IndisputableMonolith.Ecology.TrophicCascadeFromJCost
The module applies the canonical J-cost band to ecology by defining discrete trophic levels and certifying cascades via J-cost non-negativity on biomass ratios. It introduces TrophicLevel, trophicLevelCount, and TrophicCascadeCert as the core objects that instantiate the six-clause template for food-web energy transfer. Ecologists deriving stability bounds from Recognition Science would cite this for its direct use of J(1)=0 and J(x)≥0. The module is a definition module importing the reusable J-band without internal proofs.
claimThe module defines $TrophicLevel$ as the discrete strata in a food chain, $trophicLevelCount : TrophicLevel → ℕ$ enumerating levels, and the certificate $TrophicCascadeCert$ asserting that J-cost on consecutive trophic ratios satisfies matched-zero $J(1)=0$ and nonnegativity $J(x)≥0$ for $x>0$.
background
This module sits in the ecology domain and imports the CanonicalJBand template, which supplies the reusable six-clause J-cost-on-ratio structure used across master cert chains. The upstream template guarantees matched-zero: J(1)=0 and nonneg: J(x)≥0 for x>0, with J drawn from the Recognition Science functional equation. TrophicLevel encodes the integer-indexed layers from primary producers upward, while trophicLevelCount tracks the rung count on the phi-ladder. The setting derives cascade constraints from the same J-function that forces D=3 and the eight-tick octave elsewhere in the framework.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the ecology-specific opening in the B-tier whole-science cert chain by instantiating the J-cost band for trophic structures. It feeds TrophicCascadeCert into higher domain certifications that link the Recognition Composition Law to observed food-web ratios. No downstream uses are recorded, leaving the definitions as scaffolding for future ecological propositions within the Recognition Science derivation.
scope and limits
- Does not model continuous population dynamics or differential equations.
- Does not incorporate nutrient cycles or external forcing terms.
- Does not validate numerical predictions against field data.
- Does not extend the J-band beyond the six supplied clauses.