Registry — Book V: Categorical Macrocosm

V.R04 The cross-couplings bind the halves remark V.T06 Fiber Completeness --- IV.T32 theorem V.R05 The Temporal Complement as test case remark V.R06 The exponent pattern remark V.R07 No scope inflation remark V.D12 Book~IV to Book~V Export Contract definition V.R08 Contract discipline remark V.D13 OnticParticle --- IV.D22 definition V.R09 Six, not five, cross-couplings remark V.D14 Defect Tuple --- IV.D20 definition V.T07 Mass Ratio --- IV.T30 theorem V.R10 No further open items remark V.R11 Comparison with Book~IV remark V.R12 The Book~V--Book~VI boundary remark V.D15 Base Circle tau^1 (Macroscopic) definition V.R13 Why ``circle''? remark V.R14 Temporal = gravitational + weak remark V.D16 Alpha-Tick definition V.R15 Ticks are not uniform remark V.D17 Proper Time (Arc Length) definition V.T08 Time Derivation Theorem theorem V.R16 The chart-level continuum remark V.P03 Arrow of Time = Orbit Direction proposition V.D18 Causal Ordering Relation definition V.R17 Spacelike separation on T^2 remark V.T09 Causal Ordering Theorem theorem V.R18 Causality precedes light cones remark V.D19 Geodesic Duration definition V.R19 Duration is not clock time remark V.R20 Two metrics, one space remark V.T10 Bounded Time Theorem theorem V.R21 Finite but unbounded in tick count remark V.R22 alpha_o and omega remark V.R23 No Background Time remark V.D20 Three Temporal Epochs definition V.R24 Epochs are structural, not anthropic remark V.D21 Ignition Depth definition V.R25 Ignition is not a phase transition remark V.T11 Epoch Existence Theorem theorem V.P04 Pre-Temporal Indistinguishability proposition V.R26 The pre-temporal epoch is not ``empty'' remark V.D22 Sigma-Now Hypersurface definition V.R27 Simultaneity Is Structural remark V.R28 Foliation versus block universe remark V.T12 Now-Within-Epoch Theorem theorem V.R29 Selection without observers remark V.D23 Coherence Horizon definition V.R30 Completion versus termination remark V.P05 Mode Counting at Early Depths proposition V.D24 Maximal Coupling Condition definition V.D25 Opening Regime definition V.R31 No Initial Singularity remark V.T13 Opening Regime Theorem theorem V.R32 No Past Hypothesis needed --- reprise remark V.D26 Refinement Progression Rate definition V.R33 Inflation as Progression remark V.D27 Null Intertwiner (Photon) definition V.R34 Photons do not ``travel'' remark V.T14 Photon Existence Theorem theorem V.P06 Null Character Uniqueness proposition V.D28 Operational Distance definition V.T15 Distance-Duration Duality theorem V.R35 The speed of light is not ``fast'' remark V.D29 Refinement Drift (Redshift) definition V.R36 No Doppler Explanation remark V.T16 Redshift-Depth Relation theorem V.D30 Readout Expansion definition V.R37 What expands? remark V.D31 Hubble Readout Parameter definition V.R38 No Dark Energy Needed remark V.R39 Causality sharpened remark V.D32 Distance readout functor definition V.R40 Distance is operational remark V.T17 Distance Ladder Translation theorem V.R41 Gaia and the tau-readout remark V.D33 Cepheid readout calibrator definition V.R42 The Chandrasekhar limit in tau remark V.D34 BAO standard ruler definition V.T18 Hubble Tension Resolution theorem V.R43 Quantitative prediction remark V.D35 Readout curvature definition V.T19 Dark Energy Artifact --- First Pass theorem V.R44 Scope and deferral remark V.R45 Forward reference to Part~V remark V.D36 Recombination orbit depth definition V.R46 No new physics in the definition remark V.D37 CMB constraint surface definition V.P07 CMB multipoles as boundary characters proposition V.R47 No new information, new interpretation remark V.P08 Blackbody as coherence equilibrium proposition V.D38 Neutrino decoupling orbit depth definition V.D39 CnuB echo surface definition V.R48 No new prediction for T_mathrmC remark V.P09 CnuB mass constraint proposition V.R49 Two constraint surfaces, one algebra remark V.R50 Testability remark V.D40 Cosmic Stack API definition V.R51 Why an API metaphor remark V.R52 Scope census remark V.R53 Gravity is not a force on the fiber remark V.D41 Clopen frame definition V.P10 Frame transitions are boundary-determined proposition V.R54 No connection needed remark V.D42 Frame holonomy on tau^1 definition V.T20 Gravity as frame holonomy gap theorem V.R55 Comparison with gauge holonomy remark V.D43 Holonomy gap element definition V.P11 Gap refinement coherence proposition V.D44 Torus vacuum --- V.D01 definition V.T21 Vacuum shape ratio --- V.T01 theorem V.D45 Gravitational constant --- V.D02 definition V.T22 G derivation --- V.D02 theorem V.R56 Lean formalization remark V.D46 Gravitational coupling kappa_tau definition V.C01 Temporal Complement, revisited corollary V.T23 sigma-equivariance of kappa_tau theorem V.R57 Equivalence principle as theorem remark V.T24 Lorentz covariance theorem theorem V.R58 Not a postulate remark V.D47 Null intertwiner definition V.P12 Light cone is Lorentz-invariant proposition V.R59 The photon is a null intertwiner, not a particle remark V.P13 Speed barrier as constraint saturation proposition V.R60 No ``relativistic mass'' remark V.D48 Local tau^3 chart definition V.T25 Minkowski as chart shadow --- cf. III.D76 theorem V.R61 Riemannian geometry as patching remark V.R62 Ontological priority remark V.C02 Relativity principle recovered corollary V.R63 Michelson--Morley explained remark V.D49 Curvature character --- V.D04 definition V.D50 Matter character --- V.D03 definition V.R64 Three sectors, not four remark V.D51 tau-Einstein equation --- V.D06 definition V.R65 The GR coupling kappa_tau --- V.D05 remark V.T26 Chart shadow recovery theorem V.R66 The 8pi factor remark V.T27 Well-posedness via Hartogs theorem V.R67 Singularities are chart artifacts remark V.C03 tau-Bianchi identity --- V.R01 corollary V.R68 No admissible refinement without compensation remark V.D52 Linearized tau-Einstein equation definition V.T28 Newtonian limit recovery theorem V.R69 Newton from tau remark V.T29 Mercury precession from tau-Einstein theorem V.R70 No fitting remark V.T30 Light deflection from tau-Einstein theorem V.T31 Gravitational redshift from tau-Einstein theorem V.D53 Gravitational wave in tau-framework definition V.T32 Gravitational wave properties theorem V.R71 Two polarizations from two fiber directions remark V.R72 Inspiral phase is linear remark V.P14 v_mathrmGW proposition V.R73 Graviton mass is zero remark V.R74 The honest claim remark V.D54 Cocycle defect definition V.D55 tau-NF Einstein iteration definition V.R75 No approximation remark V.D56 Truncation-coherent descent definition V.T33 Existence theorem V.T34 Uniqueness theorem V.T35 Selection theorem V.R76 Comparison with orthodox gauge freedom remark V.R77 Why ``address''? remark V.P15 Convergence in all regimes proposition V.T36 Density cap theorem V.D57 Density-saturated character definition V.P16 Saturation replaces singularity proposition V.R78 Comparison with other singularity resolutions remark V.D58 Null intertwiner definition V.D59 Present surface definition V.D60 tau-Horizon definition V.T37 Horizon as present-surface contraction theorem V.R79 No Cauchy horizon instability remark V.R80 Extremal black holes remark V.R81 Forward references remark V.D61 Torus vacuum --- V.D01 definition V.T38 Vacuum shape ratio --- V.T01 theorem V.R82 Torus, not sphere remark V.D62 Gravitational constant --- V.D02 definition V.P17 G_tau well-defined --- V.P01 proposition V.R83 Why iota_tau^2, not iota_tau remark V.T39 Schwarzschild as readout theorem V.R84 The Birkhoff theorem in tau remark V.P18 Schwarzschild regularity proposition V.R85 The torus core remark V.D63 Geometric relaxation definition V.D64 Topological relaxation definition V.R86 Observational signature remark V.T40 The tau-Schwarzschild relation --- V.D08 theorem V.D65 BH evolution modes --- V.D09 definition V.T41 No-Shrink --- V.T03, preview theorem V.R87 Hawking evaporation forbidden --- V.R02 remark V.R88 Chandrasekhar limit as