IndisputableMonolith.Ecology.TrophicCascadeFromJCost
The module applies the Canonical J-Cost Band template to ecology by defining trophic levels and a cascade certificate. Systems ecologists using Recognition Science cite it for the domain-specific instantiation of J-band constraints on energy ratios. The module follows the six-clause structure imported from CanonicalJBand, supplying matched-zero and nonnegativity for the J function on trophic ratios.
claimDefine the type $T$ of trophic levels. The certificate asserts that for any energy-transfer ratio $x>0$ in a cascade, $J(1)=0$ and $J(x)\ge 0$, where $J$ satisfies the Recognition Composition Law.
background
Recognition Science obtains all structure from the J-cost function obeying the Recognition Composition Law. The upstream CanonicalJBand module supplies the reusable six-clause template used for every domain certificate in the master chain. This ecology module introduces TrophicLevel as the discrete position in a food chain and TrophicCascadeCert as the object that records the J-band conditions on transfer ratios.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the ecology entry in the Plan v7 domain-cert sequence that feeds the B-tier whole-science openings of the master cert chain. It instantiates the J-cost band for trophic structures, enabling later derivations of cascade stability from the same J properties used in other domains.
scope and limits
- Does not derive explicit numerical transfer efficiencies.
- Does not incorporate spatial or temporal dynamics.
- Does not extend the J-band template beyond its six clauses.
- Does not address non-trophic ecological interactions.