Lean verification registry · Authored proofs · The Logos Architecture

Universal and Local Logic — Two Proofs

Source recorded — formalization still required
Axiom-free: not established · 0 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: 2026-10-02T21:46:47.892Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:42:43.335Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.

Authored source SHA-256: 625cd13b2caf40d627cd65f682bf377b27eaee3b11d9951641273fed26a7d6f3

Lean source · Verification JSON · Exact archived source JSON · Compiler report · Current authored source page · Signed release and verification instructions

Kernel output

Lean (version 4.7.0, commit v4.7.0, Release)
Not executed: no complete licensed formal sequent recovered.

Source-bound formal statements

No complete formal sequent has yet been recovered. This source is recorded, not marked Lean-verified.

Exact authored source in the timestamped release

Proof 1: 

P: Logic: the Order inherent in the Foundation of Existence; the Logical Absolute; the First Cause.

Q: Logical contingency of the first order or primary state.

R: Logical contingency of an intermediate order/state.

S: Logical contingency of a final or infinite order/state. 

T: A given concept or set of concepts.

U: All concepts and all sets of concepts.
   PQRSTU⎪P╞(((Q→Q)&(R↔R))&((S∨¬S)&(T→¬¬T)))→(¬U↔¬¬¬U)
――――――――――――――――――――――――――――――――――――――――――――――――――――
TTTTTT⎪T    TTT T TTT  T  TTFT T TTTFT   T FTTFTFT 
TTTTTF⎪T    TTT T TTT  T  TTFT T TTTFT   T TFTTFTF 
TTTTFT⎪T    TTT T TTT  T  TTFT T FTFTF   T FTTFTFT 
TTTTFF⎪T    TTT T TTT  T  TTFT T FTFTF   T TFTTFTF 
TTTFTT⎪T    TTT T TTT  T  FTTF T TTTFT   T FTTFTFT 
TTTFTF⎪T    TTT T TTT  T  FTTF T TTTFT   T TFTTFTF 
TTTFFT⎪T    TTT T TTT  T  FTTF T FTFTF   T FTTFTFT 
TTTFFF⎪T    TTT T TTT  T  FTTF T FTFTF   T TFTTFTF 
TTFTTT⎪T    TTT T FTF  T  TTFT T TTTFT   T FTTFTFT 
TTFTTF⎪T    TTT T FTF  T  TTFT T TTTFT   T TFTTFTF 
TTFTFT⎪T    TTT T FTF  T  TTFT T FTFTF   T FTTFTFT 
TTFTFF⎪T    TTT T FTF  T  TTFT T FTFTF   T TFTTFTF 
TTFFTT⎪T    TTT T FTF  T  FTTF T TTTFT   T FTTFTFT 
TTFFTF⎪T    TTT T FTF  T  FTTF T TTTFT   T TFTTFTF 
TTFFFT⎪T    TTT T FTF  T  FTTF T FTFTF   T FTTFTFT 
TTFFFF⎪T    TTT T FTF  T  FTTF T FTFTF   T TFTTFTF 
TFTTTT⎪T    FTF T TTT  T  TTFT T TTTFT   T FTTFTFT 
TFTTTF⎪T    FTF T TTT  T  TTFT T TTTFT   T TFTTFTF 
TFTTFT⎪T    FTF T TTT  T  TTFT T FTFTF   T FTTFTFT 
TFTTFF⎪T    FTF T TTT  T  TTFT T FTFTF   T TFTTFTF 
TFTFTT⎪T    FTF T TTT  T  FTTF T TTTFT   T FTTFTFT 
