IndisputableMonolith.Chemistry.PhotoelectronSpectroscopy
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
- Does not derive experimental XPS peak positions from first principles alone.
- Does not prove uniqueness of the canonical threshold among all spectroscopies.
- Does not connect binding certificates to the eight-tick octave or D = 3.
- Does not supply instrument response, cross-sections, or chemical-shift databases.
- Does not claim inhabited certificates for every element or orbital.