unit_normalization_forced
plain-language theorem explainer
The theorem records that the normalization hypothesis J(1) = 0 directly entails the same equality as its conclusion. Recognition Science workers closing the self-comparison axioms in the ledger reconstruction would cite it when converting R2 from axiom to theorem. The proof is a one-line term that returns the supplied hypothesis without additional steps.
Claim. Let $J : ℝ → ℝ$ satisfy $J(1) = 0$. Then $J(1) = 0$.
background
The Closed Observable Framework module absorbs R1, R2, R5 and R6 as structure fields rather than axioms, leaving only the Regularity Axiom for finite-description content. The J-cost function enters via self-comparison, with its normalization at unity fixed by the hypothesis. Upstream results supply the unit elements in LogicInt and LogicRat that anchor the integer and rational layers of the phi-ladder.
proof idea
The proof is a one-line term that directly applies the hypothesis h_unit.
why it matters
This declaration converts the R2 self-comparison axiom into a theorem inside the Closed Observable Framework, feeding the ledger reconstruction path. It aligns with T5 J-uniqueness in the forcing chain before the phi fixed point and eight-tick octave are derived. The module doc notes that the remaining Regularity Axiom now encodes the finite-description obligations.
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