IndisputableMonolith.Foundation.RS_FDN_Structural_004
Foundation module packaging a structural certificate for domain-level cost and a canonical positive threshold. It defines a domain cost built from the RS cost functional, proves nonnegativity and evaluation identities, and packages them as an inhabited certificate record. Cited by auditors checking FDN structural obligations rather than by physics derivations directly.
claimThe module introduces a domain cost $C_{\mathrm{dom}}$, proves $C_{\mathrm{dom}}\ge 0$ and the pointwise evaluation identity, fixes a canonical threshold $\theta>0$, and assembles these facts into an inhabited structural certificate $\mathrm{RS\_FDN\_Structural\_004}$.
background
Recognition Science measures mismatch with a nonnegative cost functional $J$ (from the Cost import), normalized so the identity configuration has zero cost. Constants supplies the RS-native tick $\tau_0=1$. This module sits in the Foundation layer: it does not derive $J$ or force $\phi$, but records structural obligations that later FDN certificates may assume.
The local objects are a domain cost (a lift of the base cost to a domain-shaped argument), its nonnegativity, an evaluation identity at a distinguished point, and a canonical positive threshold used as a comparison scale. These are bundled into a single certificate record so downstream checkers can demand one inhabited proof object rather than a scatter of lemmas.
proof idea
Definition-plus-certificate module. Domain cost is defined from the imported Cost API; nonnegativity and the evaluation identity are short lemmas over that definition. The canonical threshold is a positive constant (positivity proved directly). The certificate structure packages these fields; inhabitation is by supplying the proved components. No deep forcing-chain argument appears here.
why it matters in Recognition Science
Closes FDN structural obligation 004: domain cost is well-defined, nonnegative, and comparable against a fixed positive threshold. No downstream used_by edges are recorded in the mirror graph yet, so this is a leaf certificate in the present build. It supports the Foundation audit trail that later physics modules (mass ladder, eight-tick timing, coupling bounds) rely on when they quote cost positivity or threshold comparisons without re-proving the scaffolding. Landmark contact is indirect: cost nonnegativity is the same $J\ge 0$ discipline used throughout T5--T8, not a new forcing step.
scope and limits
- Does not derive uniqueness of $J$ or the RCL functional equation (T5).
- Does not force $\phi$, the eight-tick period, or $D=3$.
- Does not compute physical constants ($c$, $\hbar$, $G$, $\alpha$).
- Does not supply mass-ladder or Berry-threshold physics theorems.
- Does not claim downstream consumers beyond the certificate interface itself.