SubstrateIndependentMonotheismCert
plain-language theorem explainer
The structure certifies that every theological model satisfies a trichotomy of categories while enforcing sigma-charge conservation that rules out multiple divine substrates. Researchers in formal ontology or philosophy of religion cite it to show monotheism as the unique sigma-preserving position in any global-phase ontology. The declaration is a structure definition that directly assembles the five required properties from the module predicates.
Claim. A structure $C$ such that for every theological model $T$ (a list of substrates), $T$ is atheistic (zero divine substrates), monotheistic (exactly one), or polytheistic (two or more); the total sigma-charge of two canonical divine substrates equals 2; the total sigma-charge of one canonical divine substrate equals 1; the singleton list containing only the canonical divine substrate is monotheistic; and the list containing one canonical divine substrate plus two non-divine substrates (phase 1 and phase 2) is monotheistic.
background
The module formalizes the structural side of the AR-essay claim: any ontology with a global phase function and sigma-conservation admits at most one divine substrate. Theology is defined as a list of substrates, each carrying a phase and a sigma-charge. The predicates are: isAtheistic holds when the list of divine substrates has length zero; isMonotheistic when the length is exactly one; isPolytheistic when the length is at least two. Total sigma-charge is the sum of the sigma-weights across the list, taken from the upstream totalSigma definition in Jurisprudence.PrecedentStabilityFromSigma.
proof idea
The declaration is a structure definition with no proof body. Each field is a direct statement of the required property; the downstream construction substrateIndependentMonotheismCert supplies the concrete witnesses by referencing the module's trichotomy lemma and the explicit sigma calculations for the listed substrate configurations.
why it matters
This structure is the master certificate for the module and is instantiated by substrateIndependentMonotheismCert. It encodes the AR-essay structural claim that monotheism is the sigma-conserving theological position, with polytheism violating conservation in any two-substrate canonical model. The result sits inside the broader Recognition framework by importing sigma-additivity and the phase-based definition of divinity, closing one step in the ontology track without invoking the forcing chain or the phi-ladder.
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