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TauLib.BookIV

TauLib.BookIV — Categorical Microcosm

Master import file for Book IV (Categorical Microcosm) Lean modules.

Book IV = fiber T² of τ³ = τ¹ ×_f T² = spatial physics: quantum mechanics, particles, forces, atoms, chemistry, fluids.

Module Organization

Sectors (Part I: Sector Parameter Foundation)

  • SectorParameters: 5 sector instantiations with 4 defining parameters each

  • CouplingFormulas: 10 coupling formulas as rational functions of ι_τ

  • FineStructure: Fine structure constant α derivation

Physics (Part II: Physical Quantity Core)

  • QuantityFramework: 5 primary invariants, carrier types, particle ontology

  • PlanckCharacter: ℏ_τ as sector lift of ι_τ, uncertainty products

  • DefectFunctional: 4-component defect tuple, 8 fluid regimes

  • MassEnergy: Mass index, energy index, mass-energy relation

  • Thermodynamics: Entropy splitting, defect budget, No-Running Principle

Physics (Mass Ratio Derivation)

  • LemniscateCapacity: √3 from lemniscate three-fold 1−ω

  • HolonomyCorrection: π³α² from triple U(1) holonomy

  • NucleonMassSplitting: p-n mass difference, two-sector QCD−EM formula (33 ppm)

Arena (Part I: Boundary Synthesis, ch02-ch07)

  • CoherenceKernel: Coherence kernel, generator-sector assignment, uniqueness

  • RefinementTower: Refinement tower, profinite limit, proto-time, NNO

  • Tau3Arena: Base τ¹, fiber T², fibered product, master constant, 4 dimensions

  • BoundaryHolonomy: Yoneda self-image, boundary characters, bipolar decomposition

  • FiveSectors: Sector coupling atlas, temporal complement, power hierarchy

  • ActorsDynamics: Defect bundles, radiation, virtual particles, primary invariants

Calibration (Part II: Constants as Fixed-Point Readouts)

  • SIReference: SI physical constants as exact Nat pairs (calibration targets)

  • DimensionlessNearMatch: Weinberg, strong coupling range proofs

  • CalibrationAnchor: Neutron mass anchor, 5→1 collapse

  • DimensionalBridge: c, h, ε₀, μ₀, k_e derivation chain, Maxwell relation

  • ConstantsLedger: Master synthesis table with scope labels

Calibration (Part II: Extended modules)

  • SharedOntology: Shared ontological layer between τ and SI

  • DimensionlessCouplings: 5 self-couplings with numerical range proofs

  • DimensionlessCouplings2: Cross-couplings, temporal complement, power hierarchy

  • DimensionlessAlpha: Spectral and holonomy fine-structure formulas

  • RunningRegime: Beta functions, readout functors, entropy at scale

  • ConstantsLedgerExt: Coupling, scales, particle mass, structural constants tables

Calibration (Mass Ratio & Epstein Zeta)

  • EpsteinZeta: Epstein zeta function Z(s; iι_τ) on T², Chowla-Selberg structure

  • MassRatioFormula: R = m_n/m_e derivation, 10-link chain, range proofs

QuantumMechanics (Part III: QM as Address Obstruction, ch16-ch22)

  • CRAddressSpace: CR-manifold, CR-structure on τ³, character modes, admissible sublattice, spin-1/2

  • QuantumCharacters: Characters on T², charge quantization, energy duality, sharp/spread states

  • HilbertSpace: H_τ as L²-completion, inner product, ONB, entanglement, superposition

  • Quantization: Holomorphic vector fields, quantization map, canonical commutation, observables

  • AddressObstruction: Uncertainty as address obstruction, NoJointMin, Heisenberg bounds

  • Measurement: Born rule, Schrödinger equation, decoherence, classical limit

  • EnergyEntropy: Holomorphic tension, energy-entropy duality, arrow of time

MassDerivation (Part III: Breathing Modes & Electron Mass, ch23-ch25)

  • BreathingModes: Breathing operator on T², Epstein zeta, spectral distance, toroidal dominance

  • HolonomyDetail: Triple holonomy H₃, π³α² correction, holonomy range proof

  • ElectronMass: 10-link derivation chain, bulk term, Level 0 & Level 1+ formulas

Electroweak (Part IV: EM + Weak + EW Mixing, ch26-ch35)

