IndisputableMonolith.Materials.Young_Modulus_Steel_RS
Packages the Recognition Science certificate for Young's modulus of steel: a materials-sector domain cost, a positive canonical threshold, and an inhabited witness that steel's modulus meets the cost band. Continuum-elasticity or RS-materials workers cite the certificate when anchoring steel as a baseline. Structure is definitional plus non-negativity/positivity lemmas and an existence proof for the cert.
claimThe module introduces a materials domain cost $C$, proves $C\ge 0$ and evaluates it at the steel point, fixes a canonical threshold $\tau>0$, and supplies an inhabited certificate that the RS Young modulus of steel satisfies the certification predicate relative to $C$ and $\tau$.
background
Recognition Science scores mismatch with the J-cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$) and the Recognition Composition Law. The Cost import exposes that functional; Constants anchors RS-native units, including the time quantum $\tau_0=1$ tick.
Here the same cost language is specialized to continuum elasticity. A domain cost scores the elastic response of the materials sector; a canonical threshold marks the acceptance band for a predicted modulus. Steel is treated as the baseline metal whose RS Young modulus is checked against that band, not fitted as a free continuum parameter.
Sibling objects name the pieces: domain cost and its evaluation/non-negativity facts, the positive threshold, and the Young-modulus-of-steel certificate type with an inhabited instance.
proof idea
Definition-and-certificate module rather than a long derivation. It defines the materials domain cost, records an evaluation identity and non-negativity, defines a canonical threshold and proves it positive, then packages a YoungModSteelCert structure and shows the certificate type is inhabited. Supporting facts are short lemma-style results; the load-bearing step is existence of the cert witness, not a multi-stage forcing argument.
why it matters in Recognition Science
Extends the RS program from particle constants and the forcing chain (T5 J-uniqueness, T6 $\phi$, T8 $D=3$) into continuum materials. Steel's Young modulus becomes a certified RS baseline instead of an external engineering input. No downstream used_by edges are recorded yet, so the module is a leaf certificate ready for elasticity, alloy, or engineering layers that need a locked steel anchor in RS-native units.
scope and limits
- Does not derive Young's modulus from the full T0–T8 forcing chain inside this file.
- Does not treat metals or alloys other than the steel baseline certificate.
- Does not encode experimental error bars beyond the certificate predicate.
- Does not claim uniqueness of the chosen domain cost among all materials cost functionals.
- Does not connect the modulus certificate to phonon spectra or lattice dynamics.