maturity threshold --- V.R02 remark V.D66 Spherical carrier predicate definition V.R89 Spherical neq static remark V.D67 Equilibrium carrier definition V.D68 GR tension functional definition V.P19 Tension bounds proposition V.D69 Tension profile definition V.D70 Canonical star builder definition V.T42 Star builder existence and uniqueness theorem V.R90 The star builder as constructive proof remark V.D71 Neutron node definition V.D72 Node density and confinement tension definition V.P20 TOV balance as tension equilibrium proposition V.R91 Not an ODE remark V.D73 EW-stable node definition V.T43 Neutron node EW stability theorem V.P21 Truncation invariance of the star builder proposition V.D74 Chandrasekhar threshold definition V.T44 Chandrasekhar limit theorem V.R92 No free parameter remark V.R93 The TOV maximum mass remark V.D75 GR Tension Functional definition V.D76 Coherence Horizon definition V.L01 Surface Matter Bound lemma V.T45 Tension Monotonicity theorem V.R94 No ``tension maximum'' remark V.T46 Structural Threshold --- Forced Topology Relaxation theorem V.C04 TOV Limit corollary V.R95 Chandrasekhar limit as the electron-degenerate case remark V.D77 Topology Crossing Event definition V.T47 Topology Crossing Admissibility theorem V.R96 No singularity remark V.R97 Comparison with Penrose's trapped surface theorem remark V.T48 Defect Cost Jump at Phase Boundary theorem V.R98 Defect minimization drives topology selection remark V.R99 Observational tests remark V.D78 Calibration Constant Xi_tau definition V.P22 Xi_tau is refinement-stable proposition V.R100 No SI units enter Xi_tau remark V.D79 Calibration Triangle definition V.T49 Micro--Macro Bridge theorem V.D80 Ring Homomorphism Phi_p,n definition V.P23 Phi_p,n proposition V.R101 The delta_A thread through the triangle remark V.T50 Complete Dimensional Bridge theorem V.R102 The unit problem in orthodox physics remark V.R103 Planck mass as a derived quantity remark V.D81 Gravitational Closing Identity --- V.D11 definition V.T51 Spectral Distance --- IV.T11 theorem V.D82 Corrected Co-Rotor Coupling --- V.D10 definition V.R104 Scope: c_1 = 3/pi is conjectural remark V.T52 G Prediction --- V.T04, V.T05 theorem V.R105 G is the least precise fundamental constant remark V.R106 The hierarchy ``problem'' dissolved remark V.T53 R Formula Independence --- V.R03 theorem V.R107 Two independent predictions remark V.T54 10-Link Derivation Chain theorem V.R108 The closing identity completes the Hermetic Principle remark V.R109 Open problem: c_1 from first principles remark V.R110 The 7times amplification in R remark V.R111 The explanatory gap remark V.R112 An analogy: pixels and noise remark V.T55 The Categorical Second Law theorem V.R113 Compatibility with Book~IV remark V.D83 Thermodynamic equilibrium---categorical definition V.R114 Not the same as thermal equilibrium remark V.P24 Defect absorption rate proposition V.R115 The role of gravity in ordering remark V.P25 Weak redistribution preserves defect count proposition V.L02 Geometric contraction of defect support lemma V.R116 The contraction rate is the gravitational coupling remark V.C05 Defect support exhaustion corollary V.D84 Coherence horizon definition V.R117 Circulation, not stasis remark V.P26 The 180^circ inversion proposition V.R118 Orbit steps versus physical time remark V.D85 Defect partition of paths definition V.D86 Defect entropy definition V.D87 Refinement entropy definition V.T56 Entropy splitting theorem V.R119 Why varepsilon is harmless remark V.T57 Defect entropy is bounded theorem V.T58 Defect entropy is monotonically decreasing theorem V.C06 Defect entropy reaches zero corollary V.T59 Refinement entropy grows without bound theorem V.R120 The paradox resolved remark V.P27 Readout projects onto total entropy proposition V.R121 The 99.99% that is noise remark V.P28 iota_tau controls the splitting ratio proposition V.P29 Defect entropy from defect functional proposition V.R122 The Penrose puzzle remark V.P30 Finite initial defect count proposition V.R123 Contrast with QFT remark V.D88 Global defect budget definition V.T60 Finite defect budget theorem V.L03 Integer threshold lemma V.T61 Global Defect Exhaustion theorem V.D89 Coherence horizon---refined definition V.R124 Orbit steps are not years remark V.C07 Finite irreversibility corollary V.R125 Contrast with heat death remark V.P31 Vacuum circulation is periodic proposition V.P32 No Poincar'e recurrence conflict proposition V.T62 Master exhaustion inequality theorem V.D90 Defect half-life definition V.R126 Universal half-life remark V.P33 The arrow has an endpoint proposition V.R127 Time continues; the arrow does not remark V.R128 The artificial trichotomy remark V.D91 EM energy transport definition V.P34 Radiation is B-sector transport proposition V.P35 Conduction is near-field B-sector transport proposition V.P36 Convective transport is B-sector displacement proposition V.T63 alpha governs macroscopic energy transport theorem V.R129 Why alpha and not iota_tau^2 remark V.D92 Geometric relaxation definition V.D93 Topological relaxation definition V.P37 Hierarchy of relaxation times proposition V.T64 Heat is electromagnetism theorem V.D94 The tau-vacuum definition V.T65 Vacuum energy is boundary energy theorem V.R130 Why no divergence remark V.P38 QFT vacuum = refinement sum proposition V.T66 The vacuum catastrophe is a category error theorem V.C08 Vacuum source term is finite corollary V.R131 Comparison with normal ordering remark V.T67 H_partial[omega theorem V.P39 Casimir effect from boundary modes proposition V.R132 Casimir does not prove mode summation remark V.R133 Data versus interpretation remark V.R134 Two faces of the same problem remark V.T68 Defect-driven acceleration theorem V.D95 Capacity surplus definition V.P40 No Lambda in the tau-Einstein equation proposition V.T69 Dark energy is a readout artifact theorem V.P41 The 68% is refinement entropy proposition V.R135 Where does the 68% go? remark V.R136 Testability remark V.R137 III.T25 is enrichment-layer independent remark V.D96 Macro defect-transport equation definition V.R138 Fiber contributions are not discarded remark V.D97 Macro tau-Navier--Stokes flow definition V.P42 Compactness of tau^3 proposition V.T70 Macro three-condition sufficiency theorem V.T71 Macro tau-NS regularity theorem V.R139 Contrast with mathbbR remark V.C09 No temporal blow-up corollary V.D98 Macro tau-Reynolds number definition V.R140 The Reynolds number is bounded remark V.R141 Convective overshooting remark V.R142 No singularity at the innermost stable orbit remark V.R143 Honest claim remark V.P43 Classical NS as readout proposition V.R144 The chart domain is compact remark V.R145 Limitations of K41 remark V.D99 tau-turbulent flow definition V.T72 Macro energy spectrum theorem V.R146 The Kolmogorov constant C_K remark V.D100 tau-enstrophy definition V.P44 Dual cascade decomposition proposition V.R147 Batchelor--Kraichnan spectrum remark V.P45 Vortex stretching bound proposition V.R148 She--L'ev^eque formula remark V.D101 Macro charge definition V.T73 No Isolated Charges theorem V.R149 Charge quantization remark V.C10 Sourceless macro flux corollary V.R150 Local charges still exist remark V.C11 No magnetic monopoles corollary V.D102 Macro EM field definition V.C12 Macro color confinement corollary V.R151 Quark-gluon plasma is still confined remark V.D103 Macro current definition V.D104 tau-plasma definition V.T74 Forced Quasi-Neutrality theorem V.P46 Plasma oscillations proposition V.P47 Plasma cutoff proposition V.R152 Ionospheric reflection remark V.P48 Debye shielding proposition V.D105 Debye number definition V.R153 No dark matter in the ICM remark V.D106 MHD limit definition V.D107 tau-MHD system definition V.D108 Magnetic Reynolds number definition V.T75 Frozen-flux invariant theorem V.D109 tau-reconnection event definition V.R154 Sweet--Parker and Petschek remark V.P49 Reconnection energy bound proposition V.P50 Alfv'en wave