IndisputableMonolith.Materials.SputterYieldFromJCost
Sputter yield is packaged as a nonnegative domain cost built from the Recognition J-functional, together with a positive canonical energy threshold that gates ejection. Materials workers in the RS stack cite the certificate record when tying ion-impact observables to the cost layer. The module is mostly definitions plus elementary positivity and equality lemmas, closed by an inhabited certificate bundle.
claimThe module introduces a domain cost $C$ derived from the J-cost, a canonical threshold $\theta>0$, and a sputter-yield certificate asserting $C\ge 0$ and $\theta>0$, with an inhabited instance of that certificate.
background
Recognition Science measures mismatch with the J-cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), forced unique by the T5 step of the unified forcing chain and obeying the Recognition Composition Law. The Cost import supplies that functional; Constants supplies the RS-native tick $\tau_0=1$.
In the materials setting, sputter yield (atoms ejected per incident ion) is treated as a cost-gated observable: a domain cost evaluates the energetic mismatch of the impact configuration, and a canonical threshold sets the scale above which ejection is allowed. Sibling definitions name that domain cost, its pointwise evaluation, nonnegativity, the threshold and its positivity, and a certificate record bundling those facts.
proof idea
This is primarily a definition-and-certificate module, not a deep derivation. Domain cost is introduced from the imported J-cost; an equality lemma records evaluation at a point; nonnegativity and threshold positivity are elementary consequences of the cost layer. The certificate structure packages those properties, and an inhabited instance witnesses that the package is realizable. No multi-step tactic development is required beyond those wrappers.
why it matters in Recognition Science
The module places classical sputter yield inside the RS cost calculus, so materials predictions sit on the same J-functional that forces $\phi$, the eight-tick octave, and $D=3$ upstream. It is the materials-domain bridge from Cost and Constants into an observable certificate. No downstream consumers are wired in the graph yet; the natural parents would be higher materials or phenomenology theorems that quote the certificate when deriving yield curves or threshold scalings from the phi-ladder and J-cost.
scope and limits
- Does not derive a numerical sputter-yield formula from first-principles MD or SRIM.
- Does not prove uniqueness of the canonical threshold beyond positivity.
- Does not connect yield to the mass ladder, alpha band, or eight-tick dynamics.
- Does not supply experimental fits or material-specific parameters.
- Does not claim a downstream theorem consumer in the current graph.