polytheistic_two_violates_canonical
plain-language theorem explainer
A two-substrate theological model with both elements carrying unit sigma charge sums to total sigma two, outside the canonical single-charge sector. Recognition Science researchers formalizing monotheism as the sigma-conserving ontology cite this result to rule out polytheism in finite models. The proof proceeds by unfolding the total sigma definition and applying simplification tactics.
Claim. Let $T$ be the list of two substrates each with phase $0$ and sigma-charge $1$. Then the total sigma-charge of $T$ equals $2$.
background
Theology is an abbreviation for a list of substrates, where each substrate carries a phase value and a sigma charge. The canonical sector is the unique configuration with total sigma equal to one, enforced by global phase conservation across moves. This theorem belongs to the SubstrateIndependentMonotheism module, which formalizes the structural claim that monotheism is the sigma-conserving theological position while polytheism with multiple unit-sigma substrates violates that conservation.
proof idea
The proof is a tactic-mode script. It unfolds the totalSigma summation over the list of substrates and applies simp to reduce the arithmetic to the equality with two.
why it matters
This result is invoked inside substrateIndependentMonotheismCert to populate the polytheistic violation clause and inside substrate_monotheism_one_statement to complete the trichotomy statement. It supplies the concrete counterexample to polytheism required by the Anno Recognitionis essay's sigma-conservation argument. The construction aligns with the single global charge principle that parallels J-uniqueness and the forcing chain's demand for a unique fixed point.
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