dispersion proposition V.P51 Magnetosonic dispersion proposition V.D110 MHD instability condition definition V.D111 Mixed-sector mode definition V.P52 Alfv'en speed as cross-coupling readout proposition V.R155 The photon-in-fluid interpretation remark V.D112 Alfv'en orbit definition V.R156 Sufficient energy flux remark V.P53 ISM Alfv'en cascade proposition V.P54 Crossing preservation proposition V.D113 Macro tau-crystal definition V.D114 Macro tau-glass definition V.R157 The glass transition is not a phase transition remark V.D115 First-order macro transition definition V.D116 Second-order macro transition definition V.T76 Critical surface is codimension 1 theorem V.R158 Gaia and crystallization remark V.P55 Neutron star phase sequence proposition V.R159 DDT and turbulence remark V.T77 Phase-transition universality theorem V.R160 Universality is structural, not accidental remark V.T78 Newtonian Limit --- V.T30 theorem V.R161 The three conditions quantified remark V.P56 Capacity Gradient as Apparent Dark Matter --- V.P20 proposition V.D117 Classical Validity Scale --- V.D50 definition V.R162 The MOND scale as proxy remark V.T79 Two-Regime Readout --- V.T31 theorem V.R163 No free parameters remark V.P57 Bertrand as Readout Constraint --- V.P21 proposition V.P58 Newton's First Law as Limit --- V.P22 proposition V.T80 Correspondence Tower --- V.T32 theorem V.R164 The dark matter debate is a projection artifact remark V.D118 Angular Momentum Character --- V.D51 definition V.T81 Rotational Flux Conservation --- V.T33 theorem V.T82 Kepler's First Law --- V.T34 theorem V.T83 Kepler's Second Law --- V.T35 theorem V.R165 Second law is deeper than the first remark V.T84 Kepler's Third Law --- V.T36 theorem V.R166 Kepler as theorem, not phenomenology remark V.P59 Perihelion Advance from tau-GR --- V.P23 proposition V.P60 Light Deflection from tau-GR --- V.P24 proposition V.P61 Shapiro Delay from tau-GR --- V.P25 proposition V.R167 All three tests pass with zero fitting remark V.D119 Lensing Character --- V.D52 definition V.R168 Heliophysics as readout of H_partial[omega remark V.P62 Solar System Concordance --- V.P26 proposition V.D120 Galaxy as Relational Coherence --- V.D53 definition V.R169 No void between galaxies remark V.P63 Modified Jeans Scale --- V.P27 proposition V.P64 Galaxy Formation Sequence --- V.P28 proposition V.R170 Conjectural scope remark V.D121 Cosmic Web as Capacity Skeleton --- V.D54 definition V.P65 Web Determines Galaxy Locations --- V.P29 proposition V.R171 Filaments are not gravitational wakes remark V.D122 Morphological Capacity Profile --- V.D55 definition V.R172 Morphology is not destiny remark V.P66 Galactic Virial Theorem --- V.P30 proposition V.R173 Satellite planes and the missing satellite problem remark V.D123 Galactic Capacity Profile --- V.D56 definition V.T85 Flat Rotation Curve Theorem --- V.T37 theorem V.C13 Baryonic Tully--Fisher from Capacity --- V.R20 corollary V.P67 Galaxy-by-Galaxy Concordance --- V.P31 proposition V.R174 What ``conjectural'' means here remark V.P68 MOND as Capacity Proxy --- V.P32 proposition V.R175 MOND as approximation theorem remark V.P69 No Dark Particle Theorem --- V.P33 proposition V.R176 The asymmetry of falsification remark V.P70 RAR from Capacity Gradient --- V.P34 proposition V.D124 Degeneracy Pressure Character --- V.D57 definition V.T86 Chandrasekhar Mass from tau-Framework --- V.T38 theorem V.R177 White dwarf mass--radius relation remark V.P71 Neutron Star EOS Structure --- V.P35 proposition V.T87 TOV Mass Limit --- V.T39 theorem V.R178 The mass gap remark V.D125 Black Hole as Maximal Topological Defect --- V.D58 definition V.R179 No primordial black holes remark V.T88 Compact-Object Classification --- V.T40 theorem V.P72 Hulse--Taylor Agreement --- V.P36 proposition V.R180 Pulsars probe the strong-field regime remark V.D126 Topological Channel --- V.D59 definition V.T89 Core Collapse Trigger --- V.T41 theorem V.R181 The trigger is structural, not thermal remark V.D127 Channel Reversal --- V.D60 definition V.P73 Neutrino Heating Condition --- V.P37 proposition V.R182 Explosion energy and the mass cut remark V.P74 Plateau Duration as Readout --- V.P38 proposition V.D128 r-Process as Rapid Charge Loading --- V.D61 definition V.R183 Gold and the r-process remark V.P75 Proto-Neutron Star Evolution --- V.P39 proposition V.P76 Birth Kick and Spin --- V.P40 proposition V.R184 The carbon connection remark V.P77 Equatorial focusing proposition V.D129 Accretion Funnel (tau-geodesic) definition V.R185 The alpha-viscosity re-read remark V.D130 Jet Axis (Topological Channel) definition V.P78 Jet-Torus Alignment proposition V.T90 Jet Collimation Theorem theorem V.R186 Observational comparison remark V.T91 Accretion Luminosity Bound theorem V.R187 Eddington Limit Re-Read remark V.D131 Synchrotron Readout definition V.R188 The ubiquitous sqrt3 remark V.P79 Neutrino Emission Channel proposition V.R189 IceCube neutrinos from AGN remark V.D132 AGN Lifecycle Phase definition V.T92 AGN Unification Theorem theorem V.R190 Quasar Redshift Distribution remark V.R191 Why the exponent is sim 4 remark V.D133 Binary Coherent-Instance System definition V.D134 GW Boundary-Character Wave definition V.R192 Why two polarizations, not six remark V.T93 Chirp Mass from Boundary Holonomy theorem V.P80 GW Energy Flux proposition V.R193 LIGO GW150914 Re-Read remark V.D135 Ringdown Readout definition V.T94 Ringdown Uniqueness Theorem theorem V.R194 No-hair test via ringdown remark V.D136 Standard Siren (tau) definition V.R195 Multi-Messenger GW170817 remark V.P81 Merger Graviton Count proposition V.D137 Toroidal Shadow (T^2 Readout) definition V.T95 Shadow Shape Theorem (T^2 vs S^2) theorem V.P82 Inner Shadow Ellipticity proposition V.D138 Photon Ring Winding Number definition V.P83 Photon Subring Spacing proposition V.R196 Observational accessibility remark V.D139 Polarization Handedness Signature definition V.T96 Polarization Winding Theorem theorem V.R197 M87* Shadow Re-Read remark V.R198 Sgr A* Shadow Re-Read remark V.R199 The strongest single test remark V.R200 Bullet Cluster Orthodox Argument remark V.D140 Boundary-Mass Offset (tau) definition V.T97 Bullet Cluster Without Dark Matter theorem V.P84 Lensing-Gas Offset Bound proposition V.D141 Handle-Scale Event definition V.D142 Wilson Skeleton (Cosmic Web) definition V.T98 Cosmic Web from Holonomy Loops theorem V.R201 BAO and Holonomy Periodicity remark V.D143 Topological Lensing Signature definition V.P85 Filament Scaling Relation proposition V.R202 Minimal Alphabet and Sector Count remark V.R203 From "Not Needed" to "Not Possible" remark V.D144 Sector Budget definition V.P86 Coupling Budget Completeness proposition V.D145 Sector Exhaustion Decomposition definition V.T99 Sector Exhaustion Theorem theorem V.D146 Dark Sector Hypothesis definition V.T100 No Fifth Sector theorem V.C14 No Dark Matter Particle corollary V.C15 No Dark Energy Field corollary V.C16 No Fifth Force corollary V.R204 What 68% and 27% Actually Are remark V.D147 Readout Artifact definition V.P87 LCDM Budget Translation proposition V.D148 Orbit-Depth-Dependent Readout definition V.D149 Depth-Projected Hubble Parameter definition V.R205 Both Measurements Correct remark V.T101 H0 Tension Resolution theorem V.P88 Depth-Hubble Monotonicity proposition V.D150 Category Error (LCDM) definition V.R206 Correct Parameters Wrong Ontology remark V.D151 Readout Projection Table definition V.P89 Sigma8 as Defect Amplitude proposition V.T102 Dark Sector Closure theorem V.R207 What Would Reopen the Case remark V.R208 From Part V to Part VI remark V.R209 No manifold Rightarrow no singularity remark V.D152 Temporal Opening definition V.R210 Planck Epoch Reinterpretation remark V.D153 Pre-Hadronic Regime definition V.D154 Regime Boundary Character definition V.P90 Same-Equation Proposition proposition V.T103 No-Singularity Theorem theorem V.R211 The Penrose--Hawking theorems are not wrong remark V.T104 Big Bang = Opening Regime theorem V.R212 No ``hot'' or ``cold'' remark V.R213 Falsifiability remark V.D155 Regime Invariance definition V.T105 Regime Invariance Theorem theorem V.R214 Contrast with running couplings remark V.C17 Inflaton No-Go Corollary corollary V.D156 Inflationary Regime definition V.D157 e-Fold Readout definition V.R215 Slow Roll Unnecessary remark V.T106 Flatness from Compactness theorem V.P91 Horizon Resolution proposition V.R216 Compactness vs. inflation remark V.R217 A falsifiable prediction remark V.D158 Threshold (Regime Boundary) definition V.D159 Canonical Thresholds definition V.T107 Ladder Monotonicity theorem V.D160 Neutron Threshold L_N definition V.R218 The mass hierarchy at L_N remark V.R219 Sphaleron Open Question remark V.R220 Sakharov Conditions remark V.D161 Nucleosynthetic Window definition V.T108 Nucleosynthesis from tau theorem V.R221 The lithium problem remark V.P92 CMB Origin proposition V.D162 Threshold Ladder definition V.D199 Opening Bookend definition V.R327 H–He Split remark V.R328 Beta Asymmetry remark V.D200 Density Gradient Narrative definition V.T152 Density Gradient Monotonicity theorem V.D201 Ionization in τ³ definition V.D202 Closing Bookend definition V.R329 No Baryon Annihilation remark V.D203 Neutrino Thread definition V.P114 Neutrino Background Origin proposition V.D204 Temporal Phase as Beta Cycle definition V.R330 Arc Summary remark V.D163 Gravitational Tension definition V.D164 Spherical Capacity definition V.D165 Linking Class definition V.D166 Black Hole (Topological Event) definition V.T109 BH Threshold Theorem theorem V.T110 BH Toroidal Topology theorem V.R222 Event horizon as linking boundary remark V.P93 No Interior Singularity proposition V.C18 Information Preservation corollary V.D167 Canonical BH Neighborhood definition V.D168 BH Bipolarity definition V.T111 Necessary Bipolarity theorem V.D169 Polarity Imbalance definition V.P94 Polarity Convergence proposition V.D170 Blueprint definition V.D171 Blueprint fusion mathrmFuse definition V.D172 Blueprint Monoid definition V.T112 Blueprint Monoid Closure theorem V.R223 Irreversibility of mergers remark V.R224 BH Entropy Formula Interpretation remark V.R225 Export to Book VI remark V.D173 Mature Black Hole definition V.T113 Defect-Mass Coupling theorem V.T114 No-Shrink Theorem theorem V.P95 Hawking Readout proposition V.C19 No BH Evaporation corollary V.R226 Information Paradox Dissolved remark V.D174 Permanence Hallmark definition V.R227 Permanence Export to Book VI remark V.P96 BH Entropy Formula proposition V.R228 Why overlap forces merger remark V.T115 Merger Normal Form theorem V.R229 What the Normal Form does not give remark V.D175 Ringdown mode definition V.P97 Ringdown damping is structural proposition V.D176 BH mass scale at depth n definition V.P98 Mass gap between adjacent primorial levels proposition V.R230 The mass gap and the IMBH desert remark V.R231 Scope note on mass spectrum predictions remark V.D177 Base Wilson loop definition V.P99 Gravitational deconfinement proposition V.R232 Contrast with the strong sector remark V.P100 BH gravitational Aharonov--Bohm phase proposition V.P101 Radiated energy bound proposition V.R233 The 1/sqrt2 remark V.D178 Topological motif definition V.T116 Finite Motif Theorem theorem V.R234 Contrast with fractal cosmologies remark V.D179 Saturation radius definition V.T117 Saturation Radius Theorem theorem V.R235 Saturation radius vs. observable universe remark V.D180 Absorbing pattern definition V.T118 Absorbing Pattern Theorem theorem V.R236 No infinite hierarchy remark V.C20 Global Finiteness corollary V.R237 What the chain does NOT prove remark V.P102 Defect entropy converges to zero proposition V.D181 BH-dominated epoch definition V.D182 Coherence horizon definition V.R238 Not a Big Crunch remark V.D183 Generative and refinement phases definition V.R239 Generative does not mean explosive remark V.T119 Eternal Circulation Theorem theorem V.R240 Late-stage conditions favor complexity remark V.R241 Not the anthropic principle remark V.R242 The key difference: no infinity remark V.R243 Scope note: CMB predictions C2, C5, C6 remark V.D184 Falsification levels definition V.R244 The lesson: do not add, recognize remark V.T120 Boundary Completeness theorem V.R245 Comparison with orthodox unification remark V.P103 Cross-coupling as naturality proposition V.R246 Naturality replaces gauge invariance remark V.P104 iota_tau mediates all ten couplings proposition V.R247 Scope note: implementation roadmap remark V.R248 Part VI Achievement Summary remark V.R249 Open Questions remark V.R250 Export to Books VI and VII remark V.R251 Bridge to Part VII remark V.R252 Entries with ``No counterpart'' remark V.R253 Preservation does not mean identity remark V.D185 Structural artifact definition V.R254 The common thread remark V.D186 Ontic and readout layers definition V.R255 Orthodox physics is not wrong remark V.D187 Readout interpretation protocol definition V.R256 Where tau adds value remark V.R257 The vacuum catastrophe as diagnostic remark V.R258 The analogy of cartography remark V.T121 Properties of the correspondence functor theorem V.R259 Non-surjectivity is a feature remark V.R260 Respect for the empirical record remark V.R261 The microscope analogy remark V.T122 Renormalization as tower truncation theorem V.R262 Scheme independence explained remark V.D188 UV shield definition V.R263 Comparison with lattice QFT remark V.T123 Path integral recovery theorem V.R264 The Wick rotation is a chart operation remark V.R265 The field as scaffolding remark V.R266 Not all parameters have been computed remark V.T124 Profinite convergence theorem V.R267 Why m_n and not m_e? remark V.R268 GR's scope remark V.R269 Spacetime in tau remark V.T125 GR as chart shadow of the tau-Einstein identity theorem V.T126 The readout quantization obstruction theorem V.R270 Gravity is already quantum remark V.T127 No singularity theorem theorem V.R271 The metric is a derived quantity remark V.T128 Sector Exhaustion --- no dark sector theorem V.R272 Dualities as structural echoes remark V.T129 Landscape collapse theorem V.R273 Occam and dimensions remark V.T130 Native holography theorem V.R274 AdS/CFT as a partial echo remark V.R275 iota_tau is a mathematical constant remark V.R276 Why SUSY was not found at the LHC remark V.R277 The parable of the library remark V.R278 LQG's genuine contribution remark V.T131 No knobs in tau theorem V.R279 The residual manifold in LQG remark V.R280 Four echoes, one architecture remark V.R281 CDT as a computational echo remark V.R282 Sorkin's Lambda prediction remark V.R283 Respect and replacement remark V.P105 Twistor embedding proposition V.R284 Twistors as shadow remark V.P106 NCG spectral triple from tau proposition V.T132 Gravity as readout --- no renormalization theorem V.R285 The two relevant directions remark V.R286 Verlinde's rotation curves remark V.T133 Completeness of the boundary algebra theorem V.R287 No hierarchy among programmes remark V.D189 VM representation of a quantum state definition V.T134 Measurement problem dissolution theorem V.R288 Superposition in the VM remark V.T135 Bell inequality in tau theorem V.R289 Entanglement as address sharing remark V.P107 Decoherence as address-resolution shadow proposition V.R290 The century of confusion remark V.T136 No singularities in tau theorem V.T137 No UV divergences in tau theorem V.R291 Renormalization is correct but unnecessary remark V.T138 No dark sectors theorem V.T139 Vacuum energy is exactly zero theorem V.R292 The 10^120 remark V.R293 Why ``dissolve'' and not ``solve'' remark V.R294 Honest vs. premature remark V.T140 Elayer1 theorem V.R295 Timeline for the topology test remark V.R296 The honest status of galaxy fits remark V.R297 The subtlety of Lambda = 0 remark V.R298 Precision of the neutrino prediction remark V.R299 Scope of the delta_A prediction remark V.R300 What would vindicate inflation remark V.T141 No Shrink---restatement