Registry — Book VI: Categorical Life

VI.R01 Classical Definitions Fail remark VI.R02 E₂ Enrichment Positioning remark VI.D01 Polarity Functional definition VI.D02 Polarity-Typed Two-Point Object (2_τ) definition VI.P01 Low-Noise Carrier Condition proposition VI.L01 Weak-Sector Uniqueness lemma VI.T01 Parity Bridge Theorem theorem VI.D03 Three Polarity Terms definition VI.D04 τ-Distinction definition VI.D05 Finite-Lineage Carrier definition VI.D06 Macro-Torus Carrier definition VI.D07 Galactic Carrier definition VI.T02 Distinction Well-Definedness theorem VI.D08 SelfDesc Predicate definition VI.D09 Internal Evaluator definition VI.P02 Code Reconstruction proposition VI.T03 SelfDesc Closure Theorem theorem VI.T04 Layer Separation Lemma theorem VI.L02 NS-TOV Counterexample lemma VI.P03 Boundary Instability Prevents Code Closure proposition VI.D10 Life Loop Class definition VI.D11 DecodeTarget definition VI.D12 DecodeHorizon definition VI.D13 Source Sub-Class (Loop_src) definition VI.D14 Closure Sub-Class (Loop_rec) definition VI.L03 Loop Factorization lemma VI.T05 Metabolic Fiber Theorem theorem VI.T06 Consumer Mixer Uniqueness theorem VI.D15 Life Sector definition VI.D16 Persistence Sector (α-base) definition VI.D17 Agency Sector (π-base) definition VI.D18 Source Sector (γ-fiber) definition VI.D19 Closure Sector (η-fiber) definition VI.D20 Consumer Mixed Sector (γ,η) definition VI.T07 Generator Adequacy at E₂ theorem VI.L04 No Fifth Primitive Sector lemma VI.T08 Organization = Distinction Structure theorem VI.T09 Metabolism = Life Loop Class theorem VI.T10 Homeostasis = Basin Stability theorem VI.T11 Growth = Carrier Refinement theorem VI.T12 Reproduction = Blueprint Propagation theorem VI.T13 Response = SelfDesc Adjustment theorem VI.T14 Evolution = PPAS Optimization theorem VI.P04 Seven Hallmarks Complete proposition VI.D21 NoDist definition VI.D22 NoSelfDesc definition VI.T15 Virus NoDist theorem VI.L05 Neutron NoDist lemma VI.L06 NS-NoSelfDesc lemma VI.P05 Canonical Life Phase Boundary proposition VI.R03 Falsifiability Program remark VI.D23 τ³ Domain Correspondence definition VI.P06 Thermodynamic Necessity at E₂ proposition VI.P07 Calibration Constants proposition VI.R04 Calibration Constants remark VI.R05 τ³ Biology Correspondence remark VI.D24 Persistence Sector definition VI.D25 Temporal Stability Predicate definition VI.T16 Persistence as α-Base Stability theorem VI.R06 Archaea as Persistence Archetype remark VI.R07 Extremophile Catalog remark VI.D26 Abiogenesis as First Persistence Event definition VI.P08 Thermodynamic Inevitability of Life proposition VI.R08 Speed of Abiogenesis remark VI.D27 Temporal Lemniscate definition VI.T17 Circadian Rhythm as Poincaré Orbit theorem VI.P09 24-Hour Cycle as τ¹ Rotation proposition VI.D28 Homochirality definition VI.P10 L-Amino Acid Preference as Parity Shadow proposition VI.R09 Homochirality Scope Discipline remark VI.D29 Agency Sector definition VI.D30 Spatial Motility Predicate definition VI.T18 Agency as π-Base Extension theorem VI.R10 Bacteria as Agency Archetype remark VI.R11 Motility Catalog remark VI.D31 Metabolic Circulation definition VI.P11 Krebs Cycle as Loop_L Instantiation proposition VI.D32 ATP/ADP Oscillation definition VI.T19 Universal Currency Uniqueness theorem VI.D33 Membrane as Lemniscate Boundary definition VI.D34 Molecular Architecture definition VI.P12 Self-Assembly as Boundary-Induced Distinction proposition VI.D35 Three-Domain Sector Taxonomy definition VI.R12 Sector Assignment Table remark VI.R13 Eukarya as Fiber-Enabled Regime remark VI.D36 Source Sector definition VI.D37 Structure Generation Predicate definition VI.T20 Source as γ-Fiber Production theorem VI.D38 Carbon Fixation as Canonical Production definition VI.P13 Quantum Coherence in FMO Complex proposition VI.R14 Plants as Source Archetype remark VI.R15 Sessile = Pure Source remark VI.D39 Hodge Gradient at Biological Scale definition VI.T21 Turing Patterns as Hodge Eigenmode Instantiations theorem VI.P14 Reaction-Diffusion from τ³ Structure proposition VI.D40 BSD Motivic Structure of the Genetic Code definition VI.T22 Codon Degeneracy as Error Correction theorem VI.P15 Central Dogma as Morphism Composition proposition VI.D41 Closure Sector definition VI.D42 Structure Recycling Predicate definition VI.T23 Closure as η-Fiber Return theorem VI.R16 Fungi as Closure Archetype remark VI.R17 Mycelial Network Topology remark VI.D43 Aging as Defect Accumulation definition VI.P16 Repair Budget Exhaustion proposition VI.D44 Inter-Sector Web definition VI.T24 Ecosystem as Multi-Scale Poincaré Circulation theorem VI.R18 Nash Equilibria in Ecological Communities remark VI.D45 Repair Budget