TauLib · API Book

TauLib.BookVI

TauLib.BookVI — Categorical Life

Master import file for Book VI (Categorical Life) Lean modules.

Book VI = E₂ enrichment layer: from categorical structure to living systems. Life = τ-Distinction AND SelfDesc. Five life sectors from π₁(τ³).

Module Organization

LifeCore (Part 1: Foundations of Life)

  • ParityBridge: Polarity functional, weak-sector uniqueness, Parity Bridge Theorem

  • Distinction: τ-Distinction predicate (5 conditions), carrier types, well-definedness

  • SelfDesc: SelfDesc predicate, internal evaluator, closure theorem

  • LayerSep: Layer Separation Lemma, NS-TOV counterexample, loop factorization

Sectors (Parts 1-2: Life Sectors and Hallmarks)

  • LifeLoop: Life Loop class, DecodeTarget/Horizon, Metabolic Fiber Theorem

  • FourPlusOne: 5 life sectors (persistence, agency, source, closure, consumer)

  • Hallmarks: 7 hallmarks derived from Distinction+SelfDesc

  • Absence: NoDist/NoSelfDesc failure modes, virus/neutron/NS counterexamples

Persistence (Part 2: Temporal Stability)

  • PersistenceSector: Persistence sector (α-base), temporal stability, abiogenesis

  • TemporalLemniscate: Temporal lemniscate L_T, circadian rhythms, homochirality

Agency (Part 3: Spatial Motility)

  • AgencySector: Agency sector (π-base), spatial motility, chemotaxis

  • MetabolicEnergy: ATP uniqueness, membrane as L, Krebs cycle, self-assembly

Source (Part 4: Structure Generation)

  • SourceSector: Source sector (π’-fiber), structure generation, photosynthesis

  • GeneticCode: BSD genetic code, codon error correction, Turing/Hodge, central dogma

  • Epigenetics: Chromatin partition, epigenetic state, Waddington landscape, cell fate, drift

Closure (Part 5: Structure Recycling)

  • ClosureSector: Closure sector (π’‘-fiber), structure recycling, aging/death

  • Ecosystem: Inter-sector web, ecosystem Poincaré circulation, repair budget

Consumer (Part 6: Mixed Sector and Animal Life)

  • ConsumerMixer: Consumer mixer (π’,π’’), signature rigidity, bridge-head to E₃

  • FiberRegime: Eukaryotic innovations, multicellularity as colimit, development

  • Reproduction: Recombination functor, sex as second distinction

  • Evolution: PPAS fitness, evolution as optimization, fitness landscape topology

  • Immune: Cellular distinction (MHC), autoimmunity as five failure modes

  • Neural: Neural architecture as τ³ computer, sleep as lemniscate second lobe

  • Identity: SelfDesc over code not carrier, substrate replacement preserves life

CosmicLife (Part 7: Black Holes as Living Systems)

  • BHDist: Macro-torus carrier, lexicographic defect, BH Distinction Theorem

  • BHSelfDesc: BH DecodeTarget/Horizon, uniqueness, BH SelfDesc Theorem

  • CrossLimit: ω-representative, Lift_ω, Crossing-Limit Theorem, universal BH

  • GalaxyBasin: Life basins, carrier ladder, basin predicate, Anchor Lemma

Mind (Part 8: Consciousness, Language, Bridge)

  • Consciousness: Structural self-model, minimal conscious agent, VI.T38 crown jewel

  • Bridge: Enrichment saturation, extended lemniscate, language, six exports, ω-germ boundary

Current Count: 30 modules