Lean verification registry · Authored proofs · The Logos Architecture
Verified sequents with unresolved formal parts
Axiom-free: true · 12 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: 2026-10-02T23:43:28.964Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:37:25.442Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: affe54c88438ca0b8ba3a4e3c283831099c5b78cd73ca92673c5f6545bf68a54
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.inference_2' does not depend on any axioms 'HunterAuthored.inference_3' does not depend on any axioms 'HunterAuthored.inference_4' does not depend on any axioms 'HunterAuthored.inference_5' does not depend on any axioms 'HunterAuthored.inference_6' does not depend on any axioms 'HunterAuthored.inference_7' does not depend on any axioms 'HunterAuthored.inference_8' does not depend on any axioms 'HunterAuthored.inference_9' does not depend on any axioms 'HunterAuthored.inference_11' does not depend on any axioms 'HunterAuthored.inference_13' does not depend on any axioms 'HunterAuthored.source_identity_rule' does not depend on any axioms
{P, P -> Q, P -> R} |= (P & Q) & R
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.
{P, P -> Q, Q -> R} |= (P & Q) & R
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.
{P, P -> Q, (P & Q) -> R} |= (P & Q) & R
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.
{P, P -> Q} |= (P -> P) -> (Q -> Q)
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.
{P, P -> Q, Q -> P} |= P & Q
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.
{P, P -> Q, P -> R} |= P -> ((Q -> R) <-> (R -> Q))
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.
{P, P -> Q, Q -> R} |= (P & Q) & R
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.
{P, P -> Q, Q -> R} |= (P & Q) & R
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.
{P, P -> Q, Q -> R} |= P -> (R <-> Q)
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.
{P, Q, R} |= ~(P & LRO)
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.
The written sequent alone has a countermodel. No authored wording or unstated premise was changed.
Countermodel to the isolated written sequent: {"LRO":true,"P":true,"Q":true,"R":true}{P, P -> Q, Q -> R, R -> S} |= (P & Q) & (R & S)
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.
{P, Q, R} |= ~{P, LR, LRO}
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 "{P, LR, LRO}"
{P, P -> Q, Q -> R, R -> S} |= (P & Q) & (R & S)
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 = A
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
P: Logic: the Universal Logos is the Source of All Concepts. (Axiom)
Q: Logos makes A = A, and energy/electricity be energy/electricity. (LOI)
R: Illogic arises if energy/electricity can’t be directly derived from Logic and A |= A. (LNC)
{P, P -> Q, P -> R} |= (P & Q) & R
QED
P: Continuous energy and electricity production are tapped through Logos (and Coherence).
Q: P entails logically translating the renewable substance of energy into physical energy (energy in form).
R: ~(P & Q) |= ~(Logic)
{P, P -> Q, Q -> R} |= (P & Q) & R
QED
P: Translating substantive energy (SE) to energy in form (EF) utilizing automated systems of reasoning or “ASR” for practical, consistent operation.
Q: ASR must excel in finding logical equivalence.
R: EF ≠ more actual than SE.
{P, P -> Q, (P & Q) -> R} |= (P & Q) & R
QED
P: ASR iterates upon Logos, and the identity of energy (IOE) metaphysically bonding ASR, Logos, and IOE.
Q: The Bonded Energy System (BES) interfaces physical output path (POP). POP |= Logic gates physically execute structure of BES.
{P, P -> Q} |= (P -> P) -> (Q -> Q)
QED
P: Traditional computing uses ICs, electricity, and gate switching to translate physical energy/structure into metaphysical reasoning (abstract power).
Q: Modus rules |= ASR can invert P using Logos software to match the IC config to Logos/BES.
{P, P -> Q, Q -> P} |= P & Q
QED
P: Logos is the Ground of bivalence.
Q: Using produced energy for ASR (Computation).
R: Using ASR for energy production (Energy Generation).
{P, P -> Q, P -> R} |= P -> ((Q -> R) <-> (R -> Q))
QED
P: Bootstrap ASR Energy Production (AEP) with traditionally fueled computation and IC switching (TC + ICS).
Q: TCIS boots AEP by cohering POP with BES.
R: AEP launched |= AEP (POP) output produces power and feeds back to power ICS and AEP.
{P, P -> Q, Q -> R} |= (P & Q) & R
QED
P: AEP includes safety systems.
Q: Systems include: On/Off switches on: ASR operations, feedback (fb) loop, and traditional power supply; logical translation rate control; fb% variable threshold.
R: No pollution; Safety in Coherence.
{P, P -> Q, Q -> R} |= (P & Q) & R
QED
P: Logos |= Logical Necessity; Truth; Nature; coherent behavior of energy; Logic encompassing all logics; x=x for all x.
Q: AEP fully coherent with Logos—Reality’s Order—is optimized energy production.
R: ~(P & Q) |= ~(P -> P)
{P, P -> Q, Q -> R} |= P -> (R <-> Q)
QED
P: Logic |= logical simulation (LS) done with and done by logical rules and operations (LRO) on the plane of Pure Logic
Q: LS |= LS(AEP)
R: [LS(AEP) :: LRO(AEP)]
S: ~{P, Q, R} |= ~(P & LRO)
{P, P -> Q, Q -> R, R -> S} |= (P & Q) & (R & S)
QED
P: Logic |= Logical Reality (LR) is made by Logic—validated by Logic, by logical rules and operations (LRO) on the plane of Pure Logic
Q: LR |= LR(AEP)
R: [LR(AEP) :: LRO(AEP)]
S: ~{P, Q, R} |= ~{P, LR, LRO}
{P, P -> Q, Q -> R, R -> S} |= (P & Q) & (R & S)
QED