IndisputableMonolith.Foundation.RS_Forcing_Chain_Module_006
Module 006 of the RS forcing-chain series packages a domain cost functional, its nonnegativity, and a positive canonical threshold, then wraps them in an inhabited certificate. Foundation authors cite it when a later forcing step needs a uniform cost bound on admissible domains. The content is definitional plus short positivity lemmas, not a deep uniqueness argument.
claimOn the RS cost side, a domain cost $C$ is introduced with $C\ge 0$ pointwise, together with a canonical threshold $\theta>0$. The module exports an inhabited certificate bundling these facts for forcing-chain step 006.
background
Recognition Science forces physics from a single cost functional $J$ obeying the Recognition Composition Law, with the golden ratio $\varphi$ as the self-similar fixed point (forcing landmarks T5–T6). Cost and Constants supply the ambient $J$-cost and the RS tick $\tau_0=1$.
This module sits in the Foundation forcing-chain series. It introduces a domain-level cost (a real-valued functional on admissible domains) and a canonical numerical threshold against which that cost is compared. Sibling facts record evaluation at a point, nonnegativity of the domain cost, and positivity of the threshold.
The certificate object RSForcingChain006Cert is the module’s export surface: a Prop-level bundle that later chain modules can assume or inhabit without reopening the local definitions.
proof idea
Definition module with short supporting lemmas. Domain cost and the canonical threshold are introduced by definition; nonnegativity and positivity are discharged by direct appeal to the Cost layer and elementary real arithmetic. The certificate record is assembled and shown inhabited by packaging those lemmas; there is no multi-step uniqueness or fixed-point argument here.
why it matters in Recognition Science
Keeps forcing-chain bookkeeping modular: later T-steps that need a nonnegative domain cost and a strictly positive comparison scale can import the 006 certificate rather than rebuild the bounds. No downstream used-by edges are recorded yet, so the module is presently a leaf export inside Foundation. It does not itself force $\varphi$, the eight-tick octave, or $D=3$; those remain T6–T8 responsibilities. Its role is infrastructural: a clean, inhabited cost-threshold interface for the chain.
scope and limits
- Does not prove J-uniqueness or the RCL identity (T5).
- Does not force phi, the eight-tick period, or D=3.
- Does not derive mass ladders, alpha bounds, or dimensional constants.
- Does not claim downstream consumers; used_by is currently empty.
- Does not replace the global Cost module; it only packages a domain-level slice.