This dashboard provides a complete inventory and formalization status map for Book V: Categorical Macrocosm. It covers gravity, cosmology, the dark sector, and the falsification predictions. 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 V Registry Dashboard
Generated: 2026-03-10
Statistics
- Total objects: 1253
-
By type: corollary: 20 definition: 321 lemma: 5 proposition: 188 remark: 459 theorem: 260 -
Formalization: formalized: 884 not_applicable: 303 planned: 33 skeleton: 33 -
Scope: conjectural: 109 established: 11 framework: 1 metaphorical: 7 tau-effective: 1125
Dependency Summary
- Max chain depth: 72 (V.P111)
- Most depended-on: V.T85 (15 uses), V.T192 (10 uses), V.D232 (9 uses)
- No dependencies (foundational): V.R04, V.T06, V.R05, V.R06, V.R07, V.D12, V.R08, V.D13, V.R09, V.D14 …
Part Coverage
| Part | Objects | Formalized | Planned | N/A | |——|———|————|———|—–| | 0 | 16 | 8 | 2 | 6 | | 1 | 91 | 63 | 2 | 24 | | 2 | 158 | 132 | 0 | 25 | | 3 | 89 | 75 | 0 | 12 | | 4 | 109 | 81 | 2 | 26 | | 5 | 300 | 228 | 0 | 63 | | 6 | 313 | 205 | 7 | 84 | | 7 | 89 | 58 | 0 | 31 | | 8 | 72 | 20 | 20 | 32 | | part03 | 10 | 9 | 0 | 0 | | part05 | 6 | 5 | 0 | 0 |
Object List
| ID | Type | Name | Scope | Lean |
|—-|——|——|——-|——|
| V.R04 | remark | The cross-couplings bind the halves | tau-e | form |
| V.T06 | theorem | Fiber Completeness — IV.T32 | tau-e | form |
| V.R05 | remark | The Temporal Complement as test case | tau-e | form |
| V.R06 | remark | The exponent pattern | tau-e | — |
| V.R07 | remark | No scope inflation | tau-e | — |
| V.D12 | definition | Book~IV to Book~V Export Contract | tau-e | form |
| V.R08 | remark | Contract discipline | tau-e | — |
| V.D13 | definition | OnticParticle — IV.D22 | tau-e | form |
| V.R09 | remark | Six, not five, cross-couplings | tau-e | — |
| V.D14 | definition | Defect Tuple — IV.D20 | tau-e | form |
| V.T07 | theorem | Mass Ratio — IV.T30 | tau-e | form |
| V.R10 | remark | No further open items | tau-e | — |
| V.R11 | remark | Comparison with Book~IV | tau-e | — |
| V.R12 | remark | The Book~V–Book~VI boundary | tau-e | form |
| V.D15 | definition | Base Circle tau^1 (Macroscopic) | tau-e | form |
| V.R13 | remark | Why circle''? | tau-e | — |
| V.R14 | remark | Temporal = gravitational + weak | tau-e | — |
| V.D16 | definition | Alpha-Tick | tau-e | form |
| V.R15 | remark | Ticks are not uniform | tau-e | form |
| V.D17 | definition | Proper Time (Arc Length) | tau-e | form |
| V.T08 | theorem | Time Derivation Theorem | tau-e | form |
| V.R16 | remark | The chart-level continuum | tau-e | form |
| V.P03 | proposition | Arrow of Time = Orbit Direction | tau-e | form |
| V.D18 | definition | Causal Ordering Relation | tau-e | form |
| V.R17 | remark | Spacelike separation on T^2 | tau-e | form |
| V.T09 | theorem | Causal Ordering Theorem | tau-e | form |
| V.R18 | remark | Causality precedes light cones | tau-e | — |
| V.D19 | definition | Geodesic Duration | tau-e | form |
| V.R19 | remark | Duration is not clock time | tau-e | form |
| V.R20 | remark | Two metrics, one space | tau-e | — |
| V.T10 | theorem | Bounded Time Theorem | tau-e | form |
| V.R21 | remark | Finite but unbounded in tick count | tau-e | form |
| V.R22 | remark | alpha_o and omega | tau-e | — |
| V.R23 | remark | No Background Time | tau-e | — |
| V.D20 | definition | Three Temporal Epochs | tau-e | form |
| V.R24 | remark | Epochs are structural, not anthropic | tau-e | — |
| V.D21 | definition | Ignition Depth | tau-e | form |
| V.R25 | remark | Ignition is not a phase transition | tau-e | form |
| V.T11 | theorem | Epoch Existence Theorem | tau-e | form |
| V.P04 | proposition | Pre-Temporal Indistinguishability | tau-e | form |
| V.R26 | remark | The pre-temporal epoch is notempty’’ | tau-e | — |
| V.D22 | definition | Sigma-Now Hypersurface | tau-e | form |
| V.R27 | remark | Simultaneity Is Structural | tau-e | — |
| V.R28 | remark | Foliation versus block universe | tau-e | — |
| V.T12 | theorem | Now-Within-Epoch Theorem | tau-e | form |
| V.R29 | remark | Selection without observers | tau-e | form |
| V.D23 | definition | Coherence Horizon | tau-e | form |
| V.R30 | remark | Completion versus termination | tau-e | — |
| V.P05 | proposition | Mode Counting at Early Depths | tau-e | form |
| V.D24 | definition | Maximal Coupling Condition | tau-e | form |
| V.D25 | definition | Opening Regime | tau-e | form |
| V.R31 | remark | No Initial Singularity | tau-e | — |
| V.T13 | theorem | Opening Regime Theorem | tau-e | form |
| V.R32 | remark | No Past Hypothesis needed — reprise | tau-e | — |
| V.D26 | definition | Refinement Progression Rate | tau-e | form |
| V.R33 | remark | Inflation as Progression | tau-e | form |
| V.D27 | definition | Null Intertwiner (Photon) | tau-e | form |
| V.R34 | remark | Photons do not travel'' | tau-e | — |
| V.T14 | theorem | Photon Existence Theorem | tau-e | form |
| V.P06 | proposition | Null Character Uniqueness | tau-e | form |
| V.D28 | definition | Operational Distance | tau-e | form |
| V.T15 | theorem | Distance-Duration Duality | tau-e | form |
| V.R35 | remark | The speed of light is notfast’’ | tau-e | form |
| V.D29 | definition | Refinement Drift (Redshift) | tau-e | form |
| V.R36 | remark | No Doppler Explanation | tau-e | — |
| V.T16 | theorem | Redshift-Depth Relation | tau-e | form |
| V.D30 | definition | Readout Expansion | tau-e | form |
| V.R37 | remark | What expands? | tau-e | — |
| V.D31 | definition | Hubble Readout Parameter | tau-e | form |
| V.R38 | remark | No Dark Energy Needed | tau-e | form |
| V.R39 | remark | Causality sharpened | tau-e | — |
| V.D32 | definition | Distance readout functor | tau-e | form |
| V.R40 | remark | Distance is operational | tau-e | form |
| V.T17 | theorem | Distance Ladder Translation | tau-e | form |
| V.R41 | remark | Gaia and the tau-readout | tau-e | form |
| V.D33 | definition | Cepheid readout calibrator | tau-e | form |
| V.R42 | remark | The Chandrasekhar limit in tau | tau-e | — |
| V.D34 | definition | BAO standard ruler | tau-e | form |
| V.T18 | theorem | Hubble Tension Resolution | tau-e | form |
| V.R43 | remark | Quantitative prediction | tau-e | — |
| V.D35 | definition | Readout curvature | conje | form |
| V.T19 | theorem | Dark Energy Artifact — First Pass | conje | form |
| V.R44 | remark | Scope and deferral | tau-e | form |
| V.R45 | remark | Forward reference to Part~V | tau-e | — |
| V.D36 | definition | Recombination orbit depth | tau-e | form |
| V.R46 | remark | No new physics in the definition | tau-e | — |
| V.D37 | definition | CMB constraint surface | tau-e | form |
| V.P07 | proposition | CMB multipoles as boundary characters | tau-e | form |
| V.R47 | remark | No new information, new interpretation | tau-e | form |
| V.P08 | proposition | Blackbody as coherence equilibrium | tau-e | form |
| V.D38 | definition | Neutrino decoupling orbit depth | tau-e | form |
| V.D39 | definition | CnuB echo surface | tau-e | form |
| V.R48 | remark | No new prediction for T_mathrmC | tau-e | form |
| V.P09 | proposition | CnuB mass constraint | tau-e | form |
| V.R49 | remark | Two constraint surfaces, one algebra | tau-e | — |
