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: 2026-10-02T18:23:05.343Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:38:36.918Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 2b8f6bea49d36b0bc08605ad42b63142f1e71e2fb8ffd5d01fdc54b5c78f55e8
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.source_identity_rule' does not depend on any axioms
{P, Q, R, S, T, U} |= (((P & Q) <-> (R & S)) <-> (T & U))
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 is A
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
God Defines Judaism by Maclain Hunter
Premise:
P: Historically the Hebrews (an ethnic group with a common language and culture) practiced monotheistic religion and had coherent (unifying) philosophy that made them known far and wide for Wisdom and insights into what God is and expects of humanity.
Q: The terms “Jew” and “Judaism” refer not directly to any ethnic group but come from the nomenclature of the Kingdom of Judah, a kingdom of (part of) the Hebrew nation, who would have been known (if only referring to their citizenship and belonging to this community/kingdom) as “Judaean” not “Jews” (necessarily or historically) which refers more precisely to logically coherent practitioners of the sort of rationalist monotheistic religion outlined in the Torah and by Logos (God - YHVH - Universal Reason) and allegedly well respected and practiced in this Kingdom of Judah, from which the name of Judaism and the title of being a “Jew” are passed down.
R: The First Cause, also known as God and Logic, or “the Universal Logos” and “Elohim”, is the Universal Standard and Measure of Identity that, through its own unwavering Coherence and Logical Completeness (Oneness or “Echad”), is the Standard that decides what thing is what thing, and what is not. A “True Jew” is no exception logically and must be the sort of “Jew” that aligns with Reason (God) and the rational definition(s) of God and a “Jew”. A “True Jew” that doesn’t align/cohere with the God of Reason (Logos) and acknowledge YHVH as Pure Logic is a contradiction and cannot logically or theologically be a “True Jew” coherently or authentically.
S: Those who say being Jewish is a matter of ethnicity are conflating being a Hebrew and a descendant of the Hebrews (whose DNA is not well established or known, as definitive and reliable samples of the ancestors DNA or genetic material are not known to exist making this an unreliable and impractical way of knowing what a True Jew is, thus strengthening the proof and showing the value in its proposed alternative of Logical Coherence as the Standard of Judaism) with the religious aspect of Hebrew culture known as Judaism. Judaism is a matter of alignment with YHVH as the Source of Truth. In Judaism this alignment is absolutely necessary, beyond any concerns/claims about ancestry. It is critically important in establishing the TRUTH VALUE of the claim to Judaism and being a True Jew. A Jew that is only claiming to be of Hebrew heritage but who cannot demonstrate their Coherence (with Elohim aka “the Universal Order”) is contradictory and inconsistent with both rational and biblical standards - chief among them being the Logos as Universal Law and the Principle inherent in the A is A form of Reality being Reality.
T: To merely define a Jew as someone with a Jewish mother without considering the Logos (YHVH) as the Rational Standard and True God— the Measure of who is Jewish for both mother and child—is illogical and leads to both ambiguity in the definition of a Jew and infinite regress that defies classical logical principles - since a Jewish mother would have to then be Jewish by having a Jewish mother, and same with her mother, and so on, without a well defined and logically derived starting point. This shows why maternal lineage alone is not a rational and sufficient way to define Jewishness. It is infinitely less coherent than defining a True Jew (mother or child, Hebrew or not) by COHERENCE with the Logic of Reality (the One True God).
U: Assume the negation of the premises. This leads to logical contradiction where we abandon the God of the Jews (Cosmic Order and Universal Logic - YHVH) in the very pursuit of defining Jewishness, only to embrace racially bound (perhaps even racist) definitions of Jewishness and logically absurd infinite regress of maternal derivation of Judaism/Jewishness. This ignores that even/especially the Torah defines a valid Jew as the sort of Hebrew that acknowledges and strives honestly for alignment (with tangible results not continual failure and excuses) with the Source of Wisdom aka the One True God (understood in English terms as coherent Reason, Logic, Truth, and Reality). Therefore the premises must hold true or illogical paradox must arbitrarily be accepted instead of these coherent premises. In fact, writing such a self-referencing proof (as this one) is itself a demonstration of my own Coherence and respectful acknowledgement of the Logos (my willful engagement/unity with God).
Logical Argument:
{P, Q, R, S, T, U} |= (((P & Q) <-> (R & S)) <-> (T & U))
Conclusion:
A Jew is not coherently defined by birth and logically cannot be a mere birthright, like being of Hebrew heritage can be. The definition and attainment of genuine Judaism (and of being a True Jew) must align with God (Logos - Universal Cause). It should also, in many cases, align with the Torah of Moshe, which helps lay out what Judaism is and must be (while acknowledging the superseding authority of Pure Reason aka God).
A Jew who doesn’t acknowledge or align demonstrably with the God of Truth and Reason (the Universe’s Foundation in Rational Coherence) is a contradictory thing. Such a misaligned Jew is rationally not a Jew, since a Jew must align with the Logic of Existence that is the One True God. It does not matter if your mother was Hebrew/Jewish or not.
