Registry — Book VII: Categorical Metaphysics

VII.R01 E₃ Enrichment Positioning remark VII.R02 E₃ Import Contract remark VII.D01 Empirical Register definition VII.D02 Practical Register definition VII.D03 Diagrammatic Register definition VII.D04 Commitment Register definition VII.T01 Register Independence Theorem theorem VII.D05 MetaDecode Operator definition VII.D06 Metaphysics Loop Class definition VII.T02 E₃ Non-Emptiness theorem VII.L01 BH Basin Law-Code lemma VII.D07 Metaphysics Sector S_E definition VII.D08 Metaphysics Sector S_P definition VII.D09 Metaphysics Sector S_D definition VII.D10 Metaphysics Sector S_C definition VII.D11 Logos Sector S_L definition VII.T03 Sector Decomposition at E₃ theorem VII.P01 Sector Independence at E₃ proposition VII.D12 Sector Witness Bundle definition VII.D13 Sector Vacuum definition VII.D14 Sector Normaliser definition VII.L02 Shadow Soundness Lemma lemma VII.T04 Rigidity Corollary theorem VII.L03 Non-Emptiness at Each Layer lemma VII.L04 Strictness Between Layers lemma VII.T05 Canonical Ladder Theorem theorem VII.P02 Seven-Book Partition proposition VII.L05 No-New-Lobe Lemma lemma VII.L06 No-New-Crossing-Mediator Lemma lemma VII.L07 Carrier Closure Lemma lemma VII.T06 Saturation Theorem theorem VII.P03 Four-Orbit Implies Four-Layer proposition VII.D15 Bounded Witness Form definition VII.T07 Gödel Avoidance Theorem theorem VII.P04 No-Diagonal Principle proposition VII.D16 Archetype as Minimal j-Closed Fixed Point definition VII.D17 Archetype Extractor Protocol definition VII.L08 j-Closure Minimality lemma VII.T08 Archetype Existence theorem VII.D18 Boundary Archetype definition VII.P05 Boundary Archetype Minimality proposition VII.D19 Mitigation Archetype definition VII.D20 Meta-Framing Archetype definition VII.D21 Synchronicity as Kernel Invariant definition VII.T09 Cross-Register Correlation theorem VII.D22 Readout Functor definition VII.T10 Readout Functor Faithfulness theorem VII.D23 Relational Primacy Principle definition VII.R03 Historical Precursors to Relational Ontology remark VII.D24 τ-Kernel Philosophical Summary definition VII.R04 Axiom-Philosophy Correspondence remark VII.D25 Internal Set Ontology definition VII.D26 Ontic/Virtual Distinction definition VII.R05 ZFC-as-VM Philosophical Import remark VII.D27 Truth-Maker in τ (Ontological) definition VII.T11 Coherence-Correspondence Unification theorem VII.R06 Possible Worlds as Internal Domains remark VII.D28 Derived Geometry definition VII.R07 Geometry as Consequence remark VII.D29 τ³ Philosophical Framing definition VII.R08 Central Theorem Philosophical Import remark VII.D30 Bulk-Boundary Duality definition VII.D31 Law as Admissible Continuation definition VII.T12 Operator Realism theorem VII.D32 Causation as Constrained Composition definition VII.P06 Temporal Ordering from Persistence proposition VII.D33 τ-Modal Operators definition VII.T13 Modal Logic Soundness in τ theorem VII.D34 Identity as Address Persistence definition VII.R09 Panta Rhei with Invariants remark VII.D35 Mereological Composition as Colimit definition VII.P07 Special Composition Answer proposition VII.D36 Abstract Object as Structural Position definition VII.R10 Platonism-Nominalism Dissolution remark VII.D37 Six Ontic Requirements definition VII.T14 Inevitability Convergence theorem VII.P08 Each Requirement Independently Necessary proposition VII.D38 Problem Map Classification Scheme definition VII.R11 Problem Map Table remark VII.D39 Three-Layer Solipsism Resolution definition VII.T15 Bayesian Exclusion of Solipsism theorem VII.D40 Non-Dualistic Platonism definition VII.D41 ω-Uniqueness Principle definition VII.T16 ω-Uniqueness theorem VII.R12 Discovery-Invention Dissolution remark VII.D42 Knowledge as Section definition VII.T17 Gettier Dissolution theorem VII.D43 Justification as Gluing definition VII.P09 Underdetermination as Cover Failure proposition VII.D44 Perception Functor definition VII.D45 