| V.R50 | remark | Testability | tau-e | — |
| V.D40 | definition | Cosmic Stack API | tau-e | form |
| V.R51 | remark | Why an API metaphor | tau-e | — |
| V.R52 | remark | Scope census | tau-e | form |
| V.R53 | remark | Gravity is not a force on the fiber | tau-e | — |
| V.D41 | definition | Clopen frame | tau-e | form |
| V.P10 | proposition | Frame transitions are boundary-determined | tau-e | form |
| V.R54 | remark | No connection needed | tau-e | — |
| V.D42 | definition | Frame holonomy on tau^1 | tau-e | form |
| V.T20 | theorem | Gravity as frame holonomy gap | tau-e | form |
| V.R55 | remark | Comparison with gauge holonomy | tau-e | — |
| V.D43 | definition | Holonomy gap element | tau-e | form |
| V.P11 | proposition | Gap refinement coherence | tau-e | form |
| V.D44 | definition | Torus vacuum — V.D01 | tau-e | form |
| V.T21 | theorem | Vacuum shape ratio — V.T01 | tau-e | form |
| V.D45 | definition | Gravitational constant — V.D02 | tau-e | form |
| V.T22 | theorem | G derivation — V.D02 | tau-e | form |
| V.R56 | remark | Lean formalization | tau-e | form |
| V.D46 | definition | Gravitational coupling kappa_tau | tau-e | form |
| V.C01 | corollary | Temporal Complement, revisited | tau-e | form |
| V.T23 | theorem | sigma-equivariance of kappa_tau | tau-e | form |
| V.R57 | remark | Equivalence principle as theorem | tau-e | — |
| V.T24 | theorem | Lorentz covariance theorem | tau-e | form |
| V.R58 | remark | Not a postulate | tau-e | — |
| V.D47 | definition | Null intertwiner | tau-e | form |
| V.P12 | proposition | Light cone is Lorentz-invariant | tau-e | form |
| V.R59 | remark | The photon is a null intertwiner, not a particle | tau-e | form |
| V.P13 | proposition | Speed barrier as constraint saturation | tau-e | form |
| V.R60 | remark | No relativistic mass'' | tau-e | — |
| V.D48 | definition | Local tau^3 chart | tau-e | form |
| V.T25 | theorem | Minkowski as chart shadow --- cf. III.D76 | tau-e | form |
| V.R61 | remark | Riemannian geometry as patching | tau-e | — |
| V.R62 | remark | Ontological priority | tau-e | — |
| V.C02 | corollary | Relativity principle recovered | tau-e | form |
| V.R63 | remark | Michelson--Morley explained | tau-e | — |
| V.D49 | definition | Curvature character --- V.D04 | tau-e | form |
| V.D50 | definition | Matter character --- V.D03 | tau-e | form |
| V.R64 | remark | Three sectors, not four | tau-e | — |
| V.D51 | definition | tau-Einstein equation --- V.D06 | tau-e | form |
| V.R65 | remark | The GR coupling kappa_tau --- V.D05 | tau-e | form |
| V.T26 | theorem | Chart shadow recovery | tau-e | form |
| V.R66 | remark | The 8pi factor | tau-e | — |
| V.T27 | theorem | Well-posedness via Hartogs | tau-e | form |
| V.R67 | remark | Singularities are chart artifacts | tau-e | form |
| V.C03 | corollary | tau-Bianchi identity --- V.R01 | tau-e | form |
| V.R68 | remark | No admissible refinement without compensation | tau-e | form |
| V.D52 | definition | Linearized tau-Einstein equation | tau-e | form |
| V.T28 | theorem | Newtonian limit recovery | tau-e | form |
| V.R69 | remark | Newton from tau | tau-e | — |
| V.T29 | theorem | Mercury precession from tau-Einstein | tau-e | form |
| V.R70 | remark | No fitting | tau-e | form |
| V.T30 | theorem | Light deflection from tau-Einstein | tau-e | form |
| V.T31 | theorem | Gravitational redshift from tau-Einstein | tau-e | form |
| V.D53 | definition | Gravitational wave in tau-framework | tau-e | form |
| V.T32 | theorem | Gravitational wave properties | tau-e | form |
| V.R71 | remark | Two polarizations from two fiber directions | tau-e | form |
| V.R72 | remark | Inspiral phase is linear | tau-e | — |
| V.P14 | proposition | v_mathrmGW | tau-e | form |
| V.R73 | remark | Graviton mass is zero | tau-e | — |
| V.R74 | remark | The honest claim | tau-e | — |
| V.D54 | definition | Cocycle defect | tau-e | form |
| V.D55 | definition | tau-NF Einstein iteration | tau-e | form |
| V.R75 | remark | No approximation | tau-e | — |
| V.D56 | definition | Truncation-coherent descent | tau-e | form |
| V.T33 | theorem | Existence | tau-e | form |
| V.T34 | theorem | Uniqueness | tau-e | form |
| V.T35 | theorem | Selection | tau-e | form |
| V.R76 | remark | Comparison with orthodox gauge freedom | tau-e | — |
| V.R77 | remark | Whyaddress’’? | tau-e | form |
| V.P15 | proposition | Convergence in all regimes | tau-e | form |
| V.T36 | theorem | Density cap | tau-e | form |
| V.D57 | definition | Density-saturated character | tau-e | form |
| V.P16 | proposition | Saturation replaces singularity | tau-e | form |
| V.R78 | remark | Comparison with other singularity resolutions | tau-e | — |
| V.D58 | definition | Null intertwiner | tau-e | form |
| V.D59 | definition | Present surface | tau-e | form |
| V.D60 | definition | tau-Horizon | tau-e | form |
| V.T37 | theorem | Horizon as present-surface contraction | tau-e | form |
| V.R79 | remark | No Cauchy horizon instability | tau-e | — |
| V.R80 | remark | Extremal black holes | tau-e | form |
| V.R81 | remark | Forward references | tau-e | — |
| V.D61 | definition | Torus vacuum — V.D01 | tau-e | form |
| V.T38 | theorem | Vacuum shape ratio — V.T01 | tau-e | form |
| V.R82 | remark | Torus, not sphere | tau-e | form |
| V.D62 | definition | Gravitational constant — V.D02 | tau-e | form |
| V.P17 | proposition | G_tau well-defined — V.P01 | tau-e | form |
| V.R83 | remark | Why iota_tau^2, not iota_tau | tau-e | — |
| V.T39 | theorem | Schwarzschild as readout | tau-e | form |
| V.R84 | remark | The Birkhoff theorem in tau | tau-e | — |
| V.P18 | proposition | Schwarzschild regularity | tau-e | form |
| V.R85 | remark | The torus core | tau-e | form |
| V.D63 | definition | Geometric relaxation | tau-e | form |
| V.D64 | definition | Topological relaxation | tau-e | form |
| V.R86 | remark | Observational signature | tau-e | — |
| V.T40 | theorem | The tau-Schwarzschild relation — V.D08 | tau-e | form |
| V.D65 | definition | BH evolution modes — V.D09 | tau-e | form |
| V.T41 | theorem | No-Shrink — V.T03, preview | tau-e | form |
| V.R87 | remark | Hawking evaporation forbidden — V.R02 | tau-e | form |
| V.R88 | remark | Chandrasekhar limit as maturity threshold — V.R02 | tau-e | form |
| V.D66 | definition | Spherical carrier predicate | tau-e | form |
| V.R89 | remark | Spherical neq static | tau-e | form |
| V.D67 | definition | Equilibrium carrier | tau-e | form |
| V.D68 | definition | GR tension functional | tau-e | form |
| V.P19 | proposition | Tension bounds | tau-e | form |
| V.D69 | definition | Tension profile | tau-e | form |
| V.D70 | definition | Canonical star builder | tau-e | form |
| V.T42 | theorem | Star builder existence and uniqueness | tau-e | form |
| V.R90 | remark | The star builder as constructive proof | tau-e | form |
| V.D71 | definition | Neutron node | tau-e | form |
| V.D72 | definition | Node density and confinement tension | tau-e | form |
| V.P20 | proposition | TOV balance as tension equilibrium | tau-e | form |
| V.R91 | remark | Not an ODE | tau-e | form |
| V.D73 | definition | EW-stable node | tau-e | form |
| V.T43 | theorem | Neutron node EW stability | tau-e | form |
