Authored proof knowledge base · The Logos Architecture
Nested Structure by Maclain Hunter
Authored by Maclain Hunter · first-party-authored · authored-foundational-record
Stored 4P source diagnostic: unresolved · finding unverified_concern · admission held_for_format. This intake result is separate from the theorem checks of the exact propositional sequent.
Nested Structure by Maclain Hunter
Premises:
P: Recursion P: Logic is Logic and Logic is coherent; the Way of Knowing Reality and its Foundation is self-consistent; Mastery of Logic according to Logic; the relationship of P to F is logically equivalent to the self-grounding of phi in the golden ratio where phi equals one plus one divided by phi: (((P <-> P) <-> (P <-> P)) <-> ((P <-> P) <-> (P <-> P)))
Truth Table Analysis for P:
P⎪(((P↔P)↔(P↔P))↔((P↔P)↔(P↔P)))
T⎪ TTT T TTT T TTT T TTT
F⎪ FTF T FTF T FTF T FTF
(Tautology)
Q: Recursion Q: Reality is Reality and my logical reasoning and I are coherent; the Origin of Reality (or “God”) is self-consistent; my mastery of Logic according to Logic; the relationship of Q to F is logically equivalent to the self-grounding of phi in the golden ratio where phi equals one plus one divided by phi: (((Q <-> Q) <-> (Q <-> Q)) <-> ((Q <-> Q) <-> (Q <-> Q)))
Truth Table Analysis for Q:
Q⎪(((Q↔Q)↔(Q↔Q))↔((Q↔Q)↔(Q↔Q)))
T⎪ TTT T TTT T TTT T TTT
F⎪ FTF T FTF T FTF T FTF
(Tautology)
Formal Reasoning (F):
(((P <-> Q) <-> (P <-> Q)) <-> ((P <-> Q) <-> (P <-> Q))) |= (P v ~P) <-> (Q v ~Q)
Conclusion: {P, Q}:
This nested structure shows how, through recursion and the linked dynamics of the truth value of multiple premises Truth in Logic can manifest. Logic is Logic if and only if Reality is Reality and vice versa. Logic and I are coherent (unified rationally). the relationship of P and Q to F (or “Tautological Logical Structure and Form”) is logically equivalent to the self-grounding of phi in the golden ratio where phi equals one plus one divided by phi.
F = (P, Q) -> F = 1 + 1/F
Truth Table Analysis (F):
PQ⎪(((P↔Q)↔(P↔Q))↔((P↔Q)↔(P↔Q)))╞(P∨¬P)↔(Q∨¬Q)
TT⎪ TTT T TTT T TTT T TTT TTFT T TTFT
TF⎪ TFF T TFF T TFF T TFF TTFT T FTTF
FT⎪ FFT T FFT T FFT T FFT FTTF T TTFT
FF⎪ FTF T FTF T FTF T FTF FTTF T FTF
(Valid)
Q.E.D.
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.