Temporal Experience Structure definition VII.R13 Husserl-τ Correspondence remark VII.P10 Perspectival Gluing Grounds Objectivity proposition VII.R14 Intersubjectivity Conditions remark VII.R15 Embodiment as Self-Boundary remark VII.T18 Ontology-Epistemology Collapse theorem VII.R16 Consequences for Traditional Epistemology remark VII.R17 Empirical Sector Summary remark VII.D46 Pre-Symbolic Resonance definition VII.D47 Aesthetic Functional definition VII.T19 Beauty as Invariance theorem VII.R18 Beauty Across Domains remark VII.D48 Elegance as Minimal Tension definition VII.R19 Style as Categorical Invariant remark VII.R20 Golden Ratio as Kernel Shadow remark VII.P11 Fractal Beauty as Scale Invariance proposition VII.D49 Musical Consonance as Ratio Invariance definition VII.R21 Visual Composition Principles remark VII.R22 Architecture as Spatial Aesthetics remark VII.P12 Creation as Defect Minimization proposition VII.D50 The Sublime as Comprehension Boundary definition VII.R23 Kant's Sublime in Categorical Terms remark VII.R24 Environmental Beauty remark VII.D51 Language Adds Temporalization definition VII.D52 Subsymbolic Layer definition VII.D53 Temporalization Operators definition VII.T20 Language as Self-Enrichment theorem VII.T21 Syntax-Semantics Collapse theorem VII.P13 Universal Bridgeability proposition VII.D54 Pragmatic Update Operator definition VII.R25 Translation as Functor remark VII.R26 Meaning Drift as Perturbation remark VII.R27 Public Language as Infrastructure remark VII.D55 Para-Mind definition VII.P14 LLM as Subsymbolic Evidence proposition VII.D56 Prayer as ω-Addressed Communication definition VII.R28 Prayer Across Traditions remark VII.D57 Boolean Micro-Logic definition VII.T22 Single-Address Classical Logic theorem VII.D58 Bayesian Meso-Logic definition VII.T23 Scale-Dependent Logic Theorem theorem VII.D59 Internal Randomness definition VII.P15 Randomness as Internal Complexity proposition VII.T24 No External Randomness theorem VII.T25 Kolmogorov Representation theorem VII.T26 Inference from Kernel Structure theorem VII.D60 Truth-Maker in τ (Logical) definition VII.D61 Truth-Bearer as Section definition VII.T27 Alethic Unification theorem VII.P16 Alethic Pluralism proposition VII.D62 Modal Frame in τ definition VII.D63 Accessibility Morphism definition VII.T28 Kripke Soundness in τ theorem VII.L09 Modal Collapse Prevention lemma VII.D64 Paraconsistent Boundary Logic definition VII.T29 No-Explosion at Boundaries theorem VII.L10 Truth4 Paraconsistency lemma VII.R29 Diagrammatic Sector Summary remark VII.D65 Dignity as Label-Independence definition VII.T30 Dignity Universality theorem VII.D66 CI as Naturality Constraint definition VII.T31 CI-Sheaf Equivalence theorem VII.T32 No-Conflict Theorem theorem VII.L11 Duty Typing Lemma lemma VII.P17 Trolley Resolution proposition VII.D67 Fairness Protocol definition VII.P18 Fairness from CI proposition VII.D68 Moral Monodromy definition VII.T33 Monodromy as Source of Tragedy theorem VII.D69 Four Ethical Tests definition VII.P19 Ethical Defect Minimization proposition VII.P20 Animal Dignity from Distinction proposition VII.R30 Graduated Dignity Scale remark VII.R31 Intergenerational Obligations remark VII.D70 Character as Ethical Fixed Point definition VII.T34 Flourishing as Global Section theorem VII.R32 Applied Ethics Domains remark VII.D71 CI Operator Graph definition VII.T35 CI as j-Closed Fixed Point theorem VII.L12 CI Minimality Lemma lemma VII.T36 Kernel Theorem (K) theorem VII.T37 Semantic Object Construction (S) theorem VII.P21 CI Uniqueness Conjecture proposition VII.L13 First Bombshell Lemma lemma VII.D72 Commitment Register Admissibility definition VII.T38 C Register Independence theorem VII.D73 Kant-τ Correspondence definition VII.R33 Kant's Three Methodological Rules remark VII.D74 Earned/Unearned Ethics Framework definition VII.P22 Pseudo-Paradox from Type Violation proposition VII.D75 Register-Enrichment