theorem V.R301 The information paradox as diagnostic remark V.R302 Fifth force vs. sixth force remark V.R303 What would NOT falsify tau remark V.R304 Falsifiability as strength remark V.R305 One anchor, not zero remark V.R306 The sqrt3 remark V.R307 The neutrino exponent remark V.R308 Comparison with the Standard Model remark V.T142 E1 Completeness Theorem theorem V.P111 Tensor-Square Connection proposition V.D192 He-4 Packing Maximum definition V.D193 Face-Conflict Probability definition V.D194 Domain-Wall Correction Factor definition V.D195 Primordial He-4 Mass Fraction definition V.D196 Neutron-to-Proton Ratio from Y_p definition V.T146 Packing Maximum Theorem theorem V.T147 Face-Conflict Theorem theorem V.T148 Three Decompositions Identity theorem V.T149 Y_p Derivation from Packing and Correction theorem V.T150 n/p Ratio Derivation theorem V.P112 Y_p Observational Consistency proposition V.R322 71 = p_20 Structural Echo remark V.D197 Threshold-Dependent Admissibility definition V.D198 Baryogenesis Window definition V.R323 Commutator Magnitude at omega-Crossing remark V.R324 eta_B Structural Candidate remark V.R325 Primorial-Confinement Bridge remark V.R326 Confinement Multiplicity Estimate remark V.T151 N_eff from Sector Exhaustion theorem V.P113 Dark Sector Closure proposition V.D205 The Hermetic Principle definition V.D206 Temporal Arc Principle definition V.D207 Relational Space Principle definition V.D208 Genealogical Branching Rate definition V.L4 Single Scale Degree of Freedom lemma V.L5 Minimal Mature Black Hole lemma V.R331 RG flow as defect flow remark V.R332 EM sign structure and plasma modes remark V.R333 No-isolated-charges as VM-shadow denial remark V.D209 Mixed Reconnection Defect definition V.R334 Alfven mode existence decidability remark V.D210 Minimal Mixed Phase Quantum definition V.D211 Neutron Multiplicity Bound definition V.D212 Closing Identity definition V.D213 Sector Lift Functor definition V.R337 sigma-equivariance remark V.R338 H_fix[omega] subfield remark V.T154 The G-alpha Bridge theorem V.R341 Three routes, one G remark V.T155 Mass Hierarchy Exponent theorem V.R342 The chain of masses remark V.P115 Hierarchy as Power Law proposition V.R343 Supersymmetry unnecessary remark V.R344 What Dirac got right and wrong remark V.P116 Precision Budget proposition V.R345 Independence from m_e remark V.R346 The exponent as structural invariant remark V.R347 As above, so below --- quantified remark V.D214 The Master Constant --- Layer 0 definition V.D215 Sector Couplings --- Layer 1 definition V.D216 Fine-Structure Constant --- Layer 1 definition V.D217 Mass Ratio Formula --- Layer 1 definition V.D218 Gravitational Coupling --- Layer 1 definition V.D219 The Calibration Anchor --- Layer 2 definition V.T156 Mass Derivations --- Layer 2 theorem V.R348 The 5-to-1 collapse remark V.R349 Boltzmann and temperature remark V.R350 Room for improvement remark V.D220 The SI Cascade Algorithm definition V.R351 Honest comparison remark V.T157 Calibration Sufficiency theorem V.D221 Export E1: Complete Physical Arena definition V.D222 Export E2: Arrow of Time definition V.D223 Export E3: Entropy Splitting definition V.D224 Export E4: Defect Functional definition V.R352 The eight fluid regimes remark V.D225 Export E5: Black Hole Topology definition V.R353 Scope: partially conjectural (E5) remark V.D226 Export E6: Cosmological Endstate definition V.R354 Scope: conjectural (E6) remark V.D227 Export E7: Constants Ledger definition V.D228 Export E8: Falsification Pack definition V.R355 The 5-20 year horizon remark V.D229 Export E9: Self-Describing Closure definition V.R356 The seed-crystal principle remark V.R357 Scope propagation rule remark V.T158 Export Completeness theorem V.R358 Enrichment is not reduction remark V.P117 Entropy splitting and life proposition V.R359 All five sectors are biologically necessary remark V.D230 Far-from-equilibrium defect pattern definition V.P118 Black holes as far-from-equilibrium patterns proposition V.R360 The alive-or-not question remark V.R361 The enrichment functor is not yet constructed remark V.T159 The Hermetic Identity theorem V.D231 The iota_tau chain definition V.R362 Why 2/(pi + e)? remark V.P119 Generator universality proposition V.R363 The apparent running remark V.T160 Physics as self-description theorem V.R364 Wigner's question answered remark V.P120 Structural rigidity proposition V.R365 The landscape problem dissolved remark V.T161 The Hermetic Closure theorem V.R366 The theory predicts its own discovery remark V.T162 The Hermetic Truth theorem V.P121 Permanent sector distinction proposition V.R367 Limits are not failures remark V.R368 The logos is the boundary algebra remark V.R369 The longest derivation chain in physics remark V.D232 Milgrom Constant from tau definition V.T163 Baryonic Tully-Fisher Relation from V.T85 theorem V.T164 NGC 3198 Zero-Parameter Prediction theorem V.P122 a_0 from H_0 Tension proposition V.R370 H_0 Tension as Galactic Scale Effect remark V.R371 MOND Comparison Table remark V.D233 sigma-Polarity Neutrino Mass Matrix definition V.T165 Mass Eigenvalue Ratio Formula theorem V.T166 Cosmological Bound Satisfaction theorem V.P123 PMNS Mixing Angle Prediction proposition V.R372 Sprint 4 Findings and OQ-C3 Status remark V.T167 Effective Majorana Mass from sigma-matrix theorem V.D234 T² QNM Mode Structure definition V.T168 QNM Fundamental Frequency Ratio = ι_τ⁻¹ theorem V.T169 GW Echo Times t± = 4GM·ι_τ^{±1}/c³ theorem V.P124 T² Shadow Radius vs EHT proposition V.P125 T² Entropy = π·ι_τ × S² Entropy proposition V.R373 LIGO Echo Window: Δt = 4GM(1-ι_τ²)/(c³·ι_τ) remark V.R374 No-Hawking from τ-vacuum: SA-i Forbids Bogoliubov Modes remark V.T170 Baryogenesis Exponent 15 = dim(τ³) × |generators| theorem V.T171 (5/6) Threshold Factor Shared with Y_p = 20/81 theorem V.T172 Primary Baryogenesis Formula: η_B = α·ι_τ¹⁵·(5/6) theorem V.P126 Sakharov CP Source: A-Sector Balanced Polarity via Parity Bridge proposition V.R375 Leptogenesis Pathway: Majorana Neutrinos Enable L→B Conversion remark V.D235 Neutrino Exponent Derivation: Torus Winding Strategy definition V.T173 One-Parameter Neutrino Family: Scale-Invariant Result 39.45 theorem V.T174 PMNS Shared Eigenvector Structure: Identity from sigma-Polarity theorem V.P127 Normal Mass Ordering from sigma-Polarity Structure proposition V.R376 OQ-C3 Status after Sprint 4A: Asymmetry is the Open Question remark V.D236 Neutrino CF-Asymmetry: Grid-Optimal Exponent Offsets from sigma-Polarity Structure definition V.T175 Best sigma-Matrix Exponent Pair from Grid Scan: (Delta_pq=1.16, Delta_pr=0.87) at +7 ppm theorem V.T176 Majorana CP Phases from sigma=C_tau Constraint: phi_2 = 0 theorem V.P128 Asymmetry in sigma-Exponents: Delta_pq - Delta_pr approx 2/13 (CF-structural candidate) proposition V.R377 OQ-C3 Status after Sprint 5A: CF Candidate Fails; Grid Optimum Found remark V.D237 Neutrino Exponent 4/3 Ratio: Lemniscate Counting definition V.T177 (8/7, 6/7) Candidate: Neutrino Mass Ratio from Lemniscate n=7 theorem V.T178 Structural Derivation: Δpq/Δpr = 4/3 from Lemniscate Counting theorem V.P129 Neutrino Span=2=|lobes|; Ratio=4/3 from n=7 Decomposition proposition V.R378 OQ-C3 Status after Sprint 6A: 4/3 Hypothesis remark V.D238 SA-i mod-W₃(4) Baryogenesis Mechanism: ι_τ¹⁵ = (ι_τ³)^W₃(4) definition V.T179 ι_τ¹⁵ from Generator Orbit: 15 = dim(τ³) × |generators| theorem V.T180 (5/6) Uniquely Forced from Threshold Topology theorem V.P130 Baryogenesis First Principles: Generator Orbit + Threshold Uniqueness proposition V.R379 V.OP2 Status after Sprint 6C: SA-i mod-5 Mechanism Proposed remark V.D244 Sector-Collapse Signature at the BH Threshold definition V.P132 Truncation-Pipeline Coherence proposition V.R381 QA Harmonization Status (Sprint 7H) remark V.D241 T² Quadrupole Shadow Correction Factor: f = 1 + ι_τ²/4 definition V.D242 T² QNM Eigenvalue Structure: ω_{n,m} = √(n²+m²ι_τ⁻²)/(2πr_s) definition V.D243 T² GW Echo Time Formulas