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Registry Dashboard — Book VI: Categorical Life

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This dashboard provides a complete inventory and formalization status map for Book VI: Categorical Life. It covers the life definition, seven hallmarks, life sectors, and the genetic code. Each registry object carries a scope label (established, tau-effective, or conjectural) and a formalization status. Use the statistics below to assess coverage, the dependency summary to trace proof chains, and the object list to navigate to individual entries in the registry.

Book VI Registry Dashboard

Generated: 2026-03-10

Statistics

Total objects: 168
By type: definition: 70 lemma: 13 proposition: 20 remark: 25 theorem: 40
Formalization: not_applicable: 25 planned: 143
Scope: conjectural: 6 established: 21 metaphorical: 1 tau-effective: 140

Dependency Summary

Max chain depth: 9 (VI.T32)
Most depended-on: VI.D04 (14 uses), VI.D08 (11 uses), VI.D10 (8 uses)
No dependencies (foundational): VI.R01, VI.R02, VI.D01, VI.D02, VI.D03, VI.D05, VI.D06, VI.D07, VI.D09, VI.P02 …

Part Coverage

| Part | Objects | Formalized | Planned | N/A | |——|———|————|———|—–| | 0 | 2 | 0 | 0 | 2 | | 1 | 54 | 0 | 51 | 3 | | 2 | 14 | 0 | 10 | 4 | | 3 | 15 | 0 | 11 | 4 | | 4 | 13 | 0 | 11 | 2 | | 5 | 12 | 0 | 9 | 3 | | 6 | 18 | 0 | 16 | 2 | | 7 | 31 | 0 | 28 | 3 | | 8 | 9 | 0 | 7 | 2 |