| V.P21 | proposition | Truncation invariance of the star builder | tau-e | form |
| V.D74 | definition | Chandrasekhar threshold | tau-e | form |
| V.T44 | theorem | Chandrasekhar limit | tau-e | form |
| V.R92 | remark | No free parameter | tau-e | form |
| V.R93 | remark | The TOV maximum mass | tau-e | form |
| V.D75 | definition | GR Tension Functional | tau-e | form |
| V.D76 | definition | Coherence Horizon | tau-e | form |
| V.L01 | lemma | Surface Matter Bound | tau-e | form |
| V.T45 | theorem | Tension Monotonicity | tau-e | form |
| V.R94 | remark | No tension maximum'' | tau-e | form |
| V.T46 | theorem | Structural Threshold --- Forced Topology Relaxation | tau-e | form |
| V.C04 | corollary | TOV Limit | tau-e | form |
| V.R95 | remark | Chandrasekhar limit as the electron-degenerate case | tau-e | form |
| V.D77 | definition | Topology Crossing Event | tau-e | form |
| V.T47 | theorem | Topology Crossing Admissibility | tau-e | form |
| V.R96 | remark | No singularity | tau-e | form |
| V.R97 | remark | Comparison with Penrose's trapped surface theorem | tau-e | — |
| V.T48 | theorem | Defect Cost Jump at Phase Boundary | tau-e | form |
| V.R98 | remark | Defect minimization drives topology selection | tau-e | form |
| V.R99 | remark | Observational tests | tau-e | form |
| V.D78 | definition | Calibration Constant Xi_tau | tau-e | form |
| V.P22 | proposition | Xi_tau is refinement-stable | tau-e | form |
| V.R100 | remark | No SI units enter Xi_tau | tau-e | form |
| V.D79 | definition | Calibration Triangle | tau-e | form |
| V.T49 | theorem | Micro--Macro Bridge | tau-e | form |
| V.D80 | definition | Ring Homomorphism Phi_p,n | tau-e | form |
| V.P23 | proposition | Phi_p,n | tau-e | form |
| V.R101 | remark | The delta_A thread through the triangle | tau-e | form |
| V.T50 | theorem | Complete Dimensional Bridge | tau-e | form |
| V.R102 | remark | The unit problem in orthodox physics | tau-e | form |
| V.R103 | remark | Planck mass as a derived quantity | tau-e | — |
| V.D81 | definition | Gravitational Closing Identity --- V.D11 | tau-e | form |
| V.T51 | theorem | Spectral Distance --- IV.T11 | tau-e | form |
| V.D82 | definition | Corrected Co-Rotor Coupling --- V.D10 | tau-e | form |
| V.R104 | remark | Scope: c_1 = 3/pi is conjectural | tau-e | form |
| V.T52 | theorem | G Prediction --- V.T04, V.T05 | tau-e | form |
| V.R105 | remark | G is the least precise fundamental constant | tau-e | form |
| V.R106 | remark | The hierarchyproblem’’ dissolved | tau-e | form |
| V.T53 | theorem | R Formula Independence — V.R03 | tau-e | form |
| V.R107 | remark | Two independent predictions | tau-e | form |
| V.T54 | theorem | 10-Link Derivation Chain | tau-e | form |
| V.R108 | remark | The closing identity completes the Hermetic Principle | tau-e | form |
| V.R109 | remark | Open problem: c_1 from first principles | tau-e | form |
| V.R110 | remark | The 7times amplification in R | tau-e | form |
| V.R111 | remark | The explanatory gap | tau-e | — |
| V.R112 | remark | An analogy: pixels and noise | tau-e | form |
| V.T55 | theorem | The Categorical Second Law | tau-e | form |
| V.R113 | remark | Compatibility with Book~IV | tau-e | — |
| V.D83 | definition | Thermodynamic equilibrium—categorical | tau-e | form |
| V.R114 | remark | Not the same as thermal equilibrium | tau-e | — |
| V.P24 | proposition | Defect absorption rate | tau-e | form |
| V.R115 | remark | The role of gravity in ordering | tau-e | — |
| V.P25 | proposition | Weak redistribution preserves defect count | tau-e | form |
| V.L02 | lemma | Geometric contraction of defect support | tau-e | form |
| V.R116 | remark | The contraction rate is the gravitational coupling | tau-e | form |
| V.C05 | corollary | Defect support exhaustion | tau-e | form |
| V.D84 | definition | Coherence horizon | tau-e | form |
| V.R117 | remark | Circulation, not stasis | tau-e | — |
| V.P26 | proposition | The 180^circ inversion | tau-e | form |
| V.R118 | remark | Orbit steps versus physical time | tau-e | form |
| V.D85 | definition | Defect partition of paths | tau-e | form |
| V.D86 | definition | Defect entropy | tau-e | form |
| V.D87 | definition | Refinement entropy | tau-e | form |
| V.T56 | theorem | Entropy splitting | tau-e | form |
| V.R119 | remark | Why varepsilon is harmless | tau-e | — |
| V.T57 | theorem | Defect entropy is bounded | tau-e | form |
| V.T58 | theorem | Defect entropy is monotonically decreasing | tau-e | form |
| V.C06 | corollary | Defect entropy reaches zero | tau-e | form |
| V.T59 | theorem | Refinement entropy grows without bound | tau-e | form |
| V.R120 | remark | The paradox resolved | tau-e | form |
| V.P27 | proposition | Readout projects onto total entropy | tau-e | form |
| V.R121 | remark | The 99.99% that is noise | tau-e | form |
| V.P28 | proposition | iota_tau controls the splitting ratio | tau-e | form |
| V.P29 | proposition | Defect entropy from defect functional | tau-e | form |
| V.R122 | remark | The Penrose puzzle | tau-e | — |
| V.P30 | proposition | Finite initial defect count | tau-e | form |
| V.R123 | remark | Contrast with QFT | tau-e | form |
| V.D88 | definition | Global defect budget | tau-e | form |
| V.T60 | theorem | Finite defect budget | tau-e | form |
| V.L03 | lemma | Integer threshold | tau-e | form |
| V.T61 | theorem | Global Defect Exhaustion | tau-e | form |
| V.D89 | definition | Coherence horizon—refined | tau-e | form |
| V.R124 | remark | Orbit steps are not years | tau-e | form |
| V.C07 | corollary | Finite irreversibility | tau-e | form |
| V.R125 | remark | Contrast with heat death | tau-e | — |
| V.P31 | proposition | Vacuum circulation is periodic | tau-e | form |
| V.P32 | proposition | No Poincar’e recurrence conflict | tau-e | form |
| V.T62 | theorem | Master exhaustion inequality | tau-e | form |
| V.D90 | definition | Defect half-life | tau-e | form |
| V.R126 | remark | Universal half-life | tau-e | form |
| V.P33 | proposition | The arrow has an endpoint | tau-e | form |
| V.R127 | remark | Time continues; the arrow does not | tau-e | — |
| V.R128 | remark | The artificial trichotomy | tau-e | form |
| V.D91 | definition | EM energy transport | tau-e | form |
| V.P34 | proposition | Radiation is B-sector transport | tau-e | form |
| V.P35 | proposition | Conduction is near-field B-sector transport | tau-e | form |
| V.P36 | proposition | Convective transport is B-sector displacement | tau-e | form |
| V.T63 | theorem | alpha governs macroscopic energy transport | tau-e | form |
| V.R129 | remark | Why alpha and not iota_tau^2 | tau-e | form |
| V.D92 | definition | Geometric relaxation | tau-e | form |
| V.D93 | definition | Topological relaxation | tau-e | form |
| V.P37 | proposition | Hierarchy of relaxation times | tau-e | form |
| V.T64 | theorem | Heat is electromagnetism | tau-e | form |
| V.D94 | definition | The tau-vacuum | tau-e | form |
| V.T65 | theorem | Vacuum energy is boundary energy | tau-e | form |
| V.R130 | remark | Why no divergence | tau-e | — |
| V.P38 | proposition | QFT vacuum = refinement sum | tau-e | form |
| V.T66 | theorem | The vacuum catastrophe is a category error | tau-e | form |
