RS_sig
plain-language theorem explainer
Packages the Recognition Science cone-projection constants as the canonical framework signature for CPM-to-RS initiality checks. Anyone proving that multi-domain CPM universality forces the RS core invariants cites this witness. The body is a one-line structure constructor wrapping the RS-native constants bundle (K_net=1, C_proj=2).
Claim. Let $\mathrm{RS\text{-}sig}$ be the framework signature whose constants bundle is the RS cone-projection tuple $(K_{\mathrm{net}}, C_{\mathrm{proj}}, C_{\mathrm{eng}}, C_{\mathrm{disp}}) = (1, 2, 1, 1)$. This is the universal witness against which domain-level CPM constants are compared.
background
The module builds a lightweight structural bridge from CPM (cone-projection method) constants across independent domains to Recognition Science. A framework signature is minimal: it exposes only the constants bundle needed for universality checks. Matching the RS core means agreeing on the two locked invariants $K_{\mathrm{net}}=1$ and $C_{\mathrm{proj}}=2$; energy and dispersion coefficients stay free.
Upstream, the RS-native cone constants are defined with $K_{\mathrm{net}}:=1$, $C_{\mathrm{proj}}:=2$, and placeholder unit values for $C_{\mathrm{eng}}$, $C_{\mathrm{disp}}$. In the gravity layer, $C_{\mathrm{proj}}\le 2$ bounds the ILG projection kernel, while $K_{\mathrm{net}}$ encodes the eight-tick net factor. The module setting is initiality-style: when several domains match those two invariants, a unique constants witness coincides with the RS instance.
proof idea
Pure definition: construct a FrameworkSig by packing the existing RS cone-constants record. No tactics, no lemmas. Definitional equality later lets dsimp reduce the signature to the pair $(K_{\mathrm{net}},C_{\mathrm{proj}})=(1,2)$ in the matching predicates.
why it matters
This is the fixed RS pole of the CPM⇒RS bridge. Downstream, universality_implies_RS_core shows that if Hodge, RH, NS, and Goldbach domain constants all match the RS core, then the RS signature itself is a valid universal witness. universality_constants_agree strengthens that to equality of the $(K_{\mathrm{net}},C_{\mathrm{proj}})$ pair with every domain signature under the same hypothesis.
In the broader framework the locked values sit on the eight-tick octave (T7) and the $D=3$ forcing (T8): $C_{\mathrm{proj}}=2$ and unit net factor are the cone-projection invariants that exclusivity arguments compare against. The module explicitly stages a future category-theoretic uniqueness proof and physics-side exclusivity integration; this definition is the named RS object those arguments will identify.
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