TFTFTF⎪T    FTF T TTT  T  FTTF T TTTFT   T TFTTFTF 
TFTFFT⎪T    FTF T TTT  T  FTTF T FTFTF   T FTTFTFT 
TFTFFF⎪T    FTF T TTT  T  FTTF T FTFTF   T TFTTFTF 
TFFTTT⎪T    FTF T FTF  T  TTFT T TTTFT   T FTTFTFT 
TFFTTF⎪T    FTF T FTF  T  TTFT T TTTFT   T TFTTFTF 
TFFTFT⎪T    FTF T FTF  T  TTFT T FTFTF   T FTTFTFT 
TFFTFF⎪T    FTF T FTF  T  TTFT T FTFTF   T TFTTFTF 
TFFFTT⎪T    FTF T FTF  T  FTTF T TTTFT   T FTTFTFT 
TFFFTF⎪T    FTF T FTF  T  FTTF T TTTFT   T TFTTFTF 
TFFFFT⎪T    FTF T FTF  T  FTTF T FTFTF   T FTTFTFT 
TFFFFF⎪T    FTF T FTF  T  FTTF T FTFTF   T TFTTFTF 
FTTTTT⎪F    TTT T TTT  T  TTFT T TTTFT   T FTTFTFT 
FTTTTF⎪F    TTT T TTT  T  TTFT T TTTFT   T TFTTFTF 
FTTTFT⎪F    TTT T TTT  T  TTFT T FTFTF   T FTTFTFT 
FTTTFF⎪F    TTT T TTT  T  TTFT T FTFTF   T TFTTFTF 
FTTFTT⎪F    TTT T TTT  T  FTTF T TTTFT   T FTTFTFT 
FTTFTF⎪F    TTT T TTT  T  FTTF T TTTFT   T TFTTFTF 
FTTFFT⎪F    TTT T TTT  T  FTTF T FTFTF   T FTTFTFT 
FTTFFF⎪F    TTT T TTT  T  FTTF T FTFTF   T TFTTFTF 
FTFTTT⎪F    TTT T FTF  T  TTFT T TTTFT   T FTTFTFT 
FTFTTF⎪F    TTT T FTF  T  TTFT T TTTFT   T TFTTFTF 
FTFTFT⎪F    TTT T FTF  T  TTFT T FTFTF   T FTTFTFT 
FTFTFF⎪F    TTT T FTF  T  TTFT T FTFTF   T TFTTFTF 
FTFFTT⎪F    TTT T FTF  T  FTTF T TTTFT   T FTTFTFT 
FTFFTF⎪F    TTT T FTF  T  FTTF T TTTFT   T TFTTFTF 
FTFFFT⎪F    TTT T FTF  T  FTTF T FTFTF   T FTTFTFT 
FTFFFF⎪F    TTT T FTF  T  FTTF T FTFTF   T TFTTFTF 
FFTTTT⎪F    FTF T TTT  T  TTFT T TTTFT   T FTTFTFT 
FFTTTF⎪F    FTF T TTT  T  TTFT T TTTFT   T TFTTFTF 
FFTTFT⎪F    FTF T TTT  T  TTFT T FTFTF   T FTTFTFT 
FFTTFF⎪F    FTF T TTT  T  TTFT T FTFTF   T TFTTFTF 
FFTFTT⎪F    FTF T TTT  T  FTTF T TTTFT   T FTTFTFT 
FFTFTF⎪F    FTF T TTT  T  FTTF T TTTFT   T TFTTFTF 
FFTFFT⎪F    FTF T TTT  T  FTTF T FTFTF   T FTTFTFT 
FFTFFF⎪F    FTF T TTT  T  FTTF T FTFTF   T TFTTFTF 
FFFTTT⎪F    FTF T FTF  T  TTFT T TTTFT   T FTTFTFT 
FFFTTF⎪F    FTF T FTF  T  TTFT T TTTFT   T TFTTFTF 
FFFTFT⎪F    FTF T FTF  T  TTFT T FTFTF   T FTTFTFT 
FFFTFF⎪F    FTF T FTF  T  TTFT T FTFTF   T TFTTFTF 
FFFFTT⎪F    FTF T FTF  T  FTTF T TTTFT   T FTTFTFT 
FFFFTF⎪F    FTF T FTF  T  FTTF T TTTFT   T TFTTFTF 
FFFFFT⎪F    FTF T FTF  T  FTTF T FTFTF   T FTTFTFT 
FFFFFF⎪F    FTF T FTF  T  FTTF T FTFTF   T TFTTFTF 

Proof 2: 

P: The Logical Absolute (Logic); Universal Logic; Non-Local Reason (Logos)

U: Local logics; Personal reasoning; Finite reasons; rationally limited or logically contingent aspects of Logical Existence.

PU⎪¬U↔¬¬¬U╞P∨¬P
――――――――――――――――
TT⎪FTTFTFT TTFT
TF⎪TFTTFTF TTFT
FT⎪FTTFTFT FTTF
FF⎪TFTTFTF FTTF