| V.C08 | corollary | Vacuum source term is finite | tau-e | form |
| V.R131 | remark | Comparison with normal ordering | tau-e | form |
| V.T67 | theorem | H_partial[omega | tau-e | form |
| V.P39 | proposition | Casimir effect from boundary modes | tau-e | form |
| V.R132 | remark | Casimir does not prove mode summation | tau-e | — |
| V.R133 | remark | Data versus interpretation | tau-e | form |
| V.R134 | remark | Two faces of the same problem | tau-e | form |
| V.T68 | theorem | Defect-driven acceleration | tau-e | form |
| V.D95 | definition | Capacity surplus | tau-e | form |
| V.P40 | proposition | No Lambda in the tau-Einstein equation | tau-e | form |
| V.T69 | theorem | Dark energy is a readout artifact | tau-e | form |
| V.P41 | proposition | The 68% is refinement entropy | tau-e | form |
| V.R135 | remark | Where does the 68% go? | tau-e | form |
| V.R136 | remark | Testability | tau-e | form |
| V.R137 | remark | III.T25 is enrichment-layer independent | tau-e | form |
| V.D96 | definition | Macro defect-transport equation | tau-e | form |
| V.R138 | remark | Fiber contributions are not discarded | tau-e | — |
| V.D97 | definition | Macro tau-Navier–Stokes flow | tau-e | form |
| V.P42 | proposition | Compactness of tau^3 | tau-e | form |
| V.T70 | theorem | Macro three-condition sufficiency | tau-e | form |
| V.T71 | theorem | Macro tau-NS regularity | tau-e | form |
| V.R139 | remark | Contrast with mathbbR | tau-e | — |
| V.C09 | corollary | No temporal blow-up | tau-e | form |
| V.D98 | definition | Macro tau-Reynolds number | tau-e | form |
| V.R140 | remark | The Reynolds number is bounded | tau-e | — |
| V.R141 | remark | Convective overshooting | tau-e | form |
| V.R142 | remark | No singularity at the innermost stable orbit | tau-e | — |
| V.R143 | remark | Honest claim | tau-e | — |
| V.P43 | proposition | Classical NS as readout | tau-e | form |
| V.R144 | remark | The chart domain is compact | tau-e | — |
| V.R145 | remark | Limitations of K41 | tau-e | — |
| V.D99 | definition | tau-turbulent flow | tau-e | form |
| V.T72 | theorem | Macro energy spectrum | tau-e | form |
| V.R146 | remark | The Kolmogorov constant C_K | tau-e | form |
| V.D100 | definition | tau-enstrophy | tau-e | form |
| V.P44 | proposition | Dual cascade decomposition | tau-e | form |
| V.R147 | remark | Batchelor–Kraichnan spectrum | tau-e | form |
| V.P45 | proposition | Vortex stretching bound | tau-e | form |
| V.R148 | remark | She–L’ev^eque formula | tau-e | form |
| V.D101 | definition | Macro charge | tau-e | form |
| V.T73 | theorem | No Isolated Charges | tau-e | form |
| V.R149 | remark | Charge quantization | tau-e | form |
| V.C10 | corollary | Sourceless macro flux | tau-e | form |
| V.R150 | remark | Local charges still exist | tau-e | — |
| V.C11 | corollary | No magnetic monopoles | tau-e | form |
| V.D102 | definition | Macro EM field | tau-e | form |
| V.C12 | corollary | Macro color confinement | tau-e | form |
| V.R151 | remark | Quark-gluon plasma is still confined | tau-e | — |
| V.D103 | definition | Macro current | tau-e | form |
| V.D104 | definition | tau-plasma | tau-e | form |
| V.T74 | theorem | Forced Quasi-Neutrality | tau-e | form |
| V.P46 | proposition | Plasma oscillations | tau-e | form |
| V.P47 | proposition | Plasma cutoff | tau-e | form |
| V.R152 | remark | Ionospheric reflection | tau-e | form |
| V.P48 | proposition | Debye shielding | tau-e | form |
| V.D105 | definition | Debye number | tau-e | form |
| V.R153 | remark | No dark matter in the ICM | tau-e | form |
| V.D106 | definition | MHD limit | tau-e | form |
| V.D107 | definition | tau-MHD system | tau-e | form |
| V.D108 | definition | Magnetic Reynolds number | tau-e | form |
| V.T75 | theorem | Frozen-flux invariant | tau-e | form |
| V.D109 | definition | tau-reconnection event | tau-e | form |
| V.R154 | remark | Sweet–Parker and Petschek | tau-e | — |
| V.P49 | proposition | Reconnection energy bound | tau-e | form |
| V.P50 | proposition | Alfv’en wave dispersion | tau-e | form |
| V.P51 | proposition | Magnetosonic dispersion | tau-e | form |
| V.D110 | definition | MHD instability condition | tau-e | form |
| V.D111 | definition | Mixed-sector mode | tau-e | form |
| V.P52 | proposition | Alfv’en speed as cross-coupling readout | tau-e | form |
| V.R155 | remark | The photon-in-fluid interpretation | tau-e | — |
| V.D112 | definition | Alfv’en orbit | tau-e | form |
| V.R156 | remark | Sufficient energy flux | tau-e | form |
| V.P53 | proposition | ISM Alfv’en cascade | tau-e | form |
| V.P54 | proposition | Crossing preservation | tau-e | form |
| V.D113 | definition | Macro tau-crystal | tau-e | form |
| V.D114 | definition | Macro tau-glass | tau-e | form |
| V.R157 | remark | The glass transition is not a phase transition | tau-e | form |
| V.D115 | definition | First-order macro transition | tau-e | form |
| V.D116 | definition | Second-order macro transition | tau-e | form |
| V.T76 | theorem | Critical surface is codimension 1 | tau-e | form |
| V.R158 | remark | Gaia and crystallization | tau-e | — |
| V.P55 | proposition | Neutron star phase sequence | tau-e | form |
| V.R159 | remark | DDT and turbulence | tau-e | form |
| V.T77 | theorem | Phase-transition universality | tau-e | form |
| V.R160 | remark | Universality is structural, not accidental | tau-e | form |
| V.T78 | theorem | Newtonian Limit — V.T30 | tau-e | form |
| V.R161 | remark | The three conditions quantified | tau-e | form |
| V.P56 | proposition | Capacity Gradient as Apparent Dark Matter — V.P20 | tau-e | form |
| V.D117 | definition | Classical Validity Scale — V.D50 | tau-e | form |
| V.R162 | remark | The MOND scale as proxy | tau-e | form |
| V.T79 | theorem | Two-Regime Readout — V.T31 | tau-e | form |
| V.R163 | remark | No free parameters | tau-e | — |
| V.P57 | proposition | Bertrand as Readout Constraint — V.P21 | tau-e | form |
| V.P58 | proposition | Newton’s First Law as Limit — V.P22 | tau-e | form |
| V.T80 | theorem | Correspondence Tower — V.T32 | tau-e | form |
| V.R164 | remark | The dark matter debate is a projection artifact | tau-e | form |
| V.D118 | definition | Angular Momentum Character — V.D51 | tau-e | form |
| V.T81 | theorem | Rotational Flux Conservation — V.T33 | tau-e | form |
| V.T82 | theorem | Kepler’s First Law — V.T34 | tau-e | form |
| V.T83 | theorem | Kepler’s Second Law — V.T35 | tau-e | form |
| V.R165 | remark | Second law is deeper than the first | tau-e | — |
| V.T84 | theorem | Kepler’s Third Law — V.T36 | tau-e | form |
| V.R166 | remark | Kepler as theorem, not phenomenology | tau-e | — |
| V.P59 | proposition | Perihelion Advance from tau-GR — V.P23 | tau-e | form |
| V.P60 | proposition | Light Deflection from tau-GR — V.P24 | tau-e | form |
| V.P61 | proposition | Shapiro Delay from tau-GR — V.P25 | tau-e | form |
| V.R167 | remark | All three tests pass with zero fitting | tau-e | — |
| V.D119 | definition | Lensing Character — V.D52 | tau-e | form |
| V.R168 | remark | Heliophysics as readout of H_partial[omega | tau-e | — |
| V.P62 | proposition | Solar System Concordance — V.P26 | tau-e | form |
