IndisputableMonolith.Materials.RS_MAT_Structural_003
Materials certificate module for RS structural claim 003. It defines a domain cost from the RS J-cost, proves nonnegativity, fixes a positive canonical threshold, and packages an inhabited certificate record. Materials workers citing RS structural bounds would import it. The module is mostly definitional: short positivity lemmas plus a cert inhabitant.
claimThe module defines a domain cost $C_{\mathrm{dom}}$ built from the RS $J$-cost, proves $C_{\mathrm{dom}}\ge 0$ and $C_{\mathrm{dom}}(x)=C_{\mathrm{dom}}$ at the evaluation point, fixes a canonical threshold $\theta>0$, and supplies an inhabited certificate record witnessing structural claim 003.
background
Recognition Science materials modules attach structural claims to the unique cost functional forced by the Recognition Composition Law. From the Cost import, that functional is $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), the T5 J-uniqueness landmark. Domain cost here is the materials-facing specialization of $J$ on a structural domain.
The Constants import supplies RS-native units (including the time quantum $\tau_0=1$ tick). Sibling declarations name the pieces: domainCost with an evaluation identity and a nonnegativity lemma; canonicalThreshold with a positivity lemma; and RSMATStructural003Cert together with cert and cert_inhabited as the certificate interface.
The local setting is the Materials domain of the monolith: numbered RS_MAT structural packages that freeze cost-and-threshold facts for later citation rather than re-deriving the forcing chain.
proof idea
Definition-and-certificate module, not a deep proof development. domainCost is introduced from the Cost layer; domainCost_at_eq is an evaluation identity; domainCost_nonneg is an elementary nonnegativity fact inherited from $J\ge 0$. canonicalThreshold is a fixed positive scale, with canonicalThreshold_pos recording $\theta>0$. RSMATStructural003Cert bundles these into a certificate type; cert and cert_inhabited supply a canonical inhabitant. No multi-step tactic argument beyond those short lemmas.
why it matters in Recognition Science
Earns its place as the structural-003 certificate in the Materials layer of the RS monolith. It freezes a domain cost, a positive threshold, and an inhabited cert so downstream materials arguments can cite one record instead of rebuilding cost positivity. No used_by edges are recorded yet, so it is presently a leaf package. Framework contact is through J-cost (T5 J-uniqueness and the RCL) via the Cost import; it does not itself advance T6--T8 (phi, eight-tick octave, $D=3$).
scope and limits
- Does not derive a concrete material observable beyond the packaged cost and threshold.
- Does not prove uniqueness of the domain cost outside the imported J-cost facts.
- Does not link to eight-tick, phi-ladder mass, or D=3 forcing steps.
- Does not claim experimental materials data agreement.
- Does not discharge physics hypotheses beyond the certificate interface.