IndisputableMonolith.Physics.ElasticMod4
Module packaging domain-cost and threshold infrastructure for elastic-modulus side conditions in RS-native units. Defines a nonnegative domain cost, a strictly positive canonical threshold, and an inhabited certificate bundle ElasticMod4Cert. Physicists citing RS continuum or lattice elasticity would pull these lemmas. Content is mostly definitional with short nonnegativity and positivity proofs.
claimThe module introduces a domain cost $C$ (nonnegative, with an evaluation identity at equality), a canonical threshold $\theta>0$, and an inhabited certificate package asserting the elastic-modulus side conditions used by Recognition Science continuum bookkeeping.
background
Recognition Science measures mismatch with the J-cost from the Cost import: the unique symmetric generator forced by the Recognition Composition Law. Constants supplies the RS time quantum $\tau_0=1$ tick, so continuum rates are expressed in tick-normalized units.
This physics module sits downstream of those two imports and introduces a domain-restricted cost together with a canonical numerical threshold. The domain cost is the local mismatch functional against which elastic response is compared; the threshold is the positive cutoff that separates subcritical from supercritical strain bookkeeping.
Sibling names indicate the usual RS certificate pattern: pure definitions, elementary positivity or nonnegativity lemmas, then a bundled Prop-level certificate and a proof that the bundle is inhabited.
proof idea
Definition-heavy module. domainCost and canonicalThreshold are introduced as defs; domainCost_nonneg and canonicalThreshold_pos are short nonnegativity/positivity arguments from the Cost and Constants infrastructure. domainCost_at_eq records the on-shell evaluation identity. ElasticMod4Cert packages the side conditions; cert and cert_inhabited discharge inhabitance of that bundle. No deep tactic scripts: algebraic identities and positivity inheritance from J-cost.
why it matters in Recognition Science
Supplies the elastic-modulus certificate layer for RS continuum physics. No downstream edges are recorded yet in the mirror graph, so the module presently stands as a self-contained physics packaging point rather than a proved parent of a named forcing-chain theorem. It ties local strain bookkeeping to the same J-cost and tick units used elsewhere in the monolith (Constants, Cost), keeping elastic side conditions in the same certificate style as mass-ladder and coupling certificates. Lands in the Physics domain rather than the T0–T8 foundation chain.
scope and limits
- Does not derive continuum elastodynamics or wave speeds from first principles.
- Does not fix numerical elastic constants beyond the canonical threshold positivity.
- Does not connect to the T0–T8 forcing chain or D=3 uniqueness.
- Does not prove material stability or thermodynamic consistency of the modulus.
- Does not supply experimental fits or SI-unit conversions.