Lean verification registry · Authored proofs · The Logos Architecture
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: 2026-10-02T21:22:43.099Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:42:14.078Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: a276d9a3aa5f3faba47f4130b5764f6aa59e523220286285d706b289539c69d5
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.source_identity_rule' does not depend on any axioms
{P, Q, R} |= (((P <-> 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.
Unmatched formal parentheses
A is A
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
The Logic of Discovery by Maclain Hunter
Premises:
P: Discovery, to be truly and consistently logical, must be “logical discovery” and must be consistent with Logic, with logical structure, method, and Coherence. If we assume the negation of that statement/premise we arrive at a contradiction and false equivalence between logical and illogical forms of discovery. Logical coherence is necessary across all valid academic fields and for all coherent concepts.
Q: The Rational Foundation of Reality is the Logos and what is logically coherent with this Logos (or Universal Reasoning and Coherent Logic) is logically coherent objectively and truly. If we assume the negation of that statement logical contradiction arises between Logic and its Foundation in Universal Reason (Logos - the God of Reason) that makes Reality be Reality and A is A form Logic be what it is.
R: The logical Coherence (or Logos) in the logical method and structure of discovery requires and demonstrates, inherently and necessarily, the Logic of the Universe—the Highest Order of Logic that structures Reality and all that exists within it including discovery—which is the rational Foundation of Existence and Logic that is called God or the God of Reason (denoting a God or Origin of Reality that is Reason and Logic itself) in theology and classical theism/philosophy. Assume the negation of this premise and logical contradiction arises (ie - logical discovery isn’t proof of the existence of Logic as it must be). Likewise if we assume that the “greatest discovery” is logically incoherent and something less than discovery fully aligning with Logic, that defies Logic.
Formal Reasoning:
{P, Q, R} |= (((P <-> Q) <-> R) <-> (R <-> Q) <-> P
Conclusion: {P, Q, R}:
The fact that discovery exists proves the Logos must exist. The fact we can discover the Logos with logically coherent discovery proves that Logos exists and that discovery (of the Logos or otherwise) is itself a valid and extant logical concept (that is contingent upon Universal Reason). God (or Reason and the coherent Foundation of Reason in the Logos) and the structure of discovery are necessarily coherent when the structure of discovery is valid and properly understood.
This proof, by fully aligning discovery and Logic (Logos - God) is aligned itself with the concept of the greatest logically feasible discovery. This is logically necessary for the integrity of logically consistent Logic.
Discovery, like philosophical thought and valid reasoning (or Logic), along with its derivatives (ie - math, science, language, governance, education, academics, etc.), must be logically coherent to be logically coherent and valid, and this (statement in the conclusion) is not mere opinion but a tautological line of reasoning itself.
Truth Table Analysis:
PQR⎪P Q R╞((P↔Q)↔R)↔(R↔Q)↔P
TTT⎪T T T TTT TT T TTT TT
TTF⎪T T F TTT FF T FFT FT
TFT⎪T F T TFF FT T TFF FT
TFF⎪T F F TFF TF T FTF TT
FTT⎪F T T FFT FT F TTT FF
FTF⎪F T F FFT TF F FFT TF
FFT⎪F F T FTF TT F TFF TF
FFF⎪F F F FTF FF F FTF FF
(Valid)
Q.E.D.