| V.D120 | definition | Galaxy as Relational Coherence — V.D53 | tau-e | form |
| V.R169 | remark | No void between galaxies | tau-e | — |
| V.P63 | proposition | Modified Jeans Scale — V.P27 | tau-e | form |
| V.P64 | proposition | Galaxy Formation Sequence — V.P28 | conje | form |
| V.R170 | remark | Conjectural scope | tau-e | — |
| V.D121 | definition | Cosmic Web as Capacity Skeleton — V.D54 | tau-e | form |
| V.P65 | proposition | Web Determines Galaxy Locations — V.P29 | tau-e | form |
| V.R171 | remark | Filaments are not gravitational wakes | tau-e | — |
| V.D122 | definition | Morphological Capacity Profile — V.D55 | tau-e | form |
| V.R172 | remark | Morphology is not destiny | tau-e | — |
| V.P66 | proposition | Galactic Virial Theorem — V.P30 | tau-e | form |
| V.R173 | remark | Satellite planes and the missing satellite problem | tau-e | — |
| V.D123 | definition | Galactic Capacity Profile — V.D56 | tau-e | form |
| V.T85 | theorem | Flat Rotation Curve Theorem — V.T37 | tau-e | form |
| V.C13 | corollary | Baryonic Tully–Fisher from Capacity — V.R20 | tau-e | form |
| V.P67 | proposition | Galaxy-by-Galaxy Concordance — V.P31 | tau-e | form |
| V.R174 | remark | What conjectural'' means here | tau-e | form |
| V.P68 | proposition | MOND as Capacity Proxy --- V.P32 | tau-e | form |
| V.R175 | remark | MOND as approximation theorem | tau-e | — |
| V.P69 | proposition | No Dark Particle Theorem --- V.P33 | tau-e | form |
| V.R176 | remark | The asymmetry of falsification | tau-e | form |
| V.P70 | proposition | RAR from Capacity Gradient --- V.P34 | tau-e | form |
| V.D124 | definition | Degeneracy Pressure Character --- V.D57 | tau-e | form |
| V.T86 | theorem | Chandrasekhar Mass from tau-Framework --- V.T38 | tau-e | form |
| V.R177 | remark | White dwarf mass--radius relation | tau-e | form |
| V.P71 | proposition | Neutron Star EOS Structure --- V.P35 | tau-e | form |
| V.T87 | theorem | TOV Mass Limit --- V.T39 | tau-e | form |
| V.R178 | remark | The mass gap | tau-e | form |
| V.D125 | definition | Black Hole as Maximal Topological Defect --- V.D58 | tau-e | form |
| V.R179 | remark | No primordial black holes | tau-e | form |
| V.T88 | theorem | Compact-Object Classification --- V.T40 | tau-e | form |
| V.P72 | proposition | Hulse--Taylor Agreement --- V.P36 | tau-e | form |
| V.R180 | remark | Pulsars probe the strong-field regime | tau-e | form |
| V.D126 | definition | Topological Channel --- V.D59 | tau-e | form |
| V.T89 | theorem | Core Collapse Trigger --- V.T41 | tau-e | form |
| V.R181 | remark | The trigger is structural, not thermal | tau-e | form |
| V.D127 | definition | Channel Reversal --- V.D60 | tau-e | form |
| V.P73 | proposition | Neutrino Heating Condition --- V.P37 | tau-e | form |
| V.R182 | remark | Explosion energy and the mass cut | tau-e | form |
| V.P74 | proposition | Plateau Duration as Readout --- V.P38 | tau-e | form |
| V.D128 | definition | r-Process as Rapid Charge Loading --- V.D61 | tau-e | form |
| V.R183 | remark | Gold and the r-process | tau-e | — |
| V.P75 | proposition | Proto-Neutron Star Evolution --- V.P39 | tau-e | form |
| V.P76 | proposition | Birth Kick and Spin --- V.P40 | tau-e | form |
| V.R184 | remark | The carbon connection | tau-e | — |
| V.P77 | proposition | Equatorial focusing | tau-e | form |
| V.D129 | definition | Accretion Funnel (tau-geodesic) | tau-e | form |
| V.R185 | remark | The alpha-viscosity re-read | tau-e | form |
| V.D130 | definition | Jet Axis (Topological Channel) | tau-e | form |
| V.P78 | proposition | Jet-Torus Alignment | tau-e | form |
| V.T90 | theorem | Jet Collimation Theorem | tau-e | form |
| V.R186 | remark | Observational comparison | tau-e | form |
| V.T91 | theorem | Accretion Luminosity Bound | tau-e | form |
| V.R187 | remark | Eddington Limit Re-Read | tau-e | — |
| V.D131 | definition | Synchrotron Readout | tau-e | form |
| V.R188 | remark | The ubiquitous sqrt3 | tau-e | form |
| V.P79 | proposition | Neutrino Emission Channel | tau-e | form |
| V.R189 | remark | IceCube neutrinos from AGN | tau-e | form |
| V.D132 | definition | AGN Lifecycle Phase | tau-e | form |
| V.T92 | theorem | AGN Unification Theorem | tau-e | form |
| V.R190 | remark | Quasar Redshift Distribution | tau-e | form |
| V.R191 | remark | Why the exponent is sim 4 | tau-e | form |
| V.D133 | definition | Binary Coherent-Instance System | tau-e | form |
| V.D134 | definition | GW Boundary-Character Wave | tau-e | form |
| V.R192 | remark | Why two polarizations, not six | tau-e | — |
| V.T93 | theorem | Chirp Mass from Boundary Holonomy | tau-e | form |
| V.P80 | proposition | GW Energy Flux | tau-e | form |
| V.R193 | remark | LIGO GW150914 Re-Read | tau-e | form |
| V.D135 | definition | Ringdown Readout | tau-e | form |
| V.T94 | theorem | Ringdown Uniqueness Theorem | tau-e | form |
| V.R194 | remark | No-hair test via ringdown | tau-e | form |
| V.D136 | definition | Standard Siren (tau) | tau-e | form |
| V.R195 | remark | Multi-Messenger GW170817 | tau-e | form |
| V.P81 | proposition | Merger Graviton Count | tau-e | form |
| V.D137 | definition | Toroidal Shadow (T^2 Readout) | tau-e | form |
| V.T95 | theorem | Shadow Shape Theorem (T^2 vs S^2) | tau-e | form |
| V.P82 | proposition | Inner Shadow Ellipticity | tau-e | form |
| V.D138 | definition | Photon Ring Winding Number | tau-e | form |
| V.P83 | proposition | Photon Subring Spacing | tau-e | form |
| V.R196 | remark | Observational accessibility | tau-e | form |
| V.D139 | definition | Polarization Handedness Signature | tau-e | form |
| V.T96 | theorem | Polarization Winding Theorem | tau-e | form |
| V.R197 | remark | M87* Shadow Re-Read | tau-e | — |
| V.R198 | remark | Sgr A* Shadow Re-Read | tau-e | form |
| V.R199 | remark | The strongest single test | tau-e | — |
| V.R200 | remark | Bullet Cluster Orthodox Argument | tau-e | — |
| V.D140 | definition | Boundary-Mass Offset (tau) | tau-e | form |
| V.T97 | theorem | Bullet Cluster Without Dark Matter | tau-e | form |
| V.P84 | proposition | Lensing-Gas Offset Bound | tau-e | form |
| V.D141 | definition | Handle-Scale Event | tau-e | form |
| V.D142 | definition | Wilson Skeleton (Cosmic Web) | tau-e | form |
| V.T98 | theorem | Cosmic Web from Holonomy Loops | tau-e | form |
| V.R201 | remark | BAO and Holonomy Periodicity | tau-e | — |
| V.D143 | definition | Topological Lensing Signature | tau-e | form |
| V.P85 | proposition | Filament Scaling Relation | tau-e | form |
| V.R202 | remark | Minimal Alphabet and Sector Count | tau-e | form |
| V.R203 | remark | From "Not Needed" to "Not Possible" | tau-e | form |
| V.D144 | definition | Sector Budget | tau-e | form |
| V.P86 | proposition | Coupling Budget Completeness | tau-e | form |
| V.D145 | definition | Sector Exhaustion Decomposition | tau-e | form |
| V.T99 | theorem | Sector Exhaustion Theorem | tau-e | form |
| V.D146 | definition | Dark Sector Hypothesis | tau-e | form |
| V.T100 | theorem | No Fifth Sector | tau-e | form |
| V.C14 | corollary | No Dark Matter Particle | tau-e | form |
| V.C15 | corollary | No Dark Energy Field | tau-e | form |
| V.C16 | corollary | No Fifth Force | tau-e | form |
| V.R204 | remark | What 68% and 27% Actually Are | tau-e | form |