Object List

| ID | Type | Name | Scope | Lean | |—-|——|——|——-|——| | VI.R01 | remark | Classical Definitions Fail | estab | — | | VI.R02 | remark | E₂ Enrichment Positioning | estab | — | | VI.D01 | definition | Polarity Functional | tau-e | plan | | VI.D02 | definition | Polarity-Typed Two-Point Object (2_τ) | tau-e | plan | | VI.P01 | proposition | Low-Noise Carrier Condition | tau-e | plan | | VI.L01 | lemma | Weak-Sector Uniqueness | tau-e | plan | | VI.T01 | theorem | Parity Bridge Theorem | tau-e | plan | | VI.D03 | definition | Three Polarity Terms | tau-e | plan | | VI.D04 | definition | τ-Distinction | tau-e | plan | | VI.D05 | definition | Finite-Lineage Carrier | tau-e | plan | | VI.D06 | definition | Macro-Torus Carrier | tau-e | plan | | VI.D07 | definition | Galactic Carrier | tau-e | plan | | VI.T02 | theorem | Distinction Well-Definedness | tau-e | plan | | VI.D08 | definition | SelfDesc Predicate | tau-e | plan | | VI.D09 | definition | Internal Evaluator | tau-e | plan | | VI.P02 | proposition | Code Reconstruction | tau-e | plan | | VI.T03 | theorem | SelfDesc Closure Theorem | tau-e | plan | | VI.T04 | theorem | Layer Separation Lemma | tau-e | plan | | VI.L02 | lemma | NS-TOV Counterexample | tau-e | plan | | VI.P03 | proposition | Boundary Instability Prevents Code Closure | tau-e | plan | | VI.D10 | definition | Life Loop Class | tau-e | plan | | VI.D11 | definition | DecodeTarget | tau-e | plan | | VI.D12 | definition | DecodeHorizon | tau-e | plan | | VI.D13 | definition | Source Sub-Class (Loop_src) | tau-e | plan | | VI.D14 | definition | Closure Sub-Class (Loop_rec) | tau-e | plan | | VI.L03 | lemma | Loop Factorization | tau-e | plan | | VI.T05 | theorem | Metabolic Fiber Theorem | tau-e | plan | | VI.T06 | theorem | Consumer Mixer Uniqueness | tau-e | plan | | VI.D15 | definition | Life Sector | tau-e | plan | | VI.D16 | definition | Persistence Sector (α-base) | tau-e | plan | | VI.D17 | definition | Agency Sector (π-base) | tau-e | plan | | VI.D18 | definition | Source Sector (π’-fiber) | tau-e | plan | | VI.D19 | definition | Closure Sector (π’‘-fiber) | tau-e | plan | | VI.D20 | definition | Consumer Mixed Sector (π’,π’’) | tau-e | plan | | VI.T07 | theorem | Generator Adequacy at E₂ | tau-e | plan | | VI.L04 | lemma | No Fifth Primitive Sector | tau-e | plan | | VI.T08 | theorem | Organization = Distinction Structure | tau-e | plan | | VI.T09 | theorem | Metabolism = Life Loop Class | tau-e | plan | | VI.T10 | theorem | Homeostasis = Basin Stability | tau-e | plan | | VI.T11 | theorem | Growth = Carrier Refinement | tau-e | plan | | VI.T12 | theorem | Reproduction = Blueprint Propagation | tau-e | plan | | VI.T13 | theorem | Response = SelfDesc Adjustment | tau-e | plan | | VI.T14 | theorem | Evolution = PPAS Optimization | tau-e | plan | | VI.P04 | proposition | Seven Hallmarks Complete | tau-e | plan | | VI.D21 | definition | NoDist | tau-e | plan | | VI.D22 | definition | NoSelfDesc | tau-e | plan | | VI.T15 | theorem | Virus NoDist | tau-e | plan | | VI.L05 | lemma | Neutron NoDist | tau-e | plan | | VI.L06 | lemma | NS-NoSelfDesc | tau-e | plan | | VI.P05 | proposition | Canonical Life Phase Boundary | tau-e | plan | | VI.R03 | remark | Falsifiability Program | tau-e | — | | VI.D23 | definition | τ³ Domain Correspondence | tau-e | — | | VI.P06 | proposition | Seven Categorical Forces at E₂ | tau-e | plan | | VI.P07 | proposition | Force-Sector Matching | tau-e | plan | | VI.R04 | remark | Calibration Constants | tau-e | — | | VI.R05 | remark | τ³ Biology Correspondence | tau-e | — | | VI.D24 | definition | Persistence Sector | tau-e | — | | VI.D25 | definition | Temporal Stability Predicate | tau-e | — | | VI.T16 | theorem | Persistence as α-Base Stability | tau-e | — | | VI.R06 | remark | Archaea as Persistence Archetype | tau-e | — | | VI.R07 | remark | Extremophile Catalog | estab | — | | VI.D26 | definition | Abiogenesis as First Persistence Event | conje | — | | VI.P08 | proposition | Thermodynamic Inevitability of Life | conje | plan | | VI.R08 | remark | Speed of Abiogenesis | conje | — | | VI.D27 | definition | Temporal Lemniscate | tau-e | — | | VI.T17 | theorem | Circadian Rhythm as Poincaré Orbit | tau-e | — | | VI.P09 | proposition | 24-Hour Cycle as τ¹ Rotation | tau-e | plan | | VI.D28 | definition | Homochirality | estab | — | | VI.P10 | proposition | L-Amino Acid Preference as Parity Shadow | conje | — | | VI.R09 | remark | Homochirality Scope Discipline | conje | — | | VI.D29 | definition | Agency Sector | tau-e | — | | VI.D30 | definition | Spatial Motility Predicate | tau-e | — | | VI.T18 | theorem | Agency as π-Base Extension | tau-e | — | | VI.R10 | remark | Bacteria as Agency Archetype | tau-e | — | | VI.R11 | remark | Motility Catalog | estab | — | | VI.D31 | definition | Metabolic Circulation | tau-e | — | | VI.P11 | proposition | Krebs Cycle as Loop_L Instantiation | tau-e | — | | VI.D32 | definition | ATP/ADP Oscillation | tau-e | — | | VI.T19 | theorem | Universal Currency Uniqueness | tau-e | — | | VI.D33 | definition | Membrane as Lemniscate Boundary | tau-e | — | | VI.D34 | definition | Molecular Architecture | tau-e | — | | VI.P12 | proposition | Self-Assembly as Boundary-Induced Distinction | tau-e | — | | VI.D35 | definition | Three-Domain Sector Taxonomy | tau-e | — | | VI.R12 | remark | Sector Assignment Table | tau-e | — | | VI.R13 | remark | Eukarya as Fiber-Enabled Regime | tau-e | — | | VI.D36 | definition | Source Sector | tau-e | — | | VI.D37 | definition | Structure Generation Predicate | tau-e | — | | VI.T20 | theorem | Source as π’-Fiber Production | tau-e | — | | VI.D38 | definition | Carbon Fixation as Canonical Production | estab | — | | VI.P13 | proposition | Quantum Coherence in FMO Complex | conje | — | | VI.R14 | remark | Plants as Source Archetype | tau-e | — | | VI.R15 | remark | Sessile = Pure Source | tau-e | — | | VI.D39 | definition | Hodge Gradient at Biological Scale | tau-e | — | | VI.T21 | theorem | Turing Patterns as Hodge Eigenmode Instantiations | tau-e | — | | VI.P14 | proposition | Reaction-Diffusion from τ³ Structure | tau-e | — | | VI.D40 | definition | BSD Motivic Structure of the Genetic Code | tau-e | — | | VI.T22 | theorem | Codon Degeneracy as Error Correction | tau-e | — | | VI.P15 | proposition | Central Dogma as Morphism Composition | tau-e | — | | VI.D41 | definition | Closure Sector | estab | — | | VI.D42 | definition | Structure Recycling Predicate | estab | — | | VI.T23 | theorem | Closure as π’‘-Fiber Return | estab | — | | VI.R16 | remark | Fungi as Closure Archetype | estab | — | | VI.R17 | remark | Mycelial Network Topology | estab | — | | VI.D43 | definition | Aging as Defect Accumulation | estab | — | | VI.P16 | proposition | Repair Budget Exhaustion | estab | — | | VI.D44 | definition | Inter-Sector Web | estab | — | | VI.T24 | theorem | Ecosystem as Multi-Scale Poincaré Circulation | estab | — | | VI.R18 | remark | Nash Equilibria in Ecological Communities | estab | — | | VI.D45 | definition | Repair Budget | estab | — | | VI.P17 | proposition | Metamorphosis Preserves SelfDesc | estab | — | | VI.D46 | definition | Consumer Mixer on (π’, π’’) | tau-e | — | | VI.T25 | theorem | Signature Rigidity Determines Uniqueness | tau-e | — | | VI.L07 | lemma | Consumer as Bridge-Head to E₃ | tau-e | plan | | VI.D47 | definition | Fiber-Enabled Regime | tau-e | — | | VI.R19 | remark | 1st Ed Correction: Mixer (α,π) to (π’,π’’) | tau-e | — | | VI.D48 | definition | Multicellularity as Colimit | tau-e | — | | VI.P18 | proposition | Development as Controlled Differentiation | tau-e | — | | VI.D49 | definition | Recombination Functor | tau-e | — | | VI.T26 | theorem | Sex as Second Distinction | tau-e | — | | VI.D50 | definition | PPAS Algorithm on Fitness Landscapes | tau-e | — | | VI.T27 | theorem | Evolution as Optimization | tau-e | — | | VI.R20 | remark | Fitness Landscape Topology | tau-e | — | | VI.D51 | definition | Cellular Distinction Predicate | tau-e | — | | VI.T28 | theorem | Autoimmunity as Distinction Failure | tau-e | — | | VI.D52 | definition | Neural Architecture as τ³ Computer | tau-e | — | | VI.P19 | proposition | Sleep as Temporal Lemniscate Second Lobe | tau-e | — | | VI.D53 | definition | SelfDesc over Code, Not Carrier | tau-e | — | | VI.L08 | lemma | Substrate Replacement Preserves Life-Equivalence | tau-e | — | | VI.D54 | definition | Macro-Torus Carrier T(H_BH) | tau-e | plan | | VI.D55 | definition | Lexicographic Defect Functional | tau-e | plan | | VI.D56 | definition | Frame-Closure Defect | tau-e | plan | | VI.D57 | definition | Strong-Saturation Defect | tau-e | plan | | VI.T29 | theorem | BH Distinction Theorem | tau-e | plan | | VI.D58 | definition | BH DecodeTarget | tau-e | plan | | VI.D59 | definition | BH DecodeHorizon | tau-e | plan | | VI.L09 | lemma | BH Uniqueness Lemma | tau-e | plan | | VI.L10 | lemma | BH Constancy Lemma | tau-e | plan | | VI.T30 | theorem | BH SelfDesc Theorem | tau-e | plan | | VI.D60 | definition | ω-Representative of Life | tau-e | plan | | VI.D61 | definition | Lift_ω Constructor | tau-e | plan | | VI.L11 | lemma | Primorial Ladder Convergence | tau-e | plan | | VI.T31 | theorem | BH ω-Representative: Fusion Convergence | tau-e | plan | | VI.T32 | theorem | BH Seven Hallmarks Verified | tau-e | — | | VI.R21 | remark | BH-as-Alive Is Theorem, Not Metaphor | tau-e | — | | VI.D62 | definition | Life Basin | tau-e | — | | VI.D63 | definition | Carrier Ladder | tau-e | — | | VI.D64 | definition | Basin Predicate | tau-e | — | | VI.T33 | theorem | Galaxy-SMBH Anchor Lemma | tau-e | — | | VI.L12 | lemma | Basin Fusion via SMBH Merger | tau-e | — | | VI.D65 | definition | Distinction/SelfDesc Matrix | tau-e | — | | VI.T34 | theorem | Stars Are Not Alive | tau-e | — | | VI.R22 | remark | Organism/Ecosystem/Basin Taxonomy | tau-e | — | | VI.T35 | theorem | Crossing-Limit Theorem | tau-e | plan | | VI.T36 | theorem | Universal BH = Fully Alive State | tau-e | plan | | VI.P20 | proposition | Omega Point as Life Convergence | metap | — | | VI.D66 | definition | Ontic Enrichment Ladder E₀–E₃ | tau-e | — | | VI.D67 | definition | Three Identity Regimes | tau-e | — | | VI.T37 | theorem | Enrichment Saturation Theorem | tau-e | — | | VI.R23 | remark | τ as Third Option | tau-e | — | | VI.D68 | definition | Structural Self-Model | tau-e | — | | VI.D69 | definition | Minimal Conscious Agent | tau-e | — | | VI.T38 | theorem | Consciousness as Mixed-Sector Self-Modeling | tau-e | — | | VI.D70 | definition | Extended Lemniscate | tau-e | — | | VI.T39 | theorem | Language as Shared Code | tau-e | — | | VI.R24 | remark | Computation Theme Across the Book | tau-e | — | | VI.L13 | lemma | ω-Germ Cannot Be Resolved Diagrammatically | estab | — | | VI.T40 | theorem | Six Export Contracts to Book VII | estab | — | | VI.R25 | remark | Principled Science-Faith Boundary | estab | — |