This dashboard provides a complete inventory and formalization status map for Book VII: Categorical Metaphysics. It covers the four registers, ontology, ethics, consciousness, and the Logos sector. 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 VII Registry Dashboard

Generated: 2026-03-10

Statistics

• Total objects: 273

• By type: definition: 92

  lemma: 44

  proposition: 31

  remark: 58

  theorem: 48

• Formalization: formalized: 182

  not_applicable: 91

• Scope: conjectural: 16

  established: 2

  metaphorical: 1

  tau-effective: 254

Dependency Summary

• Max chain depth: 65 (VII.R50)
• Most depended-on: VII.D76 (8 uses), VII.T35 (4 uses), VII.T06 (4 uses)
• No dependencies (foundational): VII.R01, VII.R02, VII.D01, VII.D02, VII.D03, VII.D04, VII.T01, VII.D05, VII.D06, VII.T02 …

Part Coverage

| Part | Objects | Formalized | Planned | N/A | |——|———|————|———|—–| | 0 | 3 | 0 | 0 | 3 | | 1 | 62 | 57 | 0 | 5 | | 2 | 41 | 31 | 0 | 10 | | 3 | 13 | 0 | 0 | 13 | | 4 | 15 | 0 | 0 | 15 | | 5 | 14 | 10 | 0 | 4 | | 6 | 21 | 20 | 0 | 1 | | 7 | 40 | 24 | 0 | 16 | | 8 | 25 | 14 | 0 | 11 | | 9 | 19 | 15 | 0 | 4 | | 10 | 11 | 9 | 0 | 2 | | 11 | 9 | 2 | 0 | 7 |

