TauLib · API Book

TauLib.BookV

TauLib.BookV — Categorical Macrocosm

Master import file for Book V (Categorical Macrocosm) Lean modules.

Book V = base τ¹ of τ³ = τ¹ ×_f T² = temporal physics: gravity, cosmology, black holes, thermodynamics, life.

Module Organization

Gravity (Part I: Gravitational Foundation)

  • GravitationalConstant: G_τ from torus vacuum geometry, shape ratio r/R = ι_τ

  • EinsteinEquation: τ-Einstein as boundary-character identity, κ_τ coupling

  • Schwarzschild: R = 2G_τM, BH mass index, No-Shrink theorem

  • CoRotorCoupling: co-rotor coupling κ_n, c₁ = 3/π, closing identity α_G = α¹⁸·(χκ_n/2)

  • BHTopoModes: T² QNM modes, echo times, entropy ratio, no-Hawking argument

Prologue

  • HermeticPrinciple: fiber completeness (3 fiber + 2 base = 5), temporal complement recap

  • ExportContract: 10-item export from Book IV (arena, sectors, couplings, invariants, R formula)

Temporal (Part II: Temporal Structure, ch04-ch10)

  • BaseCircle: base circle τ¹, alpha-ticks, proper time, causal ordering, geodesic duration

  • TemporalIgnition: 3 temporal epochs, ignition depth, now-hypersurface, coherence horizon

  • HighEnergy: maximal coupling, opening regime, unique τ-Einstein solutions, progression rate

  • MacroReadout: null intertwiners, operational distance, redshift, expansion, Hubble parameter

  • DistanceLadder: 5-rung distance ladder, Cepheid calibrator, BAO ruler, dark energy artifact

  • BoundaryData: CMB surface, neutrino decoupling, recombination depth, CnuB surface

  • CosmicAPI: 21-item cosmic stack API, scope distribution (19 τ-effective + 2 conjectural)

GravityField (Part III: Frame Holonomy to Closing Identity, ch11-ch20)

  • FrameHolonomy: Clopen frame, gravitational coupling, frame holonomy sector

  • LorentzNoMinkowski: Null intertwiner, Lorentz from readout (no Minkowski)

  • TauEinsteinEq: Curvature character, τ-Einstein equation derivation

  • LinearEinstein: Newtonian limit, classical gravitational tests

  • NonlinearEinstein: NF iteration, density saturation, nonlinear solutions

  • TauSchwarzschild: Schwarzschild relation, BH evolution modes

  • TOVStarBuilder: Stellar structure, Chandrasekhar limit, TOV equation

  • TOVPhaseBoundary: Coherence horizon, topology crossing, phase boundary

  • CalibrationTriangle: Calibration triangle, 3 vertices (G, κ_n, α_G)

  • ClosingIdentity: α_G closing identity, 10-link gravitational chain

Thermodynamics (Part IV: Entropy, Heat, Vacuum, ch21-ch26)

  • Inversion: Classical second law inversion, holomorphic vs defect entropy

  • EntropySplitting: S = S_def + S_ref decomposition, defect entropy decreasing

  • DefectExhaustion: Defect functional minimization, exhaustion of defect types

  • HeatEM: Heat as B-sector phenomenon, Planck distribution, Stefan-Boltzmann

  • VacuumNoVoid: No true void, vacuum character, pair production, Unruh effect

  • DarkEnergyArtifact: Dark energy as ΛCDM artifact, vacuum energy resolution

FluidMacro (Part V: Navier-Stokes, Turbulence, Plasma, ch27-ch33)

  • NavierStokesMacro: NS as τ-coarse-graining, viscous flow, Reynolds number

  • Turbulence: Turbulence onset, Kolmogorov 5/3 law, inertial range

  • ChargeObstruction: Charge-flux constraint, magnetic obstruction, Lorentz force

  • TauPlasma: Plasma, Debye screening, plasma frequency, dispersion

  • TauMHD: Magnetohydrodynamics, Alfvén waves, dynamo, reconnection

  • TauAlfven: Alfvén wave modes, dispersion, damping, magnetoacoustic

  • PhaseTransitions: Phase transitions, critical exponents, order parameters

Astrophysics (Part V/VI: Classical to Large-Scale Structure, ch34-ch45)

  • ClassicalIllusion: Classical mechanics as τ-readout limit, force-free ontology

  • KeplerSolarSystem: Kepler laws, solar system, planetary orbits

  • GalaxyRelational: Galaxy formation, relational structure, morphology

  • RotationCurves: Rotation curves, no dark matter, boundary characters

  • CompactObjects: White dwarfs, neutron stars, black holes, Chandrasekhar limit

  • Supernovae: Type Ia/II supernovae, nucleosynthesis, remnants

  • AccretionJets: Accretion disks, relativistic jets, AGN

  • BinaryMergersGW: Binary mergers, gravitational waves, LIGO/Virgo

  • EHTReread: Event Horizon Telescope reread, shadow predictions

  • BulletClusterLSS: Bullet cluster, large-scale structure, no dark matter

  • SectorExhaustion: Astrophysical sector exhaustion, all phenomena covered

  • H0TensionLCDM: Hubble tension, LCDM artifacts, τ-resolution

Cosmology (Part VI/VII: Big Bang to Boundary Unification, ch46-ch56)

  • BigBangRegime: Big bang as opening regime, temporal opening, no singularity

  • InflationRegime: Inflation as regime invariance, inflaton no-go, flatness, horizon

  • ThresholdLadder: Six canonical thresholds EW→B→N→nuc→H→γ, nucleosynthesis, CMB

  • BaryogenesisAsymmetry: η_B = α·ι_τ¹⁵·(5/6) = (121/270)·ι_τ¹⁹ upgrade to τ-effective; exponent 15 = dim(τ³)× gen

  • BHBirthTopology: BH birth as topology crossing S²→T², linking class, information preservation

  • BHBipolarFusion: Bipolar BHs, polarity imbalance, blueprint monoid, fusion closure

  • NoShrinkExtended: No-shrink theorem, Hawking readout, no evaporation, permanence hallmark

  • MergerNormalForm: Merger normal form, ringdown, primorial mass gap, Wilson loops, GW bound

  • GlobalFiniteness: Finite motifs, saturation radius, absorbing pattern, global finiteness chain

  • CosmologicalEndstate: Eternal circulation, two cosmic phases, no heat death, complexity

  • FalsificationPack: 10 testable predictions across 3 falsification levels

  • BoundaryUnification: 6 Hartogs squares, cross-coupling naturality, ι_τ mediates all 10

Orthodox (Part VII: Orthodox Correspondence, ch58-66)

  • CorrespondenceMap: Correspondence functor Phi, structural artifacts, readout protocol

  • EmergentGeometry: GR as chart shadow, no singularities, sector exhaustion, native holography

  • OtherApproaches: String theory, LQG, CDT, causal sets, twistors, NCG comparisons

  • MeasurementUnification: VM quantum states, measurement dissolution, Bell inequality, decoherence

  • FalsifiableSeams: No singularities, no UV, no dark sectors, vacuum zero, E1 full

Coda (Part VIII: Bridge to Life, ch66-72)

  • ConstantsLedger: 10-entry ledger, No Shrink restatement, testable seams, honest scope

  • BridgeToLife: Export contracts VI/VII, Hermetic Truth, profinite ergodicity, EW bridge

Current Count: 78 modules