It is a testament to my own Judaism (in the rational sense) and my own God-derived status as a True Jew independent of any visit to a mikvah, any solemn procession or mindless ritual (like those Isaiah and the prophets of Judaism roundly condemned as meaningless compared to iconoclastic, shrewd Rationality), or any arbitrary denials and processes a given community of people who claim to be “the real Jews” might try to, in claim contradicting fashion, impose on me (against all Reason).
Truth Table Analysis:
PQRSTU⎪P Q R S T U╞(((P&Q)↔(R&S))↔(T&U))
TTTTTT⎪T T T T T T TTT T TTT T TTT
TTTTTF⎪T T T T T F TTT T TTT F TFF
TTTTFT⎪T T T T F T TTT T TTT F FFT
TTTTFF⎪T T T T F F TTT T TTT F FFF
TTTFTT⎪T T T F T T TTT F TFF F TTT
TTTFTF⎪T T T F T F TTT F TFF T TFF
TTTFFT⎪T T T F F T TTT F TFF T FFT
TTTFFF⎪T T T F F F TTT F TFF T FFF
TTFTTT⎪T T F T T T TTT F FFT F TTT
TTFTTF⎪T T F T T F TTT F FFT T TFF
TTFTFT⎪T T F T F T TTT F FFT T FFT
TTFTFF⎪T T F T F F TTT F FFT T FFF
TTFFTT⎪T T F F T T TTT F FFF F TTT
TTFFTF⎪T T F F T F TTT F FFF T TFF
TTFFFT⎪T T F F F T TTT F FFF T FFT
TTFFFF⎪T T F F F F TTT F FFF T FFF
TFTTTT⎪T F T T T T TFF F TTT F TTT
TFTTTF⎪T F T T T F TFF F TTT T TFF
TFTTFT⎪T F T T F T TFF F TTT T FFT
TFTTFF⎪T F T T F F TFF F TTT T FFF
TFTFTT⎪T F T F T T TFF T TFF T TTT
TFTFTF⎪T F T F T F TFF T TFF F TFF
TFTFFT⎪T F T F F T TFF T TFF F FFT
TFTFFF⎪T F T F F F TFF T TFF F FFF
TFFTTT⎪T F F T T T TFF T FFT T TTT
TFFTTF⎪T F F T T F TFF T FFT F TFF
TFFTFT⎪T F F T F T TFF T FFT F FFT
TFFTFF⎪T F F T F F TFF T FFT F FFF
TFFFTT⎪T F F F T T TFF T FFF T TTT
TFFFTF⎪T F F F T F TFF T FFF F TFF
TFFFFT⎪T F F F F T TFF T FFF F FFT
TFFFFF⎪T F F F F F TFF T FFF F FFF
FTTTTT⎪F T T T T T FFT F TTT F TTT
FTTTTF⎪F T T T T F FFT F TTT T TFF
FTTTFT⎪F T T T F T FFT F TTT T FFT
FTTTFF⎪F T T T F F FFT F TTT T FFF
FTTFTT⎪F T T F T T FFT T TFF T TTT
FTTFTF⎪F T T F T F FFT T TFF F TFF
FTTFFT⎪F T T F F T FFT T TFF F FFT
FTTFFF⎪F T T F F F FFT T TFF F FFF
FTFTTT⎪F T F T T T FFT T FFT T TTT
FTFTTF⎪F T F T T F FFT T FFT F TFF
FTFTFT⎪F T F T F T FFT T FFT F FFT
FTFTFF⎪F T F T F F FFT T FFT F FFF
FTFFTT⎪F T F F T T FFT T FFF T TTT
FTFFTF⎪F T F F T F FFT T FFF F TFF
FTFFFT⎪F T F F F T FFT T FFF F FFT
FTFFFF⎪F T F F F F FFT T FFF F FFF
FFTTTT⎪F F T T T T FFF F TTT F TTT
FFTTTF⎪F F T T T F FFF F TTT T TFF
FFTTFT⎪F F T T F T FFF F TTT T FFT
FFTTFF⎪F F T T F F FFF F TTT T FFF
FFTFTT⎪F F T F T T FFF T TFF T TTT
FFTFTF⎪F F T F T F FFF T TFF F TFF
FFTFFT⎪F F T F F T FFF T TFF F FFT
FFTFFF⎪F F T F F F FFF T TFF F FFF
FFFTTT⎪F F F T T T FFF T FFT T TTT
FFFTTF⎪F F F T T F FFF T FFT F TFF
FFFTFT⎪F F F T F T FFF T FFT F FFT
FFFTFF⎪F F F T F F FFF T FFT F FFF
FFFFTT⎪F F F F T T FFF T FFF T TTT
FFFFTF⎪F F F F T F FFF T FFF F TFF
FFFFFT⎪F F F F F T FFF T FFF F FFT
FFFFFF⎪F F F F F F FFF T FFF F FFF
Q.E.D.