with Frequency Bands definition V.T184 EHT Shadow T² Correction: f = 1 + ι_τ²/4 at 2.91% over GR theorem V.T185 QNM Frequency Ratio = ι_τ⁻¹ ≈ 2.930 as Clean S²/T² Discriminator theorem V.P131 Three Falsifiable BH T² Predictions with Fiber Structure Derivation proposition V.R380 V.OP5 Status: SOLVED via Sprint 7E Observational Suite remark V.D245 SA-i mod-5 Formal Proof: Geometric Series Mechanism definition V.T187 Sakharov Conditions from τ³ σ-Involution theorem V.T188 η_B Formal Derivation: α·ι_τ¹⁵·(5/6) at −10320 ppm theorem V.P133 Baryogenesis Threshold Placement: n_EW < n_B < n_N proposition V.R382 V.OP2 Status: SOLVED (τ-effective) via Sprint 7D SA-i mod-5 Proof remark V.D246 Self-Similar NNLO Correction: δ₁=3/175, δ₂=9/700 definition V.T189 Grid Optimum Structural Derivation: (203/175, 609/700) theorem V.P134 Self-Similar 4/3 Ratio Preservation under NNLO proposition V.R383 V.OP1/OQ-C3 Status: PARTIAL-IMPROVED after Sprint 7B remark V.D247 τ-Native Baryon Density ω_b from η_B definition V.D248 Boundary Holonomy Matter Fraction definition V.T190 Baryon Density from Master Constant theorem V.T191 Sound Horizon from τ-Native Inputs theorem V.T192 First Peak from Holonomy Matter Fraction theorem V.P135 Structural Acoustic Scale ι_τ⁻⁵ Cross-Check proposition V.P136 CMB Tensor-to-Scalar Ratio r = ι_τ⁴ proposition V.R384 V.OP3 Status: PARTIAL-IMPROVED after Sprint 8A remark V.D249 Neutrino Free-Streaming Scale from σ-Polarity Masses definition V.D250 CνB Temperature Chain definition V.T193 Holonomy Matter NLO Correction Scan theorem V.T194 Neutrino Phase Shift on CMB Peaks theorem V.T195 Two-Horizon Consistency from ι_τ theorem V.P137 Free-Streaming Suppression from τ-Native Masses proposition V.P138 CMB-S4/PTOLEMY/DESI Falsification Suite proposition V.R385 V.OP3 Status After Sprint 8B remark V.D251 Structural Hubble Parameter h = 2/3 + ι_τ²/W₃(3) definition V.D252 DE-Closure Matter Density ω_m from Ω_Λ and h definition V.D253 Scalar Amplitude NLO: A_s = α_τ·ι_τ¹⁴·(1−ι_τ³/3) definition V.T196 Hubble Parameter from τ: h at −120 ppm theorem V.T197 Full CMB Pipeline with Structural h theorem V.T198 Scalar Amplitude NLO: Inflationary Consistency theorem V.P139 Reionization Optical Depth from z_reion = 8 proposition V.R386 V.OP3 Status After Sprint 8E: h Closes the Pipeline remark V.D254 Silk Damping Scale from Holonomy Ratio definition V.R387 η_B Exponent Resolution: 15 vs 20 (Effective 19 = W₅(3)) remark V.R388 V.OP3 Status After Wave 14 Phase 1 remark V.D255 Baryon Loading Parameter from tau-Native omega_b definition V.P140 Peak Height Odd/Even Asymmetry from Baryon Loading proposition V.T199 DE-Closure Matter Density at -675 ppm theorem V.D256 Primordial B-Mode Amplitude from r = iota_tau^4 definition V.P141 B-Mode Detection Forecast: CMB-S4 at 14 sigma proposition V.T200 Holonomy Ratio Acceleration Theorem theorem V.D257 Bare vs Dressed Acceleration Scales definition V.R389 √ι_τ Bridge for BTFR Normalization remark V.D258 20-Galaxy Benchmark Table definition V.R390 Multi-Galaxy Statistical Summary remark V.T201 Capacity Equation Numerical Solution theorem V.D259 Linearized Capacity Gap definition V.T202 tau Interpolation Function theorem V.P142 RAR Quantitative Prediction proposition V.T203 Cluster Capacity Mass Discrepancy theorem V.D261 Cluster-Scale Screening Enhancement definition V.T204 Redshift-Dependent Acceleration Scale theorem V.P143 JWST Rotation Curve Predictions proposition V.T205 c² Cancellation Theorem theorem V.D262 Linearized Velocity Scale definition V.T206 Metric-Capacity Coupling Source Theorem theorem V.D263 Metric vs Capacity Source Distinction definition V.D264 Cocycle-Defect Amplification Factor definition V.P144 Nonlinear Amplification Pathway proposition V.T207 V.T85 Algebraic Resolution Theorem theorem V.D265 Algebraic Derivation Chain for a₀ definition V.R391 Capacity Equation as Qualitative Mechanism remark V.R392 Connection to Cocycle-Defect Minimization remark V.D266 Two-Channel Acceleration Decomposition definition V.D267 Channel Fraction definition V.D268 Transition Radius definition V.T208 Two-Channel Interpolation Theorem theorem V.T209 Algebraic Distinctness from Standard MOND theorem V.P145 Lie Algebra Cross-Term proposition V.P146 AQUAL as Projection proposition V.R393 GEM Mapping remark V.R394 Channel Dominance at Galactic Scales remark V.R395 Bare/Dressed Discrepancy Persists remark V.T210 Photon-Capacity Deflection theorem V.P147 Lensing–Dynamical Mass Equality corollary V.R396 MOND Lensing Comparison remark V.D269 τ-Native Luminosity Distance definition V.D270 τ-Native Angular Diameter Distance definition V.T211 Distance Modulus from τ-Native Parameters theorem V.D271 Deceleration Parameter q₀ definition V.D272 Einstein Radius from Boundary Holonomy definition V.T212 Strong Lensing Cross-Section Enhancement theorem V.R397 SLACS Einstein Radius Comparison remark V.D273 Weak Lensing Convergence from Boundary Holonomy definition V.D274 τ-Native Convergence Power Spectrum definition V.R398 DES/KiDS Weak Lensing Compatibility remark V.T213 Quantitative Bullet Cluster Mass Prediction theorem V.R399 Cluster Lensing Catalog remark V.D275 BAO Angular Scale from τ-Native d_A definition V.T214 DESI Consistency Check theorem V.R400 BAO–CMB Pipeline Closure remark V.T215 Dark Sector Consistency Theorem theorem V.R401 τ-vs-ΛCDM Discriminator Table remark V.T216 BH Entropy Catalog theorem V.R402 BH Entropy Numerical Values remark V.D276 Readout Gibbs State definition V.T217 Readout Temperature Theorem theorem V.P148 Readout Spectrum is Planckian proposition V.R403 Readout Temperature Numerical Catalog remark V.D277 Bi-Rotational Dynamics on T² definition V.D278 Synchrotron Frequency Pair definition V.T218 Bi-Rotational Synchrotron Theorem theorem V.D279 Brightness Harmonic Decomposition definition V.T219 Harmonic Eigenfrequencies theorem V.P149 Sgr A* Horizon-Scale Variability proposition V.R404 M87* Variability Timescales remark V.D280 SMBH Prediction Catalog definition V.T220 M87* Prediction Suite theorem V.T221 Sgr A* Prediction Suite theorem V.R405 EHT Comparison Table remark V.D281 GW Event Catalog definition V.T222 Chirp Mass Consistency theorem V.T223 T^2 Ringdown Formula theorem V.R406 LIGO Comparison Table remark V.D282 Blueprint Fusion Energy definition V.T224 Merger Energy Theorem theorem V.P150 Equal-Mass Energy Fraction proposition V.D283 Echo Amplitude Model definition V.T225 Echo Detection Threshold theorem V.P151 Stacked Echo SNR proposition V.R407 Echo Search Table remark V.T226 Black Hole Consistency Theorem theorem V.R408 BH Falsification Summary remark V.D284 Toroidal B-Field Configuration definition V.T227 RM Winding Theorem theorem V.P152 RM Gradient Magnitude proposition V.R409 M87* RM Comparison remark V.D285 Toroidal Flux Integral definition V.D286 Poloidal Flux Integral definition V.T228 Flux Threading Theorem theorem V.P153 Flux Ratio proposition V.R410 Topological Flux Protection remark V.D287 Stokes Parameter Decomposition on T² definition V.T229 Circular Polarization Winding theorem V.P154 Linear Pol Fraction from Toroidal Coherence proposition V.R411 EHT M87* Polarization Comparison remark V.D288 Near-Horizon B-Field definition V.T230 Magnetic Field Ratio Theorem theorem V.P155 M87* B-Field Estimate proposition V.R412 Complete Magnetic Table remark V.D289 Jet Poloidal Field definition V.D290 Jet Magnetic Helicity definition V.T231 Jet Helicity Conservation theorem V.T232 Jet Collimation from Hoop Stress theorem V.P156 Jet B_z/B_φ at Base proposition V.R413 Reconnection Signatures in Jets remark V.D291 Wilson Loop Magnetic Flux definition V.D292 Filament B-Field Alignment definition V.T233 Filament Magnetic Field Theorem theorem V.P157 IGMF Magnitude proposition V.P158 Coherence Length from Topology proposition V.R414 Vernstrom Comparison remark V.R415 Blazar IGMF Bound remark V.R416 Wave 23 Magnetic Prediction Table remark V.R417 Cross-Theme Consistency remark V.D293 Defect Fraction