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Registry Dashboard — Book VI: Categorical Life

Browse Objects Registry Overview Filter Rules

Filter rule on this page: dashboard_display — counts the five display types (definition, lemma, proposition, remark, theorem). The full registry root for VI has 217 objects across all types; this dashboard enumerates 168 of them. See the Filter Rules manifest for the authoritative definitions, or the Release Manifest for the per-book reconciliation across all surfaces.

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 —

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