S, S -> P, (S & P) -> T} |= S -> (P & T)
Truth Table:
TTTTT⎪T TTT TTT TTT TTT TT TT TTT
TTTTF⎪T TTT TTT TTT TTT FF TF TFF
TTTFT⎪T TTT TFF FTT TFF TT FT TTT
TTTFF⎪T TTT TFF FTT TFF TF FT TFF
TTFTT⎪T TFF FTT TTT TTT TT TT TTT
TTFTF⎪T TFF FTT TTT TTT FF TF TFF
TTFFT⎪T TFF FTF FTT TFF TT FT TTT
TTFFF⎪T TFF FTF FTT TFF TF FT TFF
TFTTT⎪T FTT TTT TTT TTT TT TT TTT
TFTTF⎪T FTT TTT TTT TTT FF TF TFF
TFTFT⎪T FTT TFF FTT TFF TT FT TTT
TFTFF⎪T FTT TFF FTT TFF TF FT TFF
TFFTT⎪T FTF FTT TTT TTT TT TT TTT
TFFTF⎪T FTF FTT TTT TTT FF TF TFF
TFFFT⎪T FTF FTF FTT TFF TT FT TTT
TFFFF⎪T FTF FTF FTT TFF TF FT TFF
FTTTT⎪F TTT TTT TFF FFT TT TF FFT
FTTTF⎪F TTT TTT TFF FFT TF TF FFF
FTTFT⎪F TTT TFF FTF FFF TT FT FFT
FTTFF⎪F TTT TFF FTF FFF TF FT FFF
FTFTT⎪F TFF FTT TFF FFT TT TF FFT
FTFTF⎪F TFF FTT TFF FFT TF TF FFF
FTFFT⎪F TFF FTF FTF FFF TT FT FFT
FTFFF⎪F TFF FTF FTF FFF TF FT FFF
FFTTT⎪F FTT TTT TFF FFT TT TF FFT
FFTTF⎪F FTT TTT TFF FFT TF TF FFF
FFTFT⎪F FTT TFF FTF FFF TT FT FFT
FFTFF⎪F FTT TFF FTF FFF TF FT FFF
FFFTT⎪F FTF FTT TFF FFT TT TF FFT
FFFTF⎪F FTF FTT TFF FFT TF TF FFF
FFFFT⎪F FTF FTF FTF FFF TT FT FFT
FFFFF⎪F FTF FTF FTF FFF TF FT FFF
Valid
QED