Life Loop Class
The Life Loop Class is the categorical structure of metabolism: the set of all triples (D, γ, h) consisting of a τ-distinction D, a metabolic cycle γ in End_SD(X), and a homotopy class h. Loop_L is what the Life Sector hosts; metabolism is its canonical realization (VI.T09).
τ-Definition
The Life Loop Class is the categorical structure of metabolism: the set of all triples (D, γ, h) consisting of a τ-distinction D, a metabolic cycle γ in End_SD(X), and a homotopy class h. Loop_L is what the Life Sector hosts; metabolism is its canonical realization (VI.T09).
Categorical invariant. Triple (D, γ, h) where D is a τ-distinction, γ ∈ End_SD(X) is a metabolic endomorphism cycle, and h is the homotopy class of γ. Loop_L is the union of all such triples.
Primary registry anchor:
VI.D10
τ-Derivation Chain
-
I.K0— Universe Postulate establishes the categorical kernel τ -
VI.D04— τ-Distinction defines the self/non-self predicate -
VI.D08— Self-Description Predicate — the second life predicate -
VI.D10— Life Loop Class — triples (D, γ, h) capturing metabolism categorically -
VI.T09— Metabolism is the canonical realization of Loop_L
Empirical Correlate
Biomarker: Metabolic cycles: Krebs cycle (citric acid cycle), glycolysis, urea cycle, Calvin cycle, β-oxidation, pentose phosphate pathway. Each is a closed loop in concentration space — a homotopy-class member of Loop_L.
Measurable range: Krebs cycle period: ~30-60 s in active mitochondria; glycolysis flux 1-10 μmol/min/mg in muscle; ATP turnover ~10⁵ molecules/s/mitochondrion; total ATP cycled per human per day: ~50 kg of body mass equivalent (each ATP recycled ~3000×/day).
Observation method: ¹³C metabolic flux analysis (¹³C-MFA); isotopologue tracing by LC-MS or NMR; oxygen-uptake calorimetry; in-cell NMR for cycle timing; fluorescent ATP/NADH biosensors.
Calibration anchor: LG-Y02-kinetic-pseudoscalar-channel
Anchor chain:
- VI.D10 Loop_L — categorical structure
- VI.T09 metabolism = Loop_L (canonical realization)
- VI.L18 K_χ — every cycle in Loop_L is stereochemically uniform via the parity-shadow
Manuscript reference: manuscript-sources/book-06/part01/ch07-life-loop-class.tex
Lean Coverage
Status: Planned