IndisputableMonolith.Nuclear.NeutronLifetimeStructure

   1import Mathlib
   2
   3/-!
   4# P-015: What Determines the Lifetime of the Neutron?
   5
   6Formalizes the RS structural framework for neutron lifetime.
   7
   8## Registry Item
   9- P-015: What determines the lifetime of the neutron?
  10
  11## RS Derivation Status
  12**STARTED** — Experimental bottle/beam discrepancy remains unresolved.
  13In RS, neutron lifetime is fixed by weak decay phase space (`Q^5` scaling),
  14matrix-element structure, and rung-determined mass inputs. Full numerical
  15lifetime derivation remains BLOCKED.
  16-/
  17
  18namespace IndisputableMonolith
  19namespace Nuclear
  20namespace NeutronLifetimeStructure
  21
  22/-! ## Structural Inputs -/
  23
  24/-- Free-neutron beta-decay Q value in MeV (structural placeholder). -/
  25def neutronDecayQ : ℝ := 0.782
  26
  27/-- Free-neutron mean lifetime in seconds (experimental reference scale). -/
  28def freeNeutronMeanLife : ℝ := 881
  29
  30/-- Free-neutron decay is kinematically allowed (`Q > 0`). -/
  31theorem neutron_decay_allowed : neutronDecayQ > 0 := by
  32  norm_num [neutronDecayQ]
  33
  34/-- Mean lifetime is positive. -/
  35theorem neutron_lifetime_positive : freeNeutronMeanLife > 0 := by
  36  norm_num [freeNeutronMeanLife]
  37
  38/-- Positive decay Q-value forces positive fifth-power phase-space factor (`Q^5`). -/
  39theorem neutron_decay_phase_space_positive : neutronDecayQ ^ (5 : ℕ) > 0 := by
  40  exact pow_pos neutron_decay_allowed 5
  41
  42/-- Structural placeholder for full RS lifetime formula. -/
  43def neutron_lifetime_from_ledger : Prop := neutronDecayQ > 0 ∧ freeNeutronMeanLife > 0
  44
  45theorem neutron_lifetime_structure : neutron_lifetime_from_ledger := by
  46  exact ⟨neutron_decay_allowed, neutron_lifetime_positive⟩
  47
  48/-- The ledger neutron-lifetime structure implies positive decay Q-value. -/
  49theorem neutron_lifetime_implies_decay_allowed (h : neutron_lifetime_from_ledger) :
  50    neutronDecayQ > 0 :=
  51  h.1
  52
  53/-- The ledger neutron-lifetime structure implies positive mean lifetime. -/
  54theorem neutron_lifetime_implies_positive_lifetime (h : neutron_lifetime_from_ledger) :
  55    freeNeutronMeanLife > 0 :=
  56  h.2
  57
  58/-- Neutron-lifetime structure implies positive `Q^5` phase-space scaling factor. -/
  59theorem neutron_lifetime_implies_phase_space_positive (h : neutron_lifetime_from_ledger) :
  60    neutronDecayQ ^ (5 : ℕ) > 0 :=
  61  pow_pos h.1 5
  62
  63end NeutronLifetimeStructure
  64end Nuclear
  65end IndisputableMonolith
  66