Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
Axiom-free: true · 2 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: 2026-10-02T21:22:45.308Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:40:02.706Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 7708862fbb4faeed369931fa1c0cc59ea96b840fad81ec6702e4197cbfebf3d0
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
{P, P -> Q, Q -> R, R -> S, S -> T} |= ((P & Q) -> (R & S)) -> T
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, S, T, U} |= U -> (((P & Q) & (R & S)) & T)
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.
Machine Semantics Programming Platform
Designed by Maclain Hunter
Integral Components:
P: Hardware Crawler: Code that runs the hardware sequentially and systematically through its register positions turning registers on and off to sequentially move through each and every feasible state of the hardware. It can start with turning the first register position and transistor on and all others off, and move from there to having the first two on and all others off, and so on, until all possible computable and programmable state (combinations) have been called up physically in the hardware by this software/code (written in a high level language like python).
Q: State Mapping: Code that responds to changes in hardware state by documenting the state change and storing the data associated with it, including distilling the logical structure of the state - mapping the hardware states.
R: Semantics and Halting: Computers encode semantics through logical structure, homomorphically, meaning that all semantic meaning that can be computed is inherent in all logical structure that can be reasoned (over) by the machine. This part of the code responsible for semantic translation must deduce semantic meaning of a large number of logical structures and store this information in a callable, searchable database or library that the software can then use to identify the semantic meaning of a given piece of machine code, or a given hardware state in a piece of hardware (ie - x86, ARM). The code must also study the halting behavior of a given line of code and determine if it loops infinitely or not. If yes, then the program will use Turing’s translation method to translate the non-halting code into a halting line of code - namely by wrapping the non-halting code in a halting shell. The sandbox to be established in the next atom S can be used internally by the software to test translated halting code to verify that it is correct and coherent. This data is also stored in the library to provide code that halts as a resource for programmers and end users of the software platform.
S: Sandbox/IDE: Code setting up a sandbox environment for code from the library to be explored by users of the UI (to be established in T) and an IDE style environment where coding with the semantic structure library, discovered through our hardware crawler, can be used to program new applications and software in a user friendly environment.
T: UI and Subscription Services: Code will need to establish a UI, likely in the form of a webpage, that users can access the tools and libraries through. This can be a relatively straightforward website that prioritizes user friendliness and minimalistic design. Code will need to handle subscriptions, log in’s, payments, etc. in a secure fashion. Ideally users will be able to launch their creations and softwares directly from the UI and the IDE tools integrated into the system, so they can package professional grade, ready for market software without tedious steps in between.
Formal Structure:
{P, P -> Q, Q -> R, R -> S, S -> T} |= ((P & Q) -> (R & S)) -> T
Output: {P, Q, R, S, T, U}:
The system integrates a hardware crawler, state mapping, a semantic deduction engine, halting insurance, sandbox/IDE, and the UI to make it functional for a base of programmers who subscribe to the platform (that the software undergirds).
Propositional Proof:
Let the LLM generated proof of concept be encoded as “U”, then:
{P, Q, R, S, T, U} |= U -> (((P & Q) & (R & S)) & T)
Truth Table Analysis:
PQRSTU⎪P Q R S T U╞U→(((P&Q)&(R&S))&T)
TTTTTT⎪T T T T T T TT TTT T TTT TT
TTTTTF⎪T T T T T F FT TTT T TTT TT
TTTTFT⎪T T T T F T TF TTT T TTT FF
TTTTFF⎪T T T T F F FT TTT T TTT FF
TTTFTT⎪T T T F T T TF TTT F TFF FT
TTTFTF⎪T T T F T F FT TTT F TFF FT
TTTFFT⎪T T T F F T TF TTT F TFF FF
TTTFFF⎪T T T F F F FT TTT F TFF FF
TTFTTT⎪T T F T T T TF TTT F FFT FT
TTFTTF⎪T T F T T F FT TTT F FFT FT
TTFTFT⎪T T F T F T TF TTT F FFT FF
TTFTFF⎪T T F T F F FT TTT F FFT FF
TTFFTT⎪T T F F T T TF TTT F FFF FT
TTFFTF⎪T T F F T F FT TTT F FFF FT
TTFFFT⎪T T F F F T TF TTT F FFF FF
TTFFFF⎪T T F F F F FT TTT F FFF FF
TFTTTT⎪T F T T T T TF TFF F TTT FT
TFTTTF⎪T F T T T F FT TFF F TTT FT
TFTTFT⎪T F T T F T TF TFF F TTT FF
TFTTFF⎪T F T T F F FT TFF F TTT FF
TFTFTT⎪T F T F T T TF TFF F TFF FT
TFTFTF⎪T F T F T F FT TFF F TFF FT
TFTFFT⎪T F T F F T TF TFF F TFF FF
TFTFFF⎪T F T F F F FT TFF F TFF FF
TFFTTT⎪T F F T T T TF TFF F FFT FT
TFFTTF⎪T F F T T F FT TFF F FFT FT
TFFTFT⎪T F F T F T TF TFF F FFT FF
TFFTFF⎪T F F T F F FT TFF F FFT FF
TFFFTT⎪T F F F T T TF TFF F FFF FT
TFFFTF⎪T F F F T F FT TFF F FFF FT
TFFFFT⎪T F F F F T TF TFF F FFF FF
TFFFFF⎪T F F F F F FT TFF F FFF FF
FTTTTT⎪F T T T T T TF FFT F TTT FT
FTTTTF⎪F T T T T F FT FFT F TTT FT
FTTTFT⎪F T T T F T TF FFT F TTT FF
FTTTFF⎪F T T T F F FT FFT F TTT FF
FTTFTT⎪F T T F T T TF FFT F TFF FT
FTTFTF⎪F T T F T F FT FFT F TFF FT
FTTFFT⎪F T T F F T TF FFT F TFF FF
FTTFFF⎪F T T F F F FT FFT F TFF FF
FTFTTT⎪F T F T T T TF FFT F FFT FT
FTFTTF⎪F T F T T F FT FFT F FFT FT
FTFTFT⎪F T F T F T TF FFT F FFT FF
FTFTFF⎪F T F T F F FT FFT F FFT FF
FTFFTT⎪F T F F T T TF FFT F FFF FT
FTFFTF⎪F T F F T F FT FFT F FFF FT
FTFFFT⎪F T F F F T TF FFT F FFF FF
FTFFFF⎪F T F F F F FT FFT F FFF FF
FFTTTT⎪F F T T T T TF FFF F TTT FT
FFTTTF⎪F F T T T F FT FFF F TTT FT
FFTTFT⎪F F T T F T TF FFF F TTT FF
FFTTFF⎪F F T T F F FT FFF F TTT FF
FFTFTT⎪F F T F T T TF FFF F TFF FT
FFTFTF⎪F F T F T F FT FFF F TFF FT
FFTFFT⎪F F T F F T TF FFF F TFF FF
FFTFFF⎪F F T F F F FT FFF F TFF FF
FFFTTT⎪F F F T T T TF FFF F FFT FT
FFFTTF⎪F F F T T F FT FFF F FFT FT
FFFTFT⎪F F F T F T TF FFF F FFT FF
FFFTFF⎪F F F T F F FT FFF F FFT FF
FFFFTT⎪F F F F T T TF FFF F FFF FT
FFFFTF⎪F F F F T F FT FFF F FFF FT
FFFFFT⎪F F F F F T TF FFF F FFF FF
FFFFFF⎪F F F F F F FT FFF F FFF FF
(Valid)
Q.E.D.