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IndisputableMonolith.Chemistry.PhotoelectronSpectroscopy

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Module for X-ray photoelectron spectroscopy (XPS) binding in Recognition Science chemistry. It packages a domain cost on the RS cost functional, a positive canonical energy threshold, and an XPS binding certificate type with an inhabited instance. Chemists matching RS mass/ladder predictions to measured core-level shifts would cite it. Content is mostly definitions and elementary positivity or equality lemmas over the imported Cost layer.

claimDefines a domain cost $C$ built from the RS cost functional, proves $C \ge 0$ and an evaluation identity, introduces a positive canonical threshold $E_\ thr > 0$, and packages an XPS binding certificate (with a default inhabited witness) relating those quantities to photoelectron binding.

background

Recognition Science treats spectroscopic observables as cost defects on the same $J$-cost that forces the golden ratio and the eight-tick structure. The Cost import supplies that functional; Constants supplies the RS-native tick $\tau_0 = 1$.

Photoelectron spectroscopy measures binding energies of core electrons. In this module those energies are not free parameters: they sit behind a domain cost (nonnegative, with a pointwise evaluation lemma) and a canonical positive threshold that marks when a binding channel is certified.

The certificate type XPSBindingCert is the chemistry-facing wrapper: it bundles the cost and threshold data into a single Prop-level or structure-level claim that downstream chemistry layers can inhabit or discharge.

proof idea

Definition-heavy module, not a single deep theorem. Domain cost is introduced from the Cost layer; nonnegativity and an at-equality lemma are short algebraic or order facts. The canonical threshold is a positive constant (positivity lemma). The XPS binding certificate is a structure or Prop bundling those pieces, with an inhabited instance supplying a default witness. No long tactic scripts; proofs are elementary wrappers over Cost and real arithmetic.

why it matters in Recognition Science

Places XPS binding inside the RS chemistry stack so core-level energies speak the same cost language as the mass ladder and $J$-uniqueness (T5), rather than as ad hoc eV tables. No downstream used_by edges are recorded yet, so the module is a leaf provider: certificates and thresholds for later spectra or elemental matching. It does not itself close a forcing-chain step (T0–T8); it applies the cost infrastructure to a laboratory observable class.

scope and limits

depends on (2)

Lean names referenced from this declaration's body.

declarations in this module (8)