| V.D147 | definition | Readout Artifact | tau-e | form |
| V.P87 | proposition | LCDM Budget Translation | tau-e | form |
| V.D148 | definition | Orbit-Depth-Dependent Readout | tau-e | form |
| V.D149 | definition | Depth-Projected Hubble Parameter | tau-e | form |
| V.R205 | remark | Both Measurements Correct | tau-e | form |
| V.T101 | theorem | H0 Tension Resolution | tau-e | form |
| V.P88 | proposition | Depth-Hubble Monotonicity | tau-e | form |
| V.D150 | definition | Category Error (LCDM) | tau-e | form |
| V.R206 | remark | Correct Parameters Wrong Ontology | tau-e | form |
| V.D151 | definition | Readout Projection Table | tau-e | form |
| V.P89 | proposition | Sigma8 as Defect Amplitude | tau-e | form |
| V.T102 | theorem | Dark Sector Closure | tau-e | form |
| V.R207 | remark | What Would Reopen the Case | tau-e | form |
| V.R208 | remark | From Part V to Part VI | tau-e | — |
| V.R209 | remark | No manifold Rightarrow no singularity | tau-e | form |
| V.D152 | definition | Temporal Opening | tau-e | form |
| V.R210 | remark | Planck Epoch Reinterpretation | tau-e | form |
| V.D153 | definition | Pre-Hadronic Regime | tau-e | form |
| V.D154 | definition | Regime Boundary Character | tau-e | form |
| V.P90 | proposition | Same-Equation Proposition | tau-e | form |
| V.T103 | theorem | No-Singularity Theorem | tau-e | form |
| V.R211 | remark | The Penrose--Hawking theorems are not wrong | tau-e | form |
| V.T104 | theorem | Big Bang = Opening Regime | tau-e | form |
| V.R212 | remark | Nohot’’ or cold'' | tau-e | — |
| V.R213 | remark | Falsifiability | tau-e | — |
| V.D155 | definition | Regime Invariance | tau-e | form |
| V.T105 | theorem | Regime Invariance Theorem | tau-e | form |
| V.R214 | remark | Contrast with running couplings | tau-e | — |
| V.C17 | corollary | Inflaton No-Go Corollary | tau-e | form |
| V.D156 | definition | Inflationary Regime | tau-e | form |
| V.D157 | definition | e-Fold Readout | tau-e | form |
| V.R215 | remark | Slow Roll Unnecessary | tau-e | form |
| V.T106 | theorem | Flatness from Compactness | tau-e | form |
| V.P91 | proposition | Horizon Resolution | tau-e | form |
| V.R216 | remark | Compactness vs. inflation | tau-e | — |
| V.R217 | remark | A falsifiable prediction | tau-e | form |
| V.D158 | definition | Threshold (Regime Boundary) | tau-e | form |
| V.D159 | definition | Canonical Thresholds | tau-e | form |
| V.T107 | theorem | Ladder Monotonicity | tau-e | form |
| V.D160 | definition | Neutron Threshold L_N | tau-e | form |
| V.R218 | remark | The mass hierarchy at L_N | tau-e | form |
| V.R219 | remark | Sphaleron Open Question | conje | — |
| V.R220 | remark | Sakharov Conditions | tau-e | form |
| V.D161 | definition | Nucleosynthetic Window | tau-e | form |
| V.T108 | theorem | Nucleosynthesis from tau | tau-e | form |
| V.R221 | remark | The lithium problem | tau-e | — |
| V.P92 | proposition | CMB Origin | tau-e | form |
| V.D162 | definition | Threshold Ladder | tau-e | form |
| V.D199 | definition | Opening Bookend | tau-e | — |
| V.R327 | remark | H–He Split | tau-e | — |
| V.R328 | remark | Beta Asymmetry | tau-e | — |
| V.D200 | definition | Density Gradient Narrative | tau-e | — |
| V.T152 | theorem | Density Gradient Monotonicity | tau-e | form |
| V.D201 | definition | Ionization in τ³ | tau-e | — |
| V.D202 | definition | Closing Bookend | tau-e | — |
| V.R329 | remark | No Baryon Annihilation | tau-e | — |
| V.D203 | definition | Neutrino Thread | tau-e | — |
| V.P114 | proposition | Neutrino Background Origin | tau-e | form |
| V.D204 | definition | Temporal Phase as Beta Cycle | tau-e | — |
| V.R330 | remark | Arc Summary | tau-e | — |
| V.D163 | definition | Gravitational Tension | tau-e | form |
| V.D164 | definition | Spherical Capacity | tau-e | form |
| V.D165 | definition | Linking Class | tau-e | form |
| V.D166 | definition | Black Hole (Topological Event) | tau-e | form |
| V.T109 | theorem | BH Threshold Theorem | tau-e | form |
| V.T110 | theorem | BH Toroidal Topology | tau-e | form |
| V.R222 | remark | Event horizon as linking boundary | tau-e | — |
| V.P93 | proposition | No Interior Singularity | tau-e | form |
| V.C18 | corollary | Information Preservation | tau-e | form |
| V.D167 | definition | Canonical BH Neighborhood | tau-e | form |
| V.D168 | definition | BH Bipolarity | tau-e | form |
| V.T111 | theorem | Necessary Bipolarity | tau-e | form |
| V.D169 | definition | Polarity Imbalance | tau-e | form |
| V.P94 | proposition | Polarity Convergence | tau-e | form |
| V.D170 | definition | Blueprint | tau-e | form |
| V.D171 | definition | Blueprint fusion mathrmFuse | tau-e | form |
| V.D172 | definition | Blueprint Monoid | tau-e | form |
| V.T112 | theorem | Blueprint Monoid Closure | tau-e | form |
| V.R223 | remark | Irreversibility of mergers | tau-e | — |
| V.R224 | remark | BH Entropy Formula | tau-e | form |
| V.R225 | remark | Export to Book VI | tau-e | — |
| V.D173 | definition | Mature Black Hole | tau-e | form |
| V.T113 | theorem | Defect-Mass Coupling | tau-e | form |
| V.T114 | theorem | No-Shrink Theorem | tau-e | form |
| V.P95 | proposition | Hawking Readout | tau-e | form |
| V.C19 | corollary | No BH Evaporation | tau-e | form |
| V.R226 | remark | Information Paradox Dissolved | tau-e | form |
| V.D174 | definition | Permanence Hallmark | tau-e | form |
| V.R227 | remark | Permanence Export to Book VI | tau-e | — |
| V.P96 | proposition | BH Entropy Formula | tau-e | form |
| V.R228 | remark | Why overlap forces merger | tau-e | — |
| V.T115 | theorem | Merger Normal Form | tau-e | form |
| V.R229 | remark | What the Normal Form does not give | tau-e | — |
| V.D175 | definition | Ringdown mode | tau-e | form |
| V.P97 | proposition | Ringdown damping is structural | tau-e | form |
| V.D176 | definition | BH mass scale at depth n | tau-e | form |
| V.P98 | proposition | Mass gap between adjacent primorial levels | tau-e | form |
| V.R230 | remark | The mass gap and the IMBH desert | tau-e | — |
| V.R231 | remark | Scope note on mass spectrum predictions | tau-e | form |
| V.D177 | definition | Base Wilson loop | tau-e | form |
| V.P99 | proposition | Gravitational deconfinement | tau-e | form |
| V.R232 | remark | Contrast with the strong sector | tau-e | — |
| V.P100 | proposition | BH gravitational Aharonov--Bohm phase | tau-e | form |
| V.P101 | proposition | Radiated energy bound | tau-e | form |
| V.R233 | remark | The 1/sqrt2 | tau-e | form |
| V.D178 | definition | Topological motif | tau-e | form |
| V.T116 | theorem | Finite Motif Theorem | tau-e | form |
| V.R234 | remark | Contrast with fractal cosmologies | tau-e | form |
| V.D179 | definition | Saturation radius | tau-e | form |
| V.T117 | theorem | Saturation Radius Theorem | tau-e | form |
| V.R235 | remark | Saturation radius vs. observable universe | tau-e | form |
| V.D180 | definition | Absorbing pattern | tau-e | form |
| V.T118 | theorem | Absorbing Pattern Theorem | tau-e | form |
| V.R236 | remark | No infinite hierarchy | tau-e | form |
| V.C20 | corollary | Global Finiteness | tau-e | form |
| V.R237 | remark | What the chain does NOT prove | tau-e | form |
