IndisputableMonolith.QFT

   1import IndisputableMonolith.QFT.SpinStatistics
   2import IndisputableMonolith.QFT.CPTInvariance
   3import IndisputableMonolith.QFT.Decoherence
   4import IndisputableMonolith.QFT.PauliExclusion
   5import IndisputableMonolith.QFT.NoetherTheorem
   6import IndisputableMonolith.QFT.HiggsMechanism
   7import IndisputableMonolith.QFT.Confinement
   8import IndisputableMonolith.QFT.SMatrixUnitarity
   9import IndisputableMonolith.QFT.GaugeInvariance
  10import IndisputableMonolith.QFT.UVCutoff
  11
  12/-!
  13# Quantum Field Theory Derivations from Recognition Science
  14
  15This module contains derivations of quantum field theory fundamentals from
  16the Recognition Science framework.
  17
  18## Tier 2 Derivations (from MASTER_DERIVATION_LIST_TIER2.md)
  19
  20### Completed ✅
  21- **QFT-001**: Spin-Statistics Theorem from 8-tick phase
  22- **QFT-002**: Fermion antisymmetry from odd-phase ledger entries
  23- **QFT-003**: Boson symmetry from even-phase ledger entries
  24- **QFT-004**: Pauli exclusion principle from ledger single-occupancy
  25- **QFT-005**: CPT Invariance from ledger symmetry
  26- **QFT-006**: Noether's theorem from cost stationarity
  27- **QFT-012**: S-matrix unitarity from ledger conservation
  28- **QF-009**: Decoherence timescale from Gap-45
  29
  30### Standard Model
  31- **SM-002**: Higgs mechanism from J-cost symmetry breaking
  32
  33### Completed in Phase I ✅
  34- QFT-008: Gauge invariance from ledger redundancy
  35- QFT-013: UV cutoff from discreteness
  36
  37### In Progress 🔶
  38- QFT-007: Lorentz invariance origin
  39
  40### Planned 📋
  41- QFT-009: Feynman propagator from J-cost Green's function
  42- QFT-010: Vertex factors from recognition events
  43- QFT-011: Loop diagrams from ledger cycles
  44- QFT-014: Renormalization group flow
  45- QFT-015: Running couplings
  46- QFT-016: Anomaly cancellation
  47
  48## Key Insights
  49
  501. **Spin-Statistics**: Half-integer spin → odd phase in 8-tick → antisymmetric wavefunction
  512. **CPT**: Ledger double-entry symmetry → C, P, T individually breakable but CPT preserved
  523. **Decoherence**: Gap-45 threshold → quantum-classical transition
  534. **Unitarity**: Ledger conservation → probability conservation → S†S = 1
  545. **Noether**: Cost stationarity under symmetry → conservation law
  556. **Higgs**: J-cost minimum → spontaneous symmetry breaking → mass generation
  56
  57-/
  58
  59namespace IndisputableMonolith.QFT
  60
  61/-- Summary of QFT derivations from RS. -/
  62def summary : String :=
  63  "QFT from Recognition Science (Tier 2):\n" ++
  64  "✅ Spin-Statistics: 8-tick phase mechanism\n" ++
  65  "✅ Fermion/Boson symmetry: odd/even phase ledger entries\n" ++
  66  "✅ Pauli Exclusion: ledger single-occupancy\n" ++
  67  "✅ CPT Invariance: Ledger symmetry\n" ++
  68  "✅ Noether's Theorem: cost stationarity\n" ++
  69  "✅ S-Matrix Unitarity: ledger conservation\n" ++
  70  "✅ Decoherence: Gap-45 threshold\n" ++
  71  "✅ Higgs Mechanism: J-cost symmetry breaking\n" ++
  72  "✅ Gauge Invariance: ledger redundancy\n" ++
  73  "✅ UV Cutoff: τ₀ discreteness scale\n"
  74
  75end IndisputableMonolith.QFT
  76