IndisputableMonolith.Chemistry.RS_Chem_Module_003
Chemistry module 003 packages a domain-level recognition cost and a positive canonical threshold, together with a small certificate that the cost is nonnegative and the threshold is positive. Chemists or RS auditors cite it when a reaction or species domain needs a J-cost yardstick rather than a full mass-ladder derivation. The module is mostly definitions plus elementary positivity lemmas over the imported Cost and Constants layers.
claimOn a chemistry domain one has a recognition cost $C$ (built from the RS $J$-cost) with $C \ge 0$, and a canonical threshold $\theta > 0$. A certificate object records these facts for downstream chemistry arguments.
background
Recognition Science measures mismatch with the unique cost $J(x) = (x + x^{-1})/2 - 1$ forced by the Recognition Composition Law. The Cost import supplies that functional and its elementary inequalities; Constants supplies the RS-native tick $\tau_0 = 1$.
This module sits in the Chemistry domain of the monolith. It does not re-derive $J$ or the forcing chain (T5–T8). It introduces a domain-scoped cost functional and a positive numerical threshold meant as a gate for chemical recognition events (formation, barrier crossing, or species acceptance) in RS-native units.
Sibling names indicate the surface API: domainCost and its evaluation identity, nonnegativity of that cost, a canonicalThreshold with a positivity lemma, and a thin certificate type inhabited by a default witness.
proof idea
Definition-heavy module. The cost is wired to the imported Cost layer; nonnegativity and threshold positivity are short lemmas (nonnegativity of $J$-style costs, positivity of a fixed positive constant). The certificate is an inhabited structure bundling those facts, not a deep existence proof.
why it matters in Recognition Science
Gives Chemistry a reusable cost-and-threshold interface so later reaction or bonding arguments can quote a single certified pair rather than reopen Cost. No downstream edges are recorded yet, so the module is presently a leaf in the graph: it prepares hooks for RS chemistry certificates without closing a named parent theorem. It does not touch mass-ladder rungs, $\alpha$, or the eight-tick octave; those remain in Foundation and Constants.
scope and limits
- Does not derive J-uniqueness or the forcing chain T5–T8.
- Does not compute nuclide masses or phi-ladder rungs.
- Does not prove reaction kinetics or bond energies beyond cost/threshold setup.
- Does not fix a numerical value for the threshold in SI units.
- Does not record downstream consumers in the current graph.