IndisputableMonolith.Chemistry.PolymerizationKineticFromJCost
Defines a J-cost domain cost and a canonical positive threshold used to certify polymerization kinetics in Recognition Chemistry. Supplies nonnegativity of the domain cost, equality at the evaluation point, and an inhabited PolymerizationCert bundle. Chemists or RS auditors tracking kinetic barriers from the cost functional would cite it. The module is mostly definitional scaffolding with elementary positivity lemmas.
claimIntroduce a domain cost $C$ built from the RS $J$-cost, prove $C \ge 0$ and the on-shell evaluation identity, fix a canonical threshold $\theta > 0$, and package these into an inhabited polymerization certificate asserting that the kinetic barrier is controlled by $J$.
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. Chemistry modules import Constants (RS-native units, including the tick $\tau_0$) and Cost to lift that functional into reaction-coordinate language.
This module treats polymerization as a barrier-crossing process on a domain where the effective cost is assembled from $J$. The sibling objects name that domain cost, record its nonnegativity, fix a canonical positive threshold, and wrap the data in a PolymerizationCert structure. No external kinetic model is assumed beyond the RS cost calculus.
proof idea
Definition-first module. Domain cost and canonical threshold are introduced as defs; nonnegativity and positivity are short lemmas from the known $J \ge 0$ and algebraic rearrangement. The certificate is a structure bundling those facts, with an inhabited instance supplying concrete witnesses. No deep tactic proof or external theorem application beyond Cost/Constants.
why it matters in Recognition Science
Places polymerization kinetics inside the same $J$-cost ledger used for mass ladders and forcing (T5 J-uniqueness, RCL). Downstream chemistry or materials arguments can cite the inhabited certificate rather than re-deriving barrier positivity. With empty used-by edges in the current graph, the module is a leaf interface: it closes a local kinetic claim so later reaction-network or yield estimates can assume a certified $J$-controlled threshold without reopening cost foundations.
scope and limits
- Does not derive experimental rate constants or Arrhenius prefactors.
- Does not prove uniqueness of the canonical threshold beyond positivity.
- Does not model chain-length distributions or living vs step-growth mechanisms.
- Does not connect to eight-tick timing or spatial dimension forcing (T7–T8).
- Does not supply numerical fits to polymer molecular-weight data.