IndisputableMonolith.Chemistry.RadioactivePrecursorFromJCost
Chemistry module that packages a J-cost domain functional, a positive canonical threshold, and an inhabited RadioYieldCert for radioactive-precursor yield. Nuclear and RS chemistry workers cite it when tying precursor production to the Recognition cost. Content is definitional: cost nonnegativity, threshold positivity, and a certificate inhabitant, with no deep forcing proof.
claimOn a chemistry domain one defines a nonnegative cost $C$ built from the Recognition $J$-cost, a canonical threshold $\theta>0$, and a certificate type $\mathrm{RadioYieldCert}$ asserting that radioactive-precursor yield conditions hold relative to $C$ and $\theta$; the certificate type is inhabited.
background
Recognition Science measures mismatch by the unique cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), forced at T5 of the unified chain and obeying the Recognition Composition Law. The Cost import supplies that $J$-calculus; Constants supplies the RS tick $\tau_0$.
This chemistry module lifts $J$ to a domain-level cost $C$ on precursor configurations, records $C\ge 0$ and an evaluation identity, and fixes a positive canonical threshold $\theta$ against which yield is judged. RadioYieldCert is the Prop/structure packaging those inequalities for downstream nuclear bookkeeping.
The local setting is RS-native chemistry: precursor production is admissible only when the domain cost clears the threshold in the certificate sense, not by external nuclear data tables.
proof idea
Definition module, not a forcing argument. domainCost is introduced from the Cost layer; domainCost_nonneg and domainCost_at_eq are short algebraic or positivity facts. canonicalThreshold is a concrete positive real (canonicalThreshold_pos). RadioYieldCert bundles the cost/threshold predicates; cert and cert_inhabited supply a default inhabitant so the interface is usable without further search.
why it matters in Recognition Science
Gives chemistry a first-class J-cost handle on radioactive precursors, so yield statements sit on the same cost that forces $\phi$, the eight-tick octave, and $D=3$ upstream. used_by is currently empty: the module is a leaf interface for later nuclear or isotope theorems rather than a step inside T0–T8. It closes a scaffolding gap between pure Cost and applied chemistry certificates without claiming mass-ladder or $\alpha$-band numerics.
scope and limits
- Does not derive nuclear half-lives or branching ratios from first principles.
- Does not prove uniqueness of the canonical threshold beyond positivity.
- Does not connect domainCost to the phi-ladder mass formula or rung gaps.
- Does not supply experimental cross-section data or unit conversions outside RS-native cost.
- Does not feed any recorded downstream theorem yet (used_by empty).