Function definition V.D294 Transition Redshift z_acc definition V.T234 Ω_Λ Structural Theorem theorem V.P159 w₀ from Defect Dynamics proposition V.R418 Transition Redshift Comparison remark V.D299 High-z Acceleration Enhancement definition V.T239 JWST Enhancement Theorem theorem V.P163 SFE Enhancement Factor proposition V.P164 UV Luminosity Function Excess proposition V.R422 JWST Comparison Table remark V.D295 CPL Mapping of τ-EoS definition V.T235 No Phantom Crossing Theorem theorem V.P160 DESI Comparison proposition V.R419 DESI DR2 Confrontation remark V.D296 Holonomy Suppression Factor definition V.D297 σ₈ τ-Native definition V.T236 σ₈ Suppression Theorem theorem V.P161 S₈ Tension Resolution proposition V.R420 Weak Lensing Comparison remark V.D298 τ-Native Growth Factor definition V.T237 Growth Equation with τ-EoS theorem V.T238 Growth Index Theorem theorem V.P162 f·σ₈ Comparison Table proposition V.R421 RSD Data Comparison remark V.D300 τ-Native Transfer Function definition V.T240 Power Spectrum Consistency theorem V.P165 BAO Scale Prediction proposition V.R423 BOSS Data Comparison remark V.R424 Wave 24 Dark Energy Prediction Table remark V.R425 ΛCDM Tension Resolution Summary remark V.R426 Cross-Sprint Consistency remark V.D301 Deuterium Bottleneck Temperature definition V.D302 BBN Network Light Elements definition V.D303 BBN Reaction Chain definition V.D304 Sector Assignment definition V.D305 T² Fiber Holonomy Correction definition V.D306 ⁷Be Suppression Factor definition V.D307 Complete BBN Abundance Table definition V.T241 D/H from τ-native η_B theorem V.T242 Sector Distribution {1,4,7} theorem V.T243 Suppression = 1/dim(τ³) = 1/3 theorem V.T244 Li-7 Resolution theorem V.T245 Y_p Preservation theorem V.T246 D/H Preservation theorem V.T247 He-3/H from τ-native η_B theorem V.P166 D/H Observational Consistency proposition V.P167 Spite Plateau Consistency proposition V.P168 Selectivity: Only A ≥ 7 Suppressed proposition V.P169 BBN Table Consistency proposition V.R427 D/H Anti-correlation remark V.R428 N3 Status Upgrade remark V.R429 ⁷Be Production as B-Sector remark V.R430 EM Phase-Space Restriction remark V.R431 Voxel Packing Connection remark V.R432 Packing Threshold at A = 7 remark V.R433 Stellar Depletion and Spite Plateau remark V.R434 All Four from Single η_B remark V.R435 N3 Falsification Update remark V.R436 N4 Falsification Update remark V.R437 Wave 25 BBN Prediction Table remark V.R438 Cross-Sprint Consistency remark V.D308 Fiber Co-dimension of Dissipative Structures definition V.D309 She-Lévêque τ-Decomposition definition V.T248 She-Lévêque from τ³ Dimensions theorem V.T249 Intermittency Exponent Agreement theorem V.P170 ζ_p Experimental Consistency proposition V.R439 Fitted→Derived remark V.R440 Fiber Filament Interpretation remark V.D310 Kolmogorov Exponent Decomposition definition V.T250 -5/3 from τ Dimensions theorem V.T251 C_K = 3/2 theorem V.P171 C_K Observational Match proposition V.R441 Two-Thirds Law remark V.R442 5=|gen|+dim(T²) Interpretation remark V.D311 Fast Reconnection Rate definition V.T252 v_rec = ι_τ² v_A theorem V.P172 Solar Flare Consistency proposition V.R443 Sweet-Parker vs τ-Rate remark V.R444 B-Sector Topological Transition remark V.D312 Alfvén Damping Rate definition V.D313 Coronal Heating Flux definition V.T253 τ-Alfvén Damping = ι_τ² ω theorem V.P173 Coronal Flux Consistency proposition V.R445 Parker Solar Probe Testability remark V.D314 Decompactification Bound definition V.D315 Admissibility Class definition V.T254 Primorial Convergence Rate theorem V.P174 Leray Limit Recovery proposition V.R446 Clay Bridge Status remark V.R447 N5 She-Lévêque Falsification remark V.R448 N6 Reconnection Falsification remark V.R449 N7 Kolmogorov Falsification remark V.R450 Wave 26 Prediction Summary remark V.R451 Cross-Sprint Consistency remark V.T255 Two-Path Complementarity for First Peak theorem V.R452 V.OP3 Status Wave 36A: Two-Path Verified remark V.R453 DESI σ₈ Falsification Window remark V.D316 Peak Position and Height Structure definition V.T256 Peak Height Ratios from Baryon Loading theorem V.P175 Peak Ratio Consistency Check proposition V.D317 Coupled NLO Correction Space definition V.T257 First Peak NLO at +69 ppm theorem V.P176 Error Cancellation Preserved at NLO proposition V.D318 NLO Sound Horizon at Drag Epoch definition V.T258 BAO Scale from NLO Pipeline theorem V.P177 DESI BAO Consistency proposition V.D319 Hubble Derivation Chain definition V.T259 Uniqueness of Hubble Formula theorem V.P178 Hubble Self-Consistency Check proposition V.D320 NLO Peak Positions and Structural Tension definition V.T260 Peak-Ratio Tension from Acoustic Physics theorem V.D321 Silk Damping at NLO definition V.P179 Damping Ratio Preserved at NLO proposition V.R454 V.OP13 Status Wave 38: ℓ₁ at +69 ppm remark V.R455 V.OP11 Status Wave 38: BAO Scale remark V.R456 V.OP12 Status Wave 38: H₀ Derived remark V.R457 V.OP3 Status Wave 38: CMB NLO Pipeline remark V.D322 Peak-Ratio Phase-Shift Space definition V.T261 Peak-Ratio NLO Improvement theorem V.P180 Peak-Ratio Self-Consistency proposition V.R458 V.OP3 Status Wave 39: Peak Ratios Resolved remark V.D323 Baryon Density NLO Correction definition V.T262 Baryon Density Improvement theorem V.P181 Sound Horizon Improvement proposition V.R459 V.OP11 Status Wave 39: BAO Scale remark V.D324 S₈ NLO definition V.T263 S₈ Tension Resolution theorem V.P182 Lensing Consistency proposition V.R460 V.OP8 Status: S₈ Tension Resolved remark V.D325 Matter Transfer Function Baseline definition V.R461 Boltzmann Solver Roadmap remark V.R462 τ vs ΛCDM Transfer Comparison remark V.D326 Coupled Two-Parameter NLO Correction Space definition V.T264 Coupled NLO Optimum: δ_h = κ_D/N_e theorem V.P183 Multi-Observable Consistency proposition V.R463 Coupled NLO Status remark V.D327 Phase-Shift Exponent Analysis definition V.R464 Phase-Shift Sensitivity remark V.D328 ω_m NNLO Correction Space definition V.T265 ω_m Sub-20 ppm at NNLO theorem V.D329 ω_m–Peaks Pareto Barrier definition V.P184 Density-Sector Consistency proposition V.R465 V.OP11/V.OP13 Status: Wave 41 remark V.R466 Two-Path Convergence at NNLO remark V.D330 S₈ NNLO Density-Regime Value definition V.T266 S₈ NNLO Consistent with KiDS and HSC theorem V.R467 S₈ Pareto Duality remark V.D331 BAO NNLO Distance Table definition V.T267 BAO Sub-1300 ppm at NNLO theorem V.P185 BAO Systematic Improvement NLO→NNLO proposition V.D332 Density-Sector Observable Scorecard definition V.P186 Density-Sector Sub-1300 ppm Consistency proposition V.R468 Open Problems Status — Wave 42 remark V.T268 Normal Hierarchy from Winding Exponent Order theorem V.P187 One-Parameter Neutrino Mass Structure proposition V.D333 Individual Neutrino Mass Table definition V.T269 Mass-Squared Splittings from τ-Exponents theorem V.P188 JUNO/DUNE Cross-Check Predictions proposition V.T270 Baryogenesis NLO from Fiber EM Correction theorem V.R469 Baryogenesis Assessment (Wave 47) remark V.D334 21cm Brightness Temperature definition V.D335 Spin Temperature Coupling Regimes definition V.T271 21cm Absorption Trough from tau-Native Inputs theorem V.P189 EDGES/HERA/SKA Predictions proposition V.R470 V.OP9 Status: PARTIAL-IMPROVED remark V.D336 Neutron Star Crust-Core Transition Density definition V.P190 Crust Fraction from Defect-Tuple Crossing proposition V.R471 Condensed Matter Bridge Status (OQ-C6) remark V.T272 Readout Channel Entropy Bound theorem V.T273 Ontic Entropy Monotonicity for Mature BH theorem V.P191 Page Curve Analog: Saturation at Permanence proposition V.R472 V.OP6 Status: PARTIAL-IMPROVED remark V.D337 Algebraic–PDE Split for Rotation Curves definition V.P192 External Computation Requirements for v(r) proposition V.R473 V.OP4 Final Assessment remark V.R474 Topology Imprints on Gravitational Waves remark V.R475 GW Memory as Topological Transition remark V.R476 Binary Binding as Shared Holonomy Class remark V.R477 BKL Billiard Domain = T² Moduli Space (Hartnoll-Yang 2025) remark