definition VI.P17 Metamorphosis Preserves SelfDesc proposition VI.D46 Consumer Mixer on (γ, η) definition VI.T25 Signature Rigidity Determines Uniqueness theorem VI.L07 Consumer as Bridge-Head to E₃ lemma VI.D47 Fiber-Enabled Regime definition VI.R19 1st Ed Correction: Mixer (α,π) to (γ,η) remark VI.D48 Multicellularity as Colimit definition VI.P18 Development as Controlled Differentiation proposition VI.D49 Recombination Functor definition VI.T26 Sex as Second Distinction theorem VI.D50 PPAS Algorithm on Fitness Landscapes definition VI.T27 Evolution as Optimization theorem VI.R20 Fitness Landscape Topology remark VI.D51 Cellular Distinction Predicate definition VI.T28 Autoimmunity as Distinction Failure theorem VI.D52 Neural Architecture as τ³ Computer definition VI.P19 Sleep as Temporal Lemniscate Second Lobe proposition VI.D53 SelfDesc over Code, Not Carrier definition VI.L08 Substrate Replacement Preserves Life-Equivalence lemma VI.D54 Macro-Torus Carrier T(H_BH) definition VI.D55 Lexicographic Defect Functional definition VI.D56 Frame-Closure Defect definition VI.D57 Strong-Saturation Defect definition VI.T29 BH Distinction Theorem theorem VI.D58 BH DecodeTarget definition VI.D59 BH DecodeHorizon definition VI.L09 BH Uniqueness Lemma lemma VI.L10 BH Constancy Lemma lemma VI.T30 BH SelfDesc Theorem theorem VI.D60 ω-Representative of Life definition VI.D61 Lift_ω Constructor definition VI.L11 Primorial Ladder Convergence lemma VI.T31 BH ω-Representative: Fusion Convergence theorem VI.T32 BH Seven Hallmarks Verified theorem VI.R21 BH-as-Alive Is Theorem, Not Metaphor remark VI.D62 Life Basin definition VI.D63 Carrier Ladder definition VI.D64 Basin Predicate definition VI.T33 Galaxy-SMBH Anchor Lemma theorem VI.L12 Basin Fusion via SMBH Merger lemma VI.D65 Distinction/SelfDesc Matrix definition VI.T34 Stars Are Not Alive theorem VI.R22 Organism/Ecosystem/Basin Taxonomy definition VI.T35 Crossing-Limit Theorem theorem VI.T36 Universal BH = Fully Alive State theorem VI.P20 Omega Point as Life Convergence proposition VI.D66 Ontic Enrichment Ladder E₀–E₃ definition VI.D67 Three Identity Regimes definition VI.T37 Enrichment Saturation Theorem theorem VI.R23 τ as Third Option remark VI.D68 Structural Self-Model definition VI.D69 Minimal Conscious Agent definition VI.T38 Consciousness as Mixed-Sector Self-Modeling theorem VI.D70 Extended Lemniscate definition VI.T39 Language as Shared Code theorem VI.R24 Computation Theme Across the Book remark VI.L13 ω-Germ Cannot Be Resolved Diagrammatically lemma VI.T40 Six Export Contracts to Book VII theorem VI.R25 Principled Science-Faith Boundary remark VI.D71 Polarity Propagation definition VI.D72 Chirality Seed definition VI.D73 Enantiomeric Excess at Refinement Level n definition VI.T41 Propagation Preserves Chirality theorem VI.L14 Propagation Uniqueness lemma VI.T42 Stereochemical Selection theorem VI.P21 Monotone Convergence of Enantiomeric Excess proposition VI.T43 Homochirality Universality theorem VI.R26 Homochirality Scope Upgrade remark VI.D74 Far-From-Equilibrium Regime definition VI.D75 Complexity Budget definition VI.D76 Distinction Threshold definition VI.D77 Abiogenesis Timescale Bound definition VI.L15 Complexity Monotone lemma VI.L16 Basin Is Absorbing lemma VI.T44 Attractor Existence theorem VI.T45 Timescale From Half-Life theorem VI.T46 Abiogenesis Inevitability theorem VI.R27 Geological Consistency remark VI.R28 Abiogenesis is not contingent remark VI.D78 Chromatin Partition definition VI.D79 Epigenetic State definition VI.D80 Gene Expression Profile definition VI.D81 Potency Restriction definition VI.D82 Intergenerational Transfer definition VI.D83 Waddington Landscape definition VI.D84 Cell Fate definition VI.D85 Epigenetic Drift definition VI.T47 Differentiation Is Irreversible theorem VI.T48 Reprogramming as Refinement Reversal theorem VI.T49 Drift Bounded by Repair theorem VI.P22 Cell Fate as Fixed Point proposition VI.D87 Neural Defect Level definition VI.D88 Neural Defect Tower definition VI.D89 Neurodegenerative Disease Mapping definition VI.D91 Neural Hayflick Bound definition VI.T52 Inter-Level Cascade theorem VI.P23 Neural Defect Monotonicity proposition VI.T54 Neurodegeneration = Hayflick Crossing theorem VI.D90 Sleep Repair Function definition VI.T53 Sleep Consolidates Levels 1-2 theorem VI.P24 Sleep Deprivation Accelerates Defect Crossing proposition VI.T50 Substrate Abstraction theorem VI.R29 Scope: structural, not empirical remark VI.D86 Constructive Consciousness Criteria definition VI.T51 Consciousness Criteria Equivalence theorem VI.L17 Silicon Realization lemma VI.R30 Empirical identification caveat remark VI.R31 Current AI systems remark