Correspondence definition VII.R34 Kant's Heroic Restraint remark VII.D76 Social Ontology definition VII.D77 Sphere as Shared Topos definition VII.R35 Sloterdijk-τ Correspondence remark VII.P23 Dunbar Limit as Carrier Capacity proposition VII.R36 Urban Topology remark VII.R37 Architecture as Cultural Readout remark VII.R38 Cultural Lineage as Code Stream remark VII.D78 Capital Network definition VII.P24 Fragmentation as Gluing Failure proposition VII.R39 Individuation as Structural Process remark VII.D79 Nine Global Spheres Classification definition VII.D80 Power as Morphism Structure definition VII.P25 Legitimacy as Recognition Coherence proposition VII.D81 Ritual as Social Gluing definition VII.R40 Religion as Readout Functor remark VII.D82 Mind as Internal Topos definition VII.T39 Mind-Topos Structure Theorem theorem VII.D83 Story Functor definition VII.T40 Narrative Identity as Functor theorem VII.T41 Consciousness as Global Section theorem VII.L14 Binding as Gluing lemma VII.D84 Intentionality as Morphism definition VII.D85 Qualia as Internal Morphisms definition VII.R41 Hard Problem Reformulated remark VII.T42 Self-Recognition as E₃ Operator theorem VII.T43 Free Will as Branching theorem VII.P26 Compatibilism Dissolution proposition VII.P27 Identity as Address Persistence (Mind) proposition VII.R42 Artificial Mind Criteria remark VII.R43 Metzinger-τ Comparison remark VII.T44 Emotions as Register-Crossings theorem VII.L15 Affect as Subsymbolic Pressure lemma VII.P28 Extended Mind as Carrier Extension proposition VII.R44 Commitment Sector Summary remark VII.D86 Logos Sector definition VII.T45 Logos Sector Uniqueness theorem VII.D87 D→C Bridge Functor definition VII.T46 Bridge Equivalence at S_L theorem VII.L16 Register Preservation lemma VII.P29 Four-Register Convergence at S_L proposition VII.D88 Mediator Fixed-Point Basin definition VII.R45 Logos Synchronicity remark VII.D89 Subject-Tool Collapse definition VII.T47 No Forced Stance theorem VII.R46 Crown Jewel of 2nd Edition remark VII.R47 Methodological Override Rules remark VII.D90 Generative Switch definition VII.T48 Layer-Conflation as Category Error theorem VII.R48 Archetypal Genesis Reading remark VII.R49 Genesis Synthesis remark VII.L17 Register Orthogonality lemma VII.L18 Enrichment Monotonicity lemma VII.L19 E₃ Uniqueness lemma VII.P30 Register Completeness proposition VII.L20 Crossing Point Uniqueness lemma VII.L21 Carrier Exhaustion lemma VII.L22 Bounded Witness Form Check lemma VII.P31 Enrichment Stabilization proposition VII.R50 Ladder–Saturation Bridge remark VII.R51 E₃–Consciousness Consistency remark VII.R52 Sector–Register Correspondence remark VII.L23 LT Axiom Verification lemma VII.L24 Lattice Closure lemma VII.L25 Minimality Witness lemma VII.L26 Dignity Witness lemma VII.L27 Sheaf Gluing Verification lemma VII.L28 Operator Graph Completeness lemma VII.L29 F Lattice Completeness lemma VII.L30 CI Uniqueness Derivation lemma VII.L31 OR1+OR2 Narrowing lemma VII.L32 OR3+OR4 Narrowing lemma VII.L33 OR5+OR6 Narrowing lemma VII.R53 Archetypes-CI j-Closure Bridge remark VII.R54 Book II j-Closure Consistency remark VII.R55 Part I Imports Cross-Book Check remark VII.L34 Archetypal Basis Completeness lemma VII.L35 Social Base Space Well-Definedness lemma VII.L36 Recognition Topology Generation lemma VII.L37 Social Sheaf Construction lemma VII.L38 Collective Intentionality as Glued Section lemma VII.L39 Power Morphism Well-Typed lemma VII.L40 Legitimacy Sheaf Connection lemma VII.L41 Legitimacy Dignity Connection lemma VII.L42 Legitimacy from CI lemma VII.L43 Ritual Gluing Well-Defined lemma VII.L44 Rite of Passage as Boundary Crossing lemma VII.R56 BH Basin Cross-Book Consistency remark VII.R57 Genesis-Kernel Cross-Book Consistency remark VII.D91 One Free Choice definition VII.D92 Four-Operator Consequence Architecture definition VII.R58 Layer-Conflation Diagnostic remark VII.T49 Mitigation Archetype j-Closure theorem