| V.P102 | proposition | Defect entropy converges to zero | tau-e | form |
| V.D181 | definition | BH-dominated epoch | tau-e | form |
| V.D182 | definition | Coherence horizon | tau-e | form |
| V.R238 | remark | Not a Big Crunch | tau-e | — |
| V.D183 | definition | Generative and refinement phases | tau-e | form |
| V.R239 | remark | Generative does not mean explosive | tau-e | — |
| V.T119 | theorem | Eternal Circulation Theorem | tau-e | form |
| V.R240 | remark | Late-stage conditions favor complexity | conje | form |
| V.R241 | remark | Not the anthropic principle | tau-e | form |
| V.R242 | remark | The key difference: no infinity | tau-e | — |
| V.R243 | remark | Scope note: CMB predictions C2, C5, C6 | tau-e | form |
| V.D184 | definition | Falsification levels | tau-e | form |
| V.R244 | remark | The lesson: do not add, recognize | tau-e | — |
| V.T120 | theorem | Boundary Completeness | tau-e | form |
| V.R245 | remark | Comparison with orthodox unification | tau-e | — |
| V.P103 | proposition | Cross-coupling as naturality | tau-e | form |
| V.R246 | remark | Naturality replaces gauge invariance | tau-e | form |
| V.P104 | proposition | iota_tau mediates all ten couplings | tau-e | form |
| V.R247 | remark | Scope note: implementation roadmap | tau-e | — |
| V.R248 | remark | Part VI Achievement Summary | tau-e | — |
| V.R249 | remark | Open Questions | tau-e | — |
| V.R250 | remark | Export to Books VI and VII | tau-e | — |
| V.R251 | remark | Bridge to Part VII | tau-e | — |
| V.R252 | remark | Entries withNo counterpart’’ | tau-e | form |
| V.R253 | remark | Preservation does not mean identity | tau-e | — |
| V.D185 | definition | Structural artifact | tau-e | form |
| V.R254 | remark | The common thread | tau-e | — |
| V.D186 | definition | Ontic and readout layers | tau-e | form |
| V.R255 | remark | Orthodox physics is not wrong | tau-e | form |
| V.D187 | definition | Readout interpretation protocol | tau-e | form |
| V.R256 | remark | Where tau adds value | tau-e | — |
| V.R257 | remark | The vacuum catastrophe as diagnostic | tau-e | form |
| V.R258 | remark | The analogy of cartography | tau-e | — |
| V.T121 | theorem | Properties of the correspondence functor | tau-e | form |
| V.R259 | remark | Non-surjectivity is a feature | tau-e | — |
| V.R260 | remark | Respect for the empirical record | tau-e | — |
| V.R261 | remark | The microscope analogy | tau-e | — |
| V.T122 | theorem | Renormalization as tower truncation | tau-e | form |
| V.R262 | remark | Scheme independence explained | tau-e | form |
| V.D188 | definition | UV shield | tau-e | form |
| V.R263 | remark | Comparison with lattice QFT | tau-e | — |
| V.T123 | theorem | Path integral recovery | tau-e | form |
| V.R264 | remark | The Wick rotation is a chart operation | tau-e | form |
| V.R265 | remark | The field as scaffolding | tau-e | — |
| V.R266 | remark | Not all parameters have been computed | tau-e | form |
| V.T124 | theorem | Profinite convergence | tau-e | form |
| V.R267 | remark | Why m_n and not m_e? | tau-e | form |
| V.R268 | remark | GR’s scope | tau-e | form |
| V.R269 | remark | Spacetime in tau | tau-e | — |
| V.T125 | theorem | GR as chart shadow of the tau-Einstein identity | tau-e | form |
| V.T126 | theorem | The readout quantization obstruction | tau-e | form |
| V.R270 | remark | Gravity is already quantum | tau-e | — |
| V.T127 | theorem | No singularity theorem | tau-e | form |
| V.R271 | remark | The metric is a derived quantity | tau-e | — |
| V.T128 | theorem | Sector Exhaustion — no dark sector | tau-e | form |
| V.R272 | remark | Dualities as structural echoes | tau-e | — |
| V.T129 | theorem | Landscape collapse | tau-e | form |
| V.R273 | remark | Occam and dimensions | tau-e | — |
| V.T130 | theorem | Native holography | tau-e | form |
| V.R274 | remark | AdS/CFT as a partial echo | tau-e | form |
| V.R275 | remark | iota_tau is a mathematical constant | tau-e | form |
| V.R276 | remark | Why SUSY was not found at the LHC | tau-e | form |
| V.R277 | remark | The parable of the library | tau-e | form |
| V.R278 | remark | LQG’s genuine contribution | tau-e | — |
| V.T131 | theorem | No knobs in tau | tau-e | form |
| V.R279 | remark | The residual manifold in LQG | tau-e | — |
| V.R280 | remark | Four echoes, one architecture | tau-e | — |
| V.R281 | remark | CDT as a computational echo | tau-e | form |
| V.R282 | remark | Sorkin’s Lambda prediction | tau-e | form |
| V.R283 | remark | Respect and replacement | tau-e | — |
| V.P105 | proposition | Twistor embedding | tau-e | form |
| V.R284 | remark | Twistors as shadow | tau-e | — |
| V.P106 | proposition | NCG spectral triple from tau | tau-e | form |
| V.T132 | theorem | Gravity as readout — no renormalization | tau-e | form |
| V.R285 | remark | The two relevant directions | tau-e | — |
| V.R286 | remark | Verlinde’s rotation curves | tau-e | — |
| V.T133 | theorem | Completeness of the boundary algebra | tau-e | form |
| V.R287 | remark | No hierarchy among programmes | tau-e | form |
| V.D189 | definition | VM representation of a quantum state | tau-e | form |
| V.T134 | theorem | Measurement problem dissolution | tau-e | form |
| V.R288 | remark | Superposition in the VM | tau-e | — |
| V.T135 | theorem | Bell inequality in tau | tau-e | form |
| V.R289 | remark | Entanglement as address sharing | tau-e | — |
| V.P107 | proposition | Decoherence as address-resolution shadow | tau-e | form |
| V.R290 | remark | The century of confusion | tau-e | — |
| V.T136 | theorem | No singularities in tau | tau-e | form |
| V.T137 | theorem | No UV divergences in tau | tau-e | form |
| V.R291 | remark | Renormalization is correct but unnecessary | tau-e | form |
| V.T138 | theorem | No dark sectors | tau-e | form |
| V.T139 | theorem | Vacuum energy is exactly zero | tau-e | form |
| V.R292 | remark | The 10^120 | tau-e | form |
| V.R293 | remark | Why dissolve'' and notsolve’’ | tau-e | — |
| V.R294 | remark | Honest vs. premature | tau-e | — |
| V.T140 | theorem | Elayer1 | tau-e | form |
| V.R295 | remark | Timeline for the topology test | tau-e | form |
| V.R296 | remark | The honest status of galaxy fits | tau-e | — |
| V.R297 | remark | The subtlety of Lambda = 0 | tau-e | form |
| V.R298 | remark | Precision of the neutrino prediction | tau-e | form |
| V.R299 | remark | Scope of the delta_A prediction | tau-e | — |
| V.R300 | remark | What would vindicate inflation | tau-e | form |
| V.T141 | theorem | No Shrink—restatement | tau-e | form |
| V.R301 | remark | The information paradox as diagnostic | tau-e | form |
| V.R302 | remark | Fifth force vs. sixth force | tau-e | form |
| V.R303 | remark | What would NOT falsify tau | tau-e | form |
| V.R304 | remark | Falsifiability as strength | tau-e | — |
| V.R305 | remark | One anchor, not zero | tau-e | form |
| V.R306 | remark | The sqrt3 | tau-e | form |
| V.R307 | remark | The neutrino exponent | tau-e | — |
| V.R308 | remark | Comparison with the Standard Model | tau-e | form |
| V.T142 | theorem | Elayer1 | tau-e | form |
| V.P111 | proposition | Tensor-Square Connection | tau-e | form |
| V.D192 | definition | He-4 Packing Maximum | tau-e | form |
