IndisputableMonolith.Materials.SolarCellEfficiency_FromJCost
Materials module that packages solar-cell efficiency claims in terms of the Recognition Science J-cost. It defines a domain cost on efficiency ratios, a canonical positive threshold, and an inhabited perovskite solar certificate. Device theorists cite the cost nonnegativity and threshold positivity lemmas. The file is mostly definitions plus short algebraic certificates, not a long derivation.
claimOn efficiency ratios $x>0$, define a domain cost from the J-cost $J(x)=(x+x^{-1})/2-1$, prove it is nonnegative, fix a canonical positive threshold, and exhibit an inhabited perovskite solar-cell certificate that the cost meets that threshold.
background
Recognition Science forces the unique symmetric cost $J(x)=(x+x^{-1})/2-1$ (T5) and works in RS-native units from the Constants module. The Cost import supplies that functional and its elementary identities.
This materials module lifts $J$ to a domain cost on solar-cell efficiency ratios: a nonnegative scalar that vanishes only at the self-dual point $x=1$. A canonical threshold is fixed as the comparison scale for acceptable loss. The perovskite certificate is a Prop-level bundle asserting that the domain cost of the modeled cell sits on the correct side of that threshold.
Local setting is condensed-matter / PV device modeling inside the RS ladder, not a re-derivation of $J$ itself.
proof idea
Definition-heavy module. Domain cost is introduced as a thin wrapper around $J$; equality-at-evaluation and nonnegativity are short lemmas from Cost. Canonical threshold is a positive constant with a one-line positivity proof. The perovskite certificate is a structure (or Prop) inhabited by an explicit witness cert, so cert_inhabited is constructive rather than a deep tactic script.
why it matters in Recognition Science
Places PV efficiency inside the same J-cost language used for the forcing chain (T5 J-uniqueness and the Recognition Composition Law). No downstream modules currently import it (used_by empty), so it is a leaf materials application: a certificate shape that later device or band-gap developments can consume. It does not touch mass rungs, alpha, or the eight-tick octave; it only exports a cost-threshold interface for perovskite cells.
scope and limits
- Does not derive Shockley–Queisser or any continuum semiconductor PDE.
- Does not claim measured lab efficiencies; only a J-cost certificate shape.
- Does not force the numerical threshold from T0–T8; threshold is module-local.
- Does not treat tandem, organic, or non-perovskite chemistries.
- Does not connect to mass-ladder rungs or alpha bounds.