universality_implies_RS_core
plain-language theorem explainer
If a CPM universality witness has Hodge, RH, NS, and Goldbach constants matching the RS core invariants ($K_{net}=1$, $C_{proj}=2$), then the RS cone signature itself matches those invariants. Paper-facing re-export of the Initiality corollary, usable without the exclusivity adapter. Proof is a one-line term wrapper into Initiality.
Claim. Let $U$ be a CPM universality witness. If the constants of its Hodge, Riemann-hypothesis, Navier–Stokes, and Goldbach domains each satisfy $K_{\mathrm{net}}=1$ and $C_{\mathrm{proj}}=2$, then the RS cone signature constants also satisfy $K_{\mathrm{net}}=1$ and $C_{\mathrm{proj}}=2$.
background
This module re-exports the CPM-to-RS universality corollary for paper citation without importing the exclusivity adapter, avoiding import cycles. It depends only on the Initiality scaffold.
A constants bundle matches the RS core when $K_{\mathrm{net}}=1$ and $C_{\mathrm{proj}}=2$; energy and dispersion constants stay free. The RS signature packages the RS cone constants as the universal framework witness. Universality is a structure bundling four domain frameworks (Hodge, RH, NS, Goldbach), each carrying its own constants record.
Upstream, Initiality states the same implication and notes that the RS signature is definitionally $(1,2,,)$ on $(K_{\mathrm{net}},C_{\mathrm{proj}},_,_)$.
proof idea
One-line term wrapper: apply Initiality.universality_implies_RS_core to the same universality witness and hypothesis. The underlying Initiality proof introduces the four-domain hypothesis and discards it, then unfolds the RS signature and the core-match predicate; the conclusion holds definitionally because the RS cone is built with $K_{\mathrm{net}}=1$ and $C_{\mathrm{proj}}=2$.
why it matters
Paper-facing export of the CPM universality corollary: once the four domain constants match the RS core invariants, the RS signature is a valid universal witness. Downstream it is the same Initiality statement ("Universality implies that all domain constants match the RS core invariants; hence the RS signature is a valid universal witness"), re-homed so citations need not pull exclusivity.
Sits in the verification CPM bridge, not in the T0–T8 forcing chain. It packages the claim that RS cone constants serve as the universal witness under the core-match side conditions, without asserting exclusivity among frameworks.
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