  • PhotonMode: Photon as null transport mode, U(1) holonomy, electric charge quantization

  • GaugeInvariance: EM principal bundle, gauge connections, field strength tensor

  • GaugeInvariance2: Wilson loops, non-abelian gauge structure, Aharonov-Bohm phase

  • TauMaxwell: Maxwell equations from boundary characters, Coulomb law, wave equation

  • AlphaDerivation: Fine-structure constant derivation, spectral + holonomy formulas

  • WeakChirality: Polarity as chirality, parity violation, W/Z boson structure

  • WeakChirality2: Chirality selection rules, SU(2)_L assignment

  • WeakHolonomy: SU(2) generators, W boson mass from holonomy

  • WeakHolonomy2: Weinberg angle, Z boson mass, rho parameter

  • NeutrinoMode: Neutrino flavors, PMNS matrix, mass hierarchy

  • MajoranaStructure: σ = C_τ proof chain, Majorana theorem, 0νββ prediction

  • EWMixing: Hypercharge, neutral boson mixing, EW unification

  • TauHiggs: Higgs mechanism from crossing, physical vacuum

  • TauHiggs2: Higgs mass prediction, Yukawa couplings, hierarchy problem

  • EWSynthesis: 9 EW quantities, √3 triad, synthesis ledger

Strong (Part V: Strong Sector, ch37-ch44)

  • StrongVacuum: C-sector, strong defect functional, vacuum construction, truncation coherence

  • ColorHolonomy: Color charge from eta-circle, ternary structure, SU(3), Wilson loops

  • Confinement: Confinement theorem, color singlets, linear potential, proton stability

  • GapMetaTheorem: Holonomy sector framework, kernel hypotheses, gap meta-theorem

  • YangMillsGap: Plaquette defect, spectral gap, mass gap theorem, orthodox bridge conjecture

  • StrongCoupling: Pi-lift construction, alpha_s^*, no ontic running, asymptotic freedom

  • QuarksGluons: Quark modes, generations, gluon count, mesons, baryons

  • VacuumCatastrophe: Boundary-first normalization, earned modes, no vacuum catastrophe

Particles (Part VI: Particle Spectrum, ch45-ch51)

  • SectorAtlas: Complete sector taxonomy, 9 canonical generators, generator adequacy

  • ThreeGenerations: Three generations from lemniscate, Koide Q=2/3, mass exponents

  • BetaDecay: Beta decay, hydrogen atom, Bohr radius, Rydberg constant, fine structure

  • HadronsNuclei: Mesons, baryons, nucleon mass, nuclear shells, magic numbers, iron peak

  • PeriodicTable: Periodic table, Madelung rule, bonding types, molecular geometry

  • SpectrumComplete: Ontic entity criterion, ontic register, spectrum completeness

  • StrongCP: θ_QCD = 0 from SA-i, neutron EDM = 0, no axion required (τ-native PQ)

ManyBody (Part VII: Many-Body & Condensed Matter, ch52-ch54)

  • DefectFunctionalExt: Macroscopic defect tuple, interaction corrections, tower compatibility, sector additivity

  • DefectFunctionalExt2: Euler/NS/MHD/plasma/superfluid/superconductor regimes, temperature, phase transitions

  • FluidRegimes: tau-Euler/NS flow, regularity, crystal/glass/quasicrystal, universal order parameter

  • CondensedMatter: Melting sequence, topological branch, fiber-base factorization, fiber completeness

Coda (Part VII: Closing Arc, ch55-ch57)

  • LawsAsStructure: Tower-natural transformations, Noether corollary, UV finiteness, laws as structure

  • CompleteLedger: 66-entry ledger, scope distribution, export contracts to Books V-VII, sphaleron question

  • SelfDescribing: Neutron anchor rationale, self-enrichment, metaclosure, self-describing universe

Physics (Ontological Architecture)

  • TickUnits: 5 tick kinds as minimal endomorphisms, tick arithmetic, internal ratios

  • InternalEquations: R₀, α, κ_D as internal identities with layer discipline

  • ReadoutFunctor: R_μ with operational codomain, single anchor (m_n), 4 exact SI constants

Current Count: 87 modules