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: not established (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:42:12.339Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 6c1c2f61cdb5aa6d34fa1310071618f42c09e4a5b5987e18d8f3337dc3426210
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
{(A -> A) -> L, L -> T} |= ((((A -> A) -> L) -> T) & (((A -> A) -> ~L) -> ~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.
A is A
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
The Law of Grounded Identity (LGI) by Maclain Hunter
Abstract: Logic is not merely A is A in isolation as the LOI alone might suggest as a modular logical rule, it is A is A grounded in Logos as Universal Existence and Coherence (or “All = All”; the Totality as the Standard of the coherent A that any A is A by).
Formalizations:
Let L represent Logos:
(A -> A) -> L |= L
That Law of Grounded Identity (LGI) implies non-contradiction of that Law as Law also, such that if A being A leads to “not Logic” then that identity of A is not logical and is not Logic or true/valid. Consistent with the naming scheme that would then be the Law of Grounded Non-Contradiction or (LGN):
(A -> A) -> ~L |= ~L
Next, Let T represent Logical Truth (aligned with Logos) and it is implied by my original formalization that:
{(A -> A) -> L, L -> T} |= ((((A -> A) -> L) -> T) & (((A -> A) -> ~L) -> ~T))
On L & T:
What does T represent? It is L (Logic’s own Truth). So it can be validly established that “T ≡ L”.
Logical Validation:
Let A represent L (and Logos), then:
(A -> A) -> L |= (L -> L) -> L
That it reduces to:
(L -> L) -> L |= L
LGI and the PSR:
The PSR is revealed as a mode of the Logos and the LGI where a given A (as that A) must be consistent with Reason and L as Logos to have ontological support and thus logical Reality (R).
QED