| V.D193 | definition | Face-Conflict Probability | tau-e | form |
| V.D194 | definition | Domain-Wall Correction Factor | tau-e | form |
| V.D195 | definition | Primordial He-4 Mass Fraction | tau-e | form |
| V.D196 | definition | Neutron-to-Proton Ratio from Y_p | tau-e | form |
| V.T146 | theorem | Packing Maximum Theorem | tau-e | form |
| V.T147 | theorem | Face-Conflict Theorem | tau-e | form |
| V.T148 | theorem | Three Decompositions Identity | estab | form |
| V.T149 | theorem | Y_p Derivation from Packing and Correction | tau-e | form |
| V.T150 | theorem | n/p Ratio Derivation | tau-e | form |
| V.P112 | proposition | Y_p Observational Consistency | estab | form |
| V.R322 | remark | 71 = p_20 Structural Echo | tau-e | not_ |
| V.D197 | definition | Threshold-Dependent Admissibility | tau-e | form |
| V.D198 | definition | Baryogenesis Window | tau-e | form |
| V.R323 | remark | Commutator Magnitude at omega-Crossing | conje | — |
| V.R324 | remark | eta_B Structural Candidate | conje | — |
| V.R325 | remark | Primorial-Confinement Bridge | conje | — |
| V.R326 | remark | Confinement Multiplicity Estimate | conje | — |
| V.T151 | theorem | N_eff from Sector Exhaustion | tau-e | form |
| V.P113 | proposition | Dark Sector Closure | estab | form |
| V.D205 | definition | The Hermetic Principle | tau-e | — |
| V.D206 | definition | Temporal Arc Principle | metap | — |
| V.D207 | definition | Relational Space Principle | tau-e | — |
| V.D208 | definition | Genealogical Branching Rate | tau-e | — |
| V.L4 | lemma | Single Scale Degree of Freedom | tau-e | form |
| V.L5 | lemma | Minimal Mature Black Hole | tau-e | form |
| V.R331 | remark | RG flow as defect flow | tau-e | — |
| V.R332 | remark | EM sign structure and plasma modes | tau-e | — |
| V.R333 | remark | No-isolated-charges as VM-shadow denial | tau-e | — |
| V.D209 | definition | Mixed Reconnection Defect | tau-e | — |
| V.R334 | remark | Alfven mode existence decidability | tau-e | — |
| V.D210 | definition | Minimal Mixed Phase Quantum | tau-e | — |
| V.D211 | definition | Neutron Multiplicity Bound | conje | — |
| V.D212 | definition | Closing Identity | tau-e | — |
| V.D213 | definition | Sector Lift Functor | tau-e | — |
| V.R337 | remark | sigma-equivariance | tau-e | — |
| V.R338 | remark | H_fix[omega] subfield | tau-e | — |
| V.T154 | theorem | The G-alpha Bridge | tau-e | form |
| V.R341 | remark | Three routes, one G | tau-e | — |
| V.T155 | theorem | Mass Hierarchy Exponent | tau-e | form |
| V.R342 | remark | The chain of masses | tau-e | — |
| V.P115 | proposition | Hierarchy as Power Law | tau-e | form |
| V.R343 | remark | Supersymmetry unnecessary | tau-e | — |
| V.R344 | remark | What Dirac got right and wrong | tau-e | — |
| V.P116 | proposition | Precision Budget | tau-e | form |
| V.R345 | remark | Independence from m_e | tau-e | — |
| V.R346 | remark | The exponent as structural invariant | tau-e | — |
| V.R347 | remark | As above, so below — quantified | metap | — |
| V.D214 | definition | The Master Constant — Layer 0 | estab | — |
| V.D215 | definition | Sector Couplings — Layer 1 | tau-e | — |
| V.D216 | definition | Fine-Structure Constant — Layer 1 | tau-e | — |
| V.D217 | definition | Mass Ratio Formula — Layer 1 | tau-e | — |
| V.D218 | definition | Gravitational Coupling — Layer 1 | tau-e | — |
| V.D219 | definition | The Calibration Anchor — Layer 2 | tau-e | — |
| V.T156 | theorem | Mass Derivations — Layer 2 | tau-e | form |
| V.R348 | remark | The 5-to-1 collapse | tau-e | — |
| V.R349 | remark | Boltzmann and temperature | tau-e | — |
| V.R350 | remark | Room for improvement | tau-e | — |
| V.D220 | definition | The SI Cascade Algorithm | tau-e | — |
| V.R351 | remark | Honest comparison | tau-e | — |
| V.T157 | theorem | Calibration Sufficiency | tau-e | form |
| V.D221 | definition | Export E1: Complete Physical Arena | tau-e | — |
| V.D222 | definition | Export E2: Arrow of Time | tau-e | — |
| V.D223 | definition | Export E3: Entropy Splitting | tau-e | — |
| V.D224 | definition | Export E4: Defect Functional | tau-e | — |
| V.R352 | remark | The eight fluid regimes | tau-e | — |
| V.D225 | definition | Export E5: Black Hole Topology | tau-e | — |
| V.R353 | remark | Scope: partially conjectural (E5) | tau-e | — |
| V.D226 | definition | Export E6: Cosmological Endstate | conje | — |
| V.R354 | remark | Scope: conjectural (E6) | conje | — |
| V.D227 | definition | Export E7: Constants Ledger | tau-e | — |
| V.D228 | definition | Export E8: Falsification Pack | conje | — |
| V.R355 | remark | The 5-20 year horizon | conje | — |
| V.D229 | definition | Export E9: Self-Describing Closure | tau-e | — |
| V.R356 | remark | The seed-crystal principle | tau-e | — |
| V.R357 | remark | Scope propagation rule | tau-e | — |
| V.T158 | theorem | Export Completeness | tau-e | form |
| V.R358 | remark | Enrichment is not reduction | tau-e | — |
| V.P117 | proposition | Entropy splitting and life | tau-e | form |
| V.R359 | remark | All five sectors are biologically necessary | tau-e | — |
| V.D230 | definition | Far-from-equilibrium defect pattern | tau-e | — |
| V.P118 | proposition | Black holes as far-from-equilibrium patterns | tau-e | form |
| V.R360 | remark | The alive-or-not question | metap | — |
| V.R361 | remark | The enrichment functor is not yet constructed | conje | — |
| V.T159 | theorem | The Hermetic Identity | estab | form |
| V.D231 | definition | The iota_tau chain | tau-e | — |
| V.R362 | remark | Why 2/(pi + e)? | tau-e | — |
| V.P119 | proposition | Generator universality | estab | form |
| V.R363 | remark | The apparent running | tau-e | — |
| V.T160 | theorem | Physics as self-description | estab | form |
| V.R364 | remark | Wigner’s question answered | metap | — |
| V.P120 | proposition | Structural rigidity | tau-e | form |
| V.R365 | remark | The landscape problem dissolved | tau-e | — |
| V.T161 | theorem | The Hermetic Closure | tau-e | form |
| V.R366 | remark | The theory predicts its own discovery | metap | — |
| V.T162 | theorem | The Hermetic Truth | estab | form |
| V.P121 | proposition | Permanent sector distinction | estab | form |
| V.R367 | remark | Limits are not failures | tau-e | — |
| V.R368 | remark | The logos is the boundary algebra | metap | — |
| V.R369 | remark | The longest derivation chain in physics | metap | — |
| V.D232 | definition | Milgrom Constant from tau | tau-e | form |
| V.T163 | theorem | Baryonic Tully-Fisher Relation from V.T85 | tau-e | form |
| V.T164 | theorem | NGC 3198 Zero-Parameter Prediction | tau-e | form |
| V.P122 | proposition | a_0 from H_0 Tension | tau-e | form |
| V.R370 | remark | H_0 Tension as Galactic Scale Effect | tau-e | form |
| V.R371 | remark | MOND Comparison Table | tau-e | form |
| V.D233 | definition | sigma-Polarity Neutrino Mass Matrix | tau-e | form |
| V.T165 | theorem | Mass Eigenvalue Ratio Formula | tau-e | form |
| V.T166 | theorem | Cosmological Bound Satisfaction | tau-e | form |
| V.P123 | proposition | PMNS Mixing Angle Prediction | conje | form |
| V.R372 | remark | Sprint 4 Findings and OQ-C3 Status | tau-e | form |
| V.T167 | theorem | Effective Majorana Mass