recognition_closure_from_inevitabilities
plain-language theorem explainer
For a fixed real parameter φ, dimensionless inevitability plus absolute inevitability yield full recognition closure. RecogSpec consumers and the ClosureShim cite this when packaging the certified surface. The proof is a one-line conjunction introduction of the two hypotheses.
Claim. For any real $\varphi$, if dimensionless inevitability holds at $\varphi$ (every ledger/bridge matches the explicit universal target and that target's strong-CP, eight-tick, and Born witnesses are proved) and absolute inevitability holds at $\varphi$ (unique calibration for every ledger, bridge, and anchor triple), then recognition closure holds at $\varphi$.
background
RecogSpec packages the certified claims of Recognition Science at a fixed real scale parameter $\varphi$ (the golden ratio in the forcing chain). Dimensionless inevitability asserts two things: every ledger and bridge matches the explicit universal dimensionless target, and that target's propositional fields (strong CP vanishing, eight-tick octave, Born rule) are actually proved rather than carried as symbols. Absolute inevitability asserts unique calibration of units for every ledger, bridge, and anchor triple.
Recognition closure is defined simply as the conjunction of those two inevitability predicates. The surrounding module imports anchors, bands, bridge core, and the two-outcome Born certificate; the present declaration does not re-prove any of those ingredients. Upstream notes flag that concrete "inevitability holds" witnesses currently live in a scaffold and are intentionally excluded from the certified surface.
proof idea
Term-mode one-liner: And.intro on the two incoming hypotheses. Because recognition closure is definitionally the conjunction of dimensionless and absolute inevitability, no further rewriting or lemma application is required.
why it matters
This is the pure packaging step that turns the two inevitability interfaces into the single closure predicate used by the rest of RecogSpec. Downstream, recognition_closure_any in ClosureShim obtains the two inevitability witnesses and feeds them here to conclude recognition closure for arbitrary $\varphi$.
In the broader framework it sits at the RecogSpec boundary rather than inside the T0–T8 forcing chain: eight-tick and Born appear only as fields that dimensionless inevitability demands already be proved. It does not itself force $\varphi$, $D=3$, or the J-cost; it records that once both inevitabilities are granted, the certified closure predicate holds.
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