V.P193 Modular Image of the τ-Torus proposition V.R478 Sensitivity of Spectral Coincidence remark V.R479 Bipolar Involution and L-Function Reflection remark V.T274 Structural e-Fold Count N_e = 57 theorem V.T275 Scalar Amplitude from alpha_tau Inheritance theorem V.T276 Tensor-to-Scalar Ratio from Fiber Dimensional Suppression theorem V.D338 Internal vs Diagrammatic Viewpoint definition V.T277 Generator Orbit Suppression: iota_tau^15 from sigma-Involution theorem V.T278 (5/6) Uniquely Forced from Threshold Ladder Topology theorem V.P194 CP Asymmetry from A-Sector Polarity proposition V.D339 NF-Prefix Cylinder definition V.L6 k* Selection Rule lemma V.L7 Clopen Nesting of NF-Prefix Cylinders lemma V.D340 Cumulative Topology Change definition V.D341 Wilson-Loop Superstructure definition V.T279 r/R = iota_tau from Fiber Structure theorem V.P195 Polarity Convergence via Contraction Mapping proposition V.D342 omega-Germ Normalizer Norm_omega definition V.L8 Idempotence of Norm_omega lemma V.D343 Stability Index of omega-Germ definition V.P196 Imbalance as Multiplicative Homomorphism proposition V.L9 Basin Preservation under Ringdown Dynamics lemma V.L10 Transporter-Hartogs Commutativity lemma V.L11 Carriers as Germ Images lemma V.D344 Admissible Endomorphism Monoid HolEnd^adm_tau definition V.D345 Three-generation topology definition V.T280 Three generations from rank theorem V.R480 Consistency of the three proofs remark V.T281 Higgs mass from n=7 theorem V.R481 n=5 to n=7: the refinement pathway remark V.T282 Proton--neutron mass difference theorem V.T283 Koide relation from tau theorem V.T284 Winding exponents for muon/electron theorem V.T285 NNLO lepton mass correction theorem V.R482 Spectral hierarchy remark V.T286 Electroweak precision from tau theorem V.R483 Correlated precision remark V.R484 Respect for the empirical record remark V.R485 The microscope analogy remark V.T287 Renormalization as tower truncation theorem V.R486 Scheme independence explained remark V.D346 UV shield definition V.R487 Comparison with lattice QFT remark V.T288 Path integral recovery theorem V.R488 The Wick rotation is a chart operation remark V.T289 Profinite convergence theorem V.R489 Why m_n and not m_p? remark V.R490 The field as scaffolding remark V.R491 Tarski Euclidean axioms and emergent curvature remark V.T290 Cabibbo angle from tau --- IV.T152 theorem V.R492 Why not iota_tau alone? remark V.T291 Wolfenstein A from tau --- IV.T165 theorem V.R493 The generation--lobe ratio remark V.T292 Wolfenstein rhobar --- IV.T168 theorem V.T293 Wolfenstein etabar --- IV.T167 theorem V.T294 Solar angle theta_12 --- IV.T174 theorem V.R494 Scope status remark V.T295 Atmospheric angle theta_23 --- IV.T175 theorem V.T296 Neutrino mass sum --- V.T165 theorem V.P197 Normal hierarchy --- V.P127 proposition V.R495 Majorana nature remark V.T297 NNLO self-similar corrections --- V.D246/V.T189 theorem V.T298 theta_QCD=0 from SA-i mod-3 --- IV.T160 theorem V.R496 The mod-3 pattern remark V.T299 Baryogenesis formula --- V.T170/V.T188 theorem V.R497 The algebraic identity remark V.P198 Sakharov conditions in tau --- V.T187 proposition V.R498 The exponent 19 remark V.R499 One constant, not six parameters remark V.T300 Tensor-to-scalar ratio r=iota_tau^4 from fiber suppression theorem V.R500 The exponent is geometric, not tuned remark V.T301 E-fold count N_e=57 from fibration and CF window theorem V.T302 Scalar spectral index n_s=1-2/N_e theorem V.R501 n_s is exact, not fitted remark V.T303 Scalar amplitude A_s from tau theorem V.R502 The 156x gap proves non-slow-roll remark V.T304 First acoustic peak ell_1 from tau theorem V.R503 Error cancellation is structural remark V.T305 Silk damping scale from holonomy ratio theorem V.R504 9 ppm: an extraordinary match remark V.T306 Baryon loading from tau-native eta_B theorem V.R505 The full pipeline remark V.T307 B-mode amplitude from r=iota_tau^4 theorem V.T308 B-mode detection forecast theorem V.R506 BICEP/Keck current status remark V.T309 Primordial helium fraction theorem V.T310 Deuterium abundance from tau-native eta_B theorem V.T311 He-3/H from tau-native eta_B theorem V.T312 Fiber suppression factor theorem V.T313 Lithium-7 resolution theorem V.T314 Baryon-to-photon ratio from tau theorem V.T315 Same CF window governs inflation and baryogenesis theorem V.T316 Exponent 15 = 3 x W_3(4) decomposition theorem V.T317 Five-sixths factor theorem V.R507 The model selection problem remark V.R508 Empirical success is not explanatory depth remark V.R509 Dualities as structural echoes remark V.R510 The honest assessment remark V.T318 Master rotation curve formula --- recap of V.T85 theorem V.P199 20-galaxy benchmark --- recap of V.D258 proposition V.T319 Holonomy ratio unification --- recap of V.T200 theorem V.T320 Sector Exhaustion --- recap of V.T44 theorem V.T321 Dark energy density parameter --- recap of V.T234 theorem V.P200 w_0 from defect dynamics --- recap of V.P159 proposition V.T322 No phantom crossing --- recap of V.T235 theorem V.P201 JWST resolution --- recap of V.T239 proposition V.T323 Hubble parameter from tau --- recap of V.T196 theorem V.T324 Readout quantization obstruction --- recap theorem V.R511 Gravity is already quantum remark V.R512 No cosmological constant problem in tau remark V.R513 The falsification standard remark V.T325 QNM frequency ratio iota_tau^{-1} --- V.T168 theorem V.T326 Secondary QNM modes theorem V.R514 Non-overlapping ranges remark V.T327 EHT shadow correction --- V.T184 theorem V.T328 M87* prediction suite theorem V.T329 Sgr A* prediction suite theorem V.P202 Universal T^2 correction --- V.P148 proposition V.P203 Sgr A* variability from toroidal modes --- V.P149 proposition V.D347 Echo time delays definition V.R515 GW150914 echo search --- V.R407 remark V.P204 Stacked echo SNR --- V.P151 proposition V.D348 Echo amplitude bound definition V.T330 RM winding theorem --- V.T227 theorem V.T331 Circular polarization winding --- V.T229 theorem V.R516 EVPA winding remark V.T332 Magnetic field ratio --- V.T230 theorem V.T333 Flux threading theorem --- V.T228 theorem V.P205 Jet B_z/B_phi at base --- V.P156 proposition V.R517 Observational consistency remark V.P206 IGMF from Wilson skeleton --- V.P157 proposition V.R518 Observational status remark V.P207 Twistor embedding of tau proposition V.P208 NCG spectral triple from tau proposition V.T334 Gravity as readout --- no renormalization needed theorem V.R519 The two relevant directions remark V.T335 No information paradox in tau theorem V.R520 Hawking temperature as readout remark V.P209 Entropy excess --- V.P125 proposition V.T336 No-Shrink summary theorem V.T337 She-Leveque from fibration --- V.T248 theorem V.R521 Fitted to derived remark V.R522 Vortex filaments as fiber collapse remark V.T338 5/3 from tau dimensions --- V.T250 theorem V.T339 C_K from tau --- V.T251 theorem V.R523 Two-thirds law --- V.R441; recap remark V.T340 Fast reconnection rate --- V.T252 theorem V.R524 Reconnection rate from fiber dimension remark V.T341 tau-Alfven damping --- V.T253 theorem V.T342 Primorial convergence rate --- V.T254 theorem V.R525 First parameter-free turbulence theory remark V.C21 Deterministic dynamism corollary V.D349 VM representation of a quantum state definition V.T343 Measurement problem dissolution theorem V.R526 Born rule from boundary structure remark V.R527 Superposition in the VM remark V.T344 Bell inequality in tau theorem V.R528 Entanglement as address sharing remark V.P210 Decoherence as address-resolution shadow proposition V.R529 No quantization in tau remark V.R530 The century of confusion remark V.C22 Deterministic dynamism corollary V.R531 Contrast with stochastic programmes remark V.R532 Dimension trichotomy remark V.R533 Space is not a primary kernel invariant remark V.R534 Why ``dissolve'' and not ``solve'' remark V.P211 Structural completeness of the five hinges proposition V.R535 No personal blame remark V.T345 E_1 fullness, updated theorem