Universality
plain-language theorem explainer
Packages four independent domain signatures (Hodge conjecture, Riemann hypothesis, Navier–Stokes, Goldbach) as a single constants-level universality hypothesis. Each field is a minimal CPM framework signature carrying only the constants needed for matching. Cited by the inevitability and continuum-limit layers when arguing that one RS cone witness serves all domains. Pure structure definition: no proof obligations.
Claim. A universality record is a 4-tuple $(H_{\mathrm{Hodge}}, H_{\mathrm{RH}}, H_{\mathrm{NS}}, H_{\mathrm{Goldbach}})$ of framework signatures, each signature exposing only a constants bundle $C$. The intended reading is that the same CPM constants govern all four domains at the cone-projection level.
background
The module is a lightweight CPM-to-RS initiality skeleton. It records CPM constants for several independent domains and shows that, when those constants match the RS cone-projection invariants ($K_{\mathrm{net}}=1$, $C_{\mathrm{proj}}=2$), there is a unique constants witness coinciding with the RS instance.
A framework signature is deliberately thin: it exposes only a Constants bundle, enough for universality checks and nothing more. The four named domains (Hodge, RH, Navier–Stokes regularity, Goldbach) stand in as independent mathematical arenas that are not a priori linked by continuum physics, so agreement of their CPM constants is a strong structural claim.
Upstream continuum and Regge geometry material (simplicial Laplacian identification, hinge-aware zero modes) supplies the geometric meaning of those constants, but this structure itself only packages the signatures.
proof idea
Definitional structure with four fields and no proof body. Instantiation is by supplying four FrameworkSig values (each a constants record). Downstream lemmas such as universality_implies_RS_core and universality_constants_agree (siblings in the same module) are where the matching and uniqueness arguments live; this declaration only names the hypothesis bundle.
why it matters
Feeds the inevitability layer: choke_universality is listed as Choke Point 1 ("CPM Universality"), still marked scaffold, with consequence "CPM selection is the ONLY selection mechanism." Also referenced from ChokePoint, economic_inevitability, inevitability_upgrade, continuum-limit theorems (continuum_limit_second_order, emergence_hierarchy), glass-transition fragility, and RAR slope extraction.
In the Recognition framework this is the constants-level stand-in for a full category-theoretic initiality/uniqueness proof: if every domain's CPM signature matches the RS cone, the RS instance is the unique witness. That is the bridge from the exclusivity theorem on the physics side to cross-domain mathematical universality. It does not yet close the choke point; it only names the data the closing argument must consume.
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