Ecosystem
An ecosystem is a multi-scale Poincaré-circulation Life Basin: a τ-categorical Life Basin spanning multiple organism populations whose source / closure / consumer-mixer / persistence sub-loops compose into a stable cyclic flow. It is the smallest super-organism object stable under inter-sector exchange.
τ-Definition
An ecosystem is a multi-scale Poincaré-circulation Life Basin: a τ-categorical Life Basin spanning multiple organism populations whose source / closure / consumer-mixer / persistence sub-loops compose into a stable cyclic flow. It is the smallest super-organism object stable under inter-sector exchange.
Categorical invariant. Multi-scale Life Basin instantiating Poincaré-circulation among the four life sub-sectors; super-organismic τ-categorical Life Loop.
Primary registry anchor:
VI.T24
τ-Derivation Chain
-
I.K0— Universe Postulate -
VI.D15— Life Sector -
VI.D44— Inter-Sector Web — distinct life sub-sectors interlock at ecosystem scale -
VI.D62— Life Basin — ecosystem is a basin spanning multiple populations -
VI.T24— Ecosystem as Multi-Scale Poincaré Circulation — the canonical τ-categorical witness -
VI.R22— Organism/Ecosystem/Basin Taxonomy — ecosystem rung of the carrier ladder
Empirical Correlate
Biomarker: Functionally complementary species pools (producers, consumers, decomposers), nutrient cycles (C, N, P), energy flow (trophic pyramid), shared abiotic envelope (climate, soil, water chemistry), trophic-network connectance.
Measurable range: Net primary productivity 0.1-3 kg C/m²/yr; species richness 10-10⁴ (per km²); trophic levels 2-5 (rarely more); nutrient turnover 1 day (microbial) to 10³ years (carbon in old-growth forest).
Observation method: Long-term ecological research (LTER), eDNA biodiversity surveys, eddy-covariance flux towers, isotope tracing (¹³C, ¹⁵N), remote-sensing primary productivity (MODIS NDVI), food-web reconstruction.
Calibration anchor: LG-Y02-kinetic-pseudoscalar-channel
Anchor chain:
- VI.L18 chirality channel (life anchor)
- all biomolecules in every species share homochirality
- ecosystem-scale chemistry (e.g., D-glucose, L-amino-acid biomass) is uniformly K_χ-anchored
Manuscript reference: manuscript-sources/book-06/part05/ch31-ecosystems.tex
Lean Coverage
Status: Planned