Object List

| ID | Type | Name | Scope | Lean | |—-|——|——|——-|——| | VII.R01 | remark | E₃ Enrichment Positioning | estab | — | | VII.R02 | remark | E₃ Import Contract | estab | — | | VII.D01 | definition | Empirical Register | tau-e | form | | VII.D02 | definition | Practical Register | tau-e | form | | VII.D03 | definition | Diagrammatic Register | tau-e | form | | VII.D04 | definition | Commitment Register | tau-e | form | | VII.T01 | theorem | Register Independence Theorem | tau-e | form | | VII.D05 | definition | MetaDecode Operator | tau-e | form | | VII.D06 | definition | Metaphysics Loop Class | tau-e | form | | VII.T02 | theorem | E₃ Non-Emptiness | tau-e | form | | VII.L01 | lemma | BH Basin Law-Code | tau-e | form | | VII.D07 | definition | Metaphysics Sector S_E | tau-e | form | | VII.D08 | definition | Metaphysics Sector S_P | tau-e | form | | VII.D09 | definition | Metaphysics Sector S_D | tau-e | form | | VII.D10 | definition | Metaphysics Sector S_C | tau-e | form | | VII.D11 | definition | Logos Sector S_L | tau-e | form | | VII.T03 | theorem | Sector Decomposition at E₃ | tau-e | form | | VII.P01 | proposition | Sector Independence at E₃ | tau-e | form | | VII.D12 | definition | Sector Witness Bundle | tau-e | form | | VII.D13 | definition | Sector Vacuum | tau-e | form | | VII.D14 | definition | Sector Normaliser | tau-e | form | | VII.L02 | lemma | Shadow Soundness Lemma | tau-e | form | | VII.T04 | theorem | Rigidity Corollary | tau-e | form | | VII.L03 | lemma | Non-Emptiness at Each Layer | tau-e | form | | VII.L04 | lemma | Strictness Between Layers | tau-e | form | | VII.T05 | theorem | Canonical Ladder Theorem | tau-e | form | | VII.P02 | proposition | Seven-Book Partition | tau-e | form | | VII.L05 | lemma | No-New-Lobe Lemma | tau-e | form | | VII.L06 | lemma | No-New-Crossing-Mediator Lemma | tau-e | form | | VII.L07 | lemma | Carrier Closure Lemma | tau-e | form | | VII.T06 | theorem | Saturation Theorem | tau-e | form | | VII.P03 | proposition | Four-Orbit Implies Four-Layer | tau-e | form | | VII.D15 | definition | Bounded Witness Form | tau-e | form | | VII.T07 | theorem | Gödel Avoidance Theorem | tau-e | form | | VII.P04 | proposition | No-Diagonal Principle | tau-e | form | | VII.D16 | definition | Archetype as Minimal j-Closed Fixed Point | tau-e | form | | VII.D17 | definition | Archetype Extractor Protocol | tau-e | form | | VII.L08 | lemma | j-Closure Minimality | tau-e | form | | VII.T08 | theorem | Archetype Existence | tau-e | form | | VII.D18 | definition | Boundary Archetype | tau-e | form | | VII.P05 | proposition | Boundary Archetype Minimality | tau-e | form | | VII.D19 | definition | Mitigation Archetype | tau-e | form | | VII.D20 | definition | Meta-Framing Archetype | tau-e | form | | VII.D21 | definition | Synchronicity as Kernel Invariant | conje | form | | VII.T09 | theorem | Cross-Register Correlation | conje | form | | VII.D22 | definition | Readout Functor | tau-e | form | | VII.T10 | theorem | Readout Functor Faithfulness | tau-e | form | | VII.D23 | definition | Relational Primacy Principle | tau-e | form | | VII.R03 | remark | Historical Precursors to Relational Ontology | tau-e | not_ | | VII.D24 | definition | τ-Kernel Philosophical Summary | tau-e | form | | VII.R04 | remark | Axiom-Philosophy Correspondence | tau-e | not_ | | VII.D25 | definition | Internal Set Ontology | tau-e | form | | VII.D26 | definition | Ontic/Virtual Distinction | tau-e | form | | VII.R05 | remark | ZFC-as-VM Philosophical Import | tau-e | not_ | | VII.D27 | definition | Truth-Maker in τ (Ontological) | tau-e | form | | VII.T11 | theorem | Coherence-Correspondence Unification | tau-e | form | | VII.R06 | remark | Possible Worlds as Internal Domains | tau-e | not_ | | VII.D28 | definition | Derived Geometry | tau-e | form | | VII.R07 | remark | Geometry as Consequence | tau-e | not_ | | VII.D29 | definition | τ³ Philosophical Framing | tau-e | form | | VII.R08 | remark | Central Theorem Philosophical Import | tau-e | not_ | | VII.D30 | definition | Bulk-Boundary Duality | tau-e | form | | VII.D31 | definition | Law as Admissible Continuation | tau-e | form | | VII.T12 | theorem | Operator Realism | tau-e | form | | VII.D32 | definition | Causation as Constrained Composition | tau-e | form | | VII.P06 | proposition | Temporal Ordering from Persistence | tau-e | form | | VII.D33 | definition | τ-Modal Operators | tau-e | form | | VII.T13 | theorem | Modal