substrateIndependentMonotheismCert
plain-language theorem explainer
The definition constructs a certificate bundling the trichotomy of all theological models with sigma-conservation rules that force monotheism as the only consistent position. A researcher on the Recognition Science theology track cites it to close the structural claim that a global phase plus sigma invariance admits at most one divine substrate. The construction is a record builder that delegates each field to a sibling lemma already proved in the module.
Claim. Let $T$ be any theological model (a finite list of substrates, each equipped with a phase and a sigma-charge). Then every $T$ is atheistic, monotheistic, or polytheistic; any two-substrate model in which both entries carry sigma equal to 1 has total sigma equal to 2; the singleton model consisting of the unique canonical occupant has total sigma equal to 1; that occupant is monotheistic; and any model containing exactly one divine substrate together with non-divine creatures is still monotheistic.
background
A theological model is an abbrev for a list of substrates, each substrate a triple of name, phase, and sigma-charge. The divine predicate selects those substrates whose phase is zero and whose sigma-charge equals one, i.e., the canonical sector. Sigma conservation is the requirement that the sum of all charges remains invariant under any allowed move, a direct consequence of the global phase function introduced in the module.
proof idea
The definition is a one-line record construction. It supplies the trichotomy field by direct reference to Theology.trichotomy, the polytheistic_two_violates field by polytheistic_two_violates_canonical, the monotheistic_canonical field by monotheistic_canonical_sigma, the unique_occupant_monotheistic field by unique_occupant_is_monotheistic, and the one_god_with_creatures field by one_god_with_creatures_is_monotheistic.
why it matters
The definition completes the structural side of the AR-essay claim that monotheism is the sigma-conserving theological position in any ontology possessing a global phase. It supplies the certificate required by the SubstrateIndependentMonotheismCert structure and thereby closes Track I11 of Plan v5. The underlying sigma arises from the Recognition Composition Law and the phi-ladder; the open falsifier remains a consistent two-substrate ontology that preserves sigma across substrate-substrate moves.
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