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Registry Dashboard — Book VII: Categorical Metaphysics

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 VII has 274 objects across all types; this dashboard enumerates 273 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 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 —

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