Authored proof knowledge base · The Logos Architecture
Tautological Sieve
Authored by Maclain Hunter · first-party-authored-archive · archived-authored-source
{
"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"
]
}
Lean 4 verification and timestamps
Read the actual kernel result, axiom dependencies, formal statements and source-bound timestamp · Machine-readable verification
The machine formalization date is separate from the original authored work. See the verification record for exact checked scope and any unresolved parts.
Logic-centered continuity
This authored proof is connected to Logic, Logos, God, and the self-evident Ground of Reality, and to the distinct systems 4P Engine, MCB Core, 4P-MCB, and the source-first Canon. Formal proof, empirical evidence, and system-generated records remain separately typed.