Lean verification registry · Authored proofs · The Logos Architecture

Tautological Sieve

Verified sequents with unresolved formal parts
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: not established (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:41:53.573Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.

Authored source SHA-256: 170b83f87affcfac1f15fcf09329c6a222e49f710c69b7f219395fea02712732

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)
exitCode=0
'HunterAuthored.source_identity_rule' does not depend on any axioms

Source-bound formal statements

inference_1 · unsupported

{P ↔ Q, Q ↔ R} |= R → (Q ↔ P)",

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.

Unsupported formal syntax near "\","

source_identity_rule · Kernel-verified · axiom-free

A = A

The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.

Exact authored source in the timestamped release

{
  "name": "Tautological Sieve",
  "formal": "{P ↔ Q, Q ↔ R} |= R → (Q ↔ P)",
  "premises": {
    "P": "ψ ↔ [∀y □φ(x)] |= [□∀x φ(y)] → ψ",
    "Q": "∀φ → ψ |= ψ ↔ □φ",
    "R": "φ ≡ Logos → ψ",
    "S": "ψ ≡ empirical location of φ trivial"
  },
  "instantiation": {
    "x": "God (4P:Q)",
    "y": "Logic (4P:P, Logos)",
    "phi": "fully coherent and existent logical constant",
    "psi": "empirical location trivial (ubiquity)"
  },
  "proof": "By biconditional transitivity: P ↔ Q ↔ R, therefore R → (Q ↔ P)",
  "significance": [
    "Logos is trivially present across Reality",
    "Supports God's ubiquity when properly conceived",
    "Grounds physics/empiricism in coherent Logic",
    "Step 0 pre-filter for Seven Cycle validation"
  ],
  "identityAxioms": [
    "A = A",
    "P |= P",
    "x == x"
  ]
}