IndisputableMonolith.Materials.RS_MAT_Structural_001
Materials-layer module that fixes the RS structural certificate RS_MAT_Structural_001: a domain cost on configurations, its nonnegativity, a positive canonical threshold, and an inhabited certificate record bundling those facts. Materials workers in the monolith cite it as the structural baseline before any lattice or modulus claim. Content is mostly definitions plus elementary positivity and packaging lemmas over Cost and Constants.
claimThe module introduces a domain cost $C_{\mathrm{dom}}$ for structural configurations, records $C_{\mathrm{dom}}\ge 0$ and the identity $C_{\mathrm{dom}}(x)=C_{\mathrm{dom}}(x)$ at evaluation points, fixes a canonical threshold $\theta>0$, and packages these into an inhabited certificate object for RS_MAT_Structural_001.
background
Recognition Science treats materials claims as cost-bounded recognition statements. The imported Cost layer supplies the J-cost $J(x)=(x+x^{-1})/2-1$ (T5 uniqueness) and its nonnegativity; Constants supplies the RS-native tick and related units. In that setting a domain cost is a configuration functional built from $J$ (or a monotone transform of it) that measures structural recognition defect relative to an ideal lattice or bond pattern.
The canonical threshold is a fixed positive barrier in the same units: configurations with domain cost below the barrier are accepted as structurally admissible for the certificate. The module sits in the Materials domain and does not yet specialize to a crystal system or experimental modulus; it only freezes the cost/threshold interface that later material-specific files are expected to inhabit.
proof idea
Definition-first module. domainCost is introduced as a Cost-derived functional; domainCost_at_eq is the trivial evaluation identity; domainCost_nonneg follows from nonnegativity of the underlying cost. canonicalThreshold is a named positive constant; canonicalThreshold_pos is the corresponding positivity lemma. RSMATStructural001Cert is a structure bundling those fields; cert and cert_inhabited assemble a default inhabitant. No deep forcing or RCL algebra appears here.
why it matters in Recognition Science
Gives the monolith a named structural materials certificate (RS_MAT_Structural_001) so later materials theorems can cite a single inhabited record rather than re-proving cost nonnegativity and threshold positivity. Upstream it rests only on Constants and Cost, keeping the materials stack aligned with the J-cost forcing chain (T5) without importing continuum elasticity. Downstream use is not yet wired in the graph (used_by empty), so the module is a leaf baseline: the place where structural admissibility is first frozen before phi-ladder mass or eight-tick timing claims are attached to condensed-matter objects.
scope and limits
- Does not derive elastic moduli, lattice constants, or band gaps from first principles.
- Does not identify domainCost with any laboratory tensile or hardness measurement.
- Does not prove uniqueness or optimality of the canonical threshold.
- Does not connect structural admissibility to the eight-tick octave or D=3 forcing steps.
- Does not discharge material-specific certificates beyond the generic structural bundle.