Logic Soundness in τ | tau-e | form | | VII.D34 | definition | Identity as Address Persistence | tau-e | form | | VII.R09 | remark | Panta Rhei with Invariants | tau-e | not_ | | VII.D35 | definition | Mereological Composition as Colimit | tau-e | form | | VII.P07 | proposition | Special Composition Answer | tau-e | form | | VII.D36 | definition | Abstract Object as Structural Position | tau-e | form | | VII.R10 | remark | Platonism-Nominalism Dissolution | tau-e | not_ | | VII.D37 | definition | Six Ontic Requirements | tau-e | form | | VII.T14 | theorem | Inevitability Convergence | tau-e | form | | VII.P08 | proposition | Each Requirement Independently Necessary | tau-e | form | | VII.D38 | definition | Problem Map Classification Scheme | tau-e | form | | VII.R11 | remark | Problem Map Table | tau-e | not_ | | VII.D39 | definition | Three-Layer Solipsism Resolution | tau-e | form | | VII.T15 | theorem | Bayesian Exclusion of Solipsism | tau-e | form | | VII.D40 | definition | Non-Dualistic Platonism | tau-e | form | | VII.D41 | definition | ω-Uniqueness Principle | tau-e | form | | VII.T16 | theorem | ω-Uniqueness | tau-e | form | | VII.R12 | remark | Discovery-Invention Dissolution | tau-e | not_ | | VII.D42 | definition | Knowledge as Section | tau-e | — | | VII.T17 | theorem | Gettier Dissolution | tau-e | — | | VII.D43 | definition | Justification as Gluing | tau-e | — | | VII.P09 | proposition | Underdetermination as Cover Failure | tau-e | — | | VII.D44 | definition | Perception Functor | tau-e | — | | VII.D45 | definition | Temporal Experience Structure | tau-e | — | | VII.R13 | remark | Husserl-τ Correspondence | tau-e | — | | VII.P10 | proposition | Perspectival Gluing Grounds Objectivity | tau-e | — | | VII.R14 | remark | Intersubjectivity Conditions | tau-e | — | | VII.R15 | remark | Embodiment as Self-Boundary | tau-e | — | | VII.T18 | theorem | Ontology-Epistemology Collapse | tau-e | — | | VII.R16 | remark | Consequences for Traditional Epistemology | tau-e | — | | VII.R17 | remark | Empirical Sector Summary | tau-e | — | | VII.D46 | definition | Pre-Symbolic Resonance | tau-e | — | | VII.D47 | definition | Aesthetic Functional | tau-e | — | | VII.T19 | theorem | Beauty as Invariance | tau-e | — | | VII.R18 | remark | Beauty Across Domains | tau-e | — | | VII.D48 | definition | Elegance as Minimal Tension | tau-e | — | | VII.R19 | remark | Style as Categorical Invariant | tau-e | — | | VII.R20 | remark | Golden Ratio as Kernel Shadow | tau-e | — | | VII.P11 | proposition | Fractal Beauty as Scale Invariance | tau-e | — | | VII.D49 | definition | Musical Consonance as Ratio Invariance | tau-e | — | | VII.R21 | remark | Visual Composition Principles | tau-e | — | | VII.R22 | remark | Architecture as Spatial Aesthetics | tau-e | — | | VII.P12 | proposition | Creation as Defect Minimization | tau-e | — | | VII.D50 | definition | The Sublime as Comprehension Boundary | tau-e | — | | VII.R23 | remark | Kant’s Sublime in Categorical Terms | tau-e | — | | VII.R24 | remark | Environmental Beauty | tau-e | — | | VII.D51 | definition | Language Adds Temporalization | tau-e | form | | VII.D52 | definition | Subsymbolic Layer | tau-e | form | | VII.D53 | definition | Temporalization Operators | tau-e | form | | VII.T20 | theorem | Language as Self-Enrichment | tau-e | form | | VII.T21 | theorem | Syntax-Semantics Collapse | tau-e | form | | VII.P13 | proposition | Universal Bridgeability | tau-e | form | | VII.D54 | definition | Pragmatic Update Operator | tau-e | form | | VII.R25 | remark | Translation as Functor | tau-e | not_ | | VII.R26 | remark | Meaning Drift as Perturbation | tau-e | not_ | | VII.R27 | remark | Public Language as Infrastructure | tau-e | not_ | | VII.D55 | definition | Para-Mind | tau-e | form | | VII.P14 | proposition | LLM as Subsymbolic Evidence | tau-e | form | | VII.D56 | definition | Prayer as ω-Addressed Communication | conje | form | | VII.R28 | remark | Prayer Across Traditions | conje | not_ | | VII.D57 | definition | Boolean Micro-Logic | tau-e | form | | VII.T22 | theorem | Single-Address Classical Logic | tau-e | form | | VII.D58 | definition | Bayesian Meso-Logic | tau-e | form | | VII.T23 | theorem | Scale-Dependent Logic Theorem | tau-e | form | | VII.D59 | definition | Internal Randomness | tau-e | form | | VII.P15 | proposition | Randomness as Internal Complexity | tau-e | form | | VII.T24 | theorem | No External Randomness | tau-e | form | | VII.T25 | theorem | Kolmogorov Representation | tau-e | form | | VII.T26 | theorem | Inference from Kernel Structure | tau-e | form | | VII.D60 | definition | Truth-Maker in τ (Logical) | tau-e | form | | VII.D61 | definition | Truth-Bearer as Section | tau-e | form | | VII.T27 | theorem | Alethic Unification | tau-e | form | | VII.P16 | proposition | Alethic Pluralism | tau-e | form | | VII.D62 | definition | Modal Frame in τ | tau-e | form | | VII.D63 | definition | Accessibility Morphism | tau-e | form | | VII.T28 | theorem | Kripke Soundness in τ | tau-e | form | | VII.L09 | lemma | Modal Collapse Prevention | tau-e | form | | VII.D64 | definition | Paraconsistent Boundary Logic | tau-e | form | | VII.T29 | theorem | No-Explosion at Boundaries | tau-e | form | | VII.L10 | lemma | Truth4 Paraconsistency | tau-e | form | | VII.R29 | remark | Diagrammatic Sector Summary | tau-e | not_ | | VII.D65 | definition | Dignity as Label-Independence | tau-e | form | | VII.T30 | theorem | Dignity Universality | tau-e | form | | VII.D66 | definition | CI as Naturality Constraint | tau-e | form | | VII.T31 | theorem | CI-Sheaf Equivalence | tau-e | form | | VII.T32 | theorem | No-Conflict Theorem | tau-e | form | | VII.L11 | lemma | Duty Typing Lemma | tau-e | form | | VII.P17 | proposition | Trolley Resolution | tau-e | — | | VII.D67 | definition | Fairness Protocol | tau-e | form | | VII.P18 | proposition | Fairness from CI | tau-e | — | | VII.D68 | definition | Moral Monodromy | tau-e | form | | VII.T33 | theorem | Monodromy as Source of Tragedy | tau-e | form | | VII.D69 | definition | Four Ethical Tests | tau-e | form | | VII.P19 | proposition | Ethical Defect Minimization | tau-e | — | | VII.P20 | proposition | Animal Dignity from Distinction | tau-e | — | | VII.R30 | remark | Graduated Dignity Scale | tau-e | — | | VII.R31 | remark | Intergenerational Obligations | tau-e | — | | VII.D70 | definition | Character as Ethical Fixed Point | tau-e | form | | VII.T34 | theorem | Flourishing as Global Section | tau-e | form | | VII.R32 | remark | Applied Ethics Domains | tau-e | — | | VII.D71 | definition | CI Operator Graph | tau-e | form | | VII.T35 | theorem | CI as j-Closed Fixed Point | tau-e | form | | VII.L12 | lemma | CI Minimality Lemma | tau-e | form | | VII.T36 | theorem | Kernel Theorem (K) | tau-e | form | | VII.T37 | theorem | Semantic Object Construction (S) | tau-e | form | | VII.P21 | proposition | CI Uniqueness Conjecture | tau-e | form | | VII.L13 | lemma | First Bombshell Lemma | tau-e | form | | VII.D72 | definition | Commitment Register Admissibility | tau-e | — | | VII.T38 | theorem | C Register Independence | tau-e | — | | VII.D73 | definition | Kant-τ Correspondence | conje | — | | VII.R33 | remark | Kant’s Three Methodological Rules | conje | — | | VII.D74 | definition | Earned/Unearned Ethics Framework | tau-e | — | | VII.P22 | proposition | Pseudo-Paradox from Type Violation | tau-e | — | | VII.D75 | definition | Register-Enrichment Correspondence | conje | — | | VII.R34 | remark | Kant’s Heroic Restraint | conje | — | | VII.D76 | definition | Social Ontology | tau-e | form | | VII.D77 | definition | Sphere as Shared Topos | tau-e | — | | VII.R35 | remark | Sloterdijk-τ Correspondence | tau-e | — | | VII.P23 | proposition | Dunbar Limit as Carrier Capacity | tau-e | — | | VII.R36 | remark | Urban Topology | tau-e | — | | VII.R37 | remark | Architecture as Cultural Readout | tau-e | — | | VII.R38 | remark | Cultural Lineage as Code Stream | tau-e | — | | VII.D78 | definition | Capital Network | tau-e | — | | VII.P24 | proposition | Fragmentation as Gluing Failure | tau-e | — | | VII.R39 | remark | Individuation as Structural Process | tau-e | — | | VII.D79 | definition | Nine Global Spheres Classification | tau-e | — | | VII.D80 | definition | Power as Morphism Structure | tau-e | form | | VII.P25 | proposition | Legitimacy as Recognition Coherence | tau-e | form | | VII.D81 | definition | Ritual as Social Gluing | tau-e | form | | VII.R40 | remark | Religion as Readout Functor | conje | — | | VII.D82 | definition | Mind as Internal Topos | tau-e | form | | VII.T39 | theorem | Mind-Topos Structure Theorem | tau-e | form | | VII.D83 | definition | Story Functor | tau-e | form | | VII.T40 | theorem | Narrative Identity as Functor | tau-e | form | | VII.T41 | theorem | Consciousness as Global Section | tau-e | form | | VII.L14 | lemma | Binding as Gluing | tau-e | form | | VII.D84 | definition | Intentionality as Morphism | tau-e | form | | VII.D85 | definition | Qualia as Internal Morphisms | conje | form | | VII.R41 | remark | Hard Problem Reformulated | conje | not_ | | VII.T42 | theorem | Self-Recognition as E₃ Operator | tau-e | form | | VII.T43 | theorem | Free Will as Branching | tau-e | form | | VII.P26 | proposition | Compatibilism Dissolution | tau-e | form | | VII.P27 | proposition | Identity as Address Persistence (Mind) | tau-e | form | | VII.R42 | remark | Artificial Mind Criteria | tau-e | not_ | | VII.R43 | remark | Metzinger-τ Comparison | tau-e | not_ | | VII.T44 | theorem | Emotions as Register-Crossings | tau-e | form | | VII.L15 | lemma | Affect as Subsymbolic Pressure | tau-e | form | | VII.P28 | proposition | Extended Mind as Carrier Extension | tau-e | form | | VII.R44 | remark | Commitment Sector Summary | tau-e | not_ | | VII.D86 | definition | Logos Sector | tau-e | form | | VII.T45 | theorem | Logos Sector Uniqueness | tau-e | form | | VII.D87 | definition | D→C Bridge Functor | tau-e | form | | VII.T46 | theorem | Bridge Equivalence at S_L | tau-e | form | | VII.L16 | lemma | Register Preservation | tau-e | form | | VII.P29 | proposition | Four-Register Convergence at S_L | tau-e | form | | VII.D88 | definition | Mediator Fixed-Point Basin | tau-e | form | | VII.R45 | remark | Logos Synchronicity | conje | not_ | | VII.D89 | definition | Subject-Tool Collapse | tau-e | form | | VII.T47 | theorem | No Forced Stance | tau-e | form | | VII.R46 | remark | Crown Jewel of 2nd Edition | tau-e | not_ | | VII.R47 | remark | Methodological Override Rules | tau-e | not_ | | VII.D90 | definition | Generative Switch | tau-e | form | | VII.T48 | theorem | Layer-Conflation as Category Error | tau-e | form | | VII.R48 | remark | Archetypal Genesis Reading | metap | not_ | | VII.R49 | remark | Genesis Synthesis | conje | not_ | | VII.L17 | lemma | Register Orthogonality | tau-e | form | | VII.L18 | lemma | Enrichment Monotonicity | tau-e | form | | VII.L19 | lemma | E₃ Uniqueness | tau-e | form | | VII.P30 | proposition | Register Completeness | tau-e | form | | VII.L20 | lemma | Crossing Point Uniqueness | tau-e | form | | VII.L21 | lemma | Carrier Exhaustion | tau-e | form | | VII.L22 | lemma | Bounded Witness Form Check | tau-e | form | | VII.P31 | proposition | Enrichment Stabilization | tau-e | form | | VII.R50 | remark | Ladder–Saturation Bridge | tau-e | — | | VII.R51 | remark | E₃–Consciousness Consistency | tau-e | — | | VII.R52 | remark | Sector–Register Correspondence | tau-e | — | | VII.L23 | lemma | LT Axiom Verification | tau-e | form | | VII.L24 | lemma | Lattice Closure | tau-e | form | | VII.L25 | lemma | Minimality Witness | tau-e | form | | VII.L26 | lemma | Dignity Witness | tau-e | form | | VII.L27 | lemma | Sheaf Gluing Verification | tau-e | form | | VII.L28 | lemma | Operator Graph Completeness | tau-e | form | | VII.L29 | lemma | F Lattice Completeness | tau-e | form | | VII.L30 | lemma | CI Uniqueness Derivation | tau-e | form | | VII.L31 | lemma | OR1+OR2 Narrowing | tau-e | form | | VII.L32 | lemma | OR3+OR4 Narrowing | tau-e | form | | VII.L33 | lemma | OR5+OR6 Narrowing | tau-e | form | | VII.R53 | remark | Archetypes-CI j-Closure Bridge | tau-e | — | | VII.R54 | remark | Book II j-Closure Consistency | tau-e | — | | VII.R55 | remark | Part I Imports Cross-Book Check | tau-e | — | | VII.L34 | lemma | Archetypal Basis Completeness | tau-e | form | | VII.L35 | lemma | Social Base Space Well-Definedness | tau-e | form | | VII.L36 | lemma | Recognition Topology Generation | tau-e | form | | VII.L37 | lemma | Social Sheaf Construction | tau-e | form | | VII.L38 | lemma | Collective Intentionality as Glued Section | tau-e | form | | VII.L39 | lemma | Power Morphism Well-Typed | tau-e | form | | VII.L40 | lemma | Legitimacy Sheaf Connection | tau-e | form | | VII.L41 | lemma | Legitimacy Dignity Connection | tau-e | form | | VII.L42 | lemma | Legitimacy from CI | tau-e | form | | VII.L43 | lemma | Ritual Gluing Well-Defined | tau-e | form | | VII.L44 | lemma | Rite of Passage as Boundary Crossing | tau-e | form | | VII.R56 | remark | BH Basin Cross-Book Consistency | tau-e | — | | VII.R57 | remark | Genesis-Kernel Cross-Book Consistency | tau-e | — | | VII.D91 | definition | One Free Choice | conje | — | | VII.D92 | definition | Four-Operator Consequence Architecture | conje | — | | VII.R58 | remark | Layer-Conflation Diagnostic | conje | — |