IndisputableMonolith.Flight.GravityBridge

   1import Mathlib
   2import IndisputableMonolith.Gravity
   3import IndisputableMonolith.Flight.Geometry
   4import IndisputableMonolith.Flight.Schedule
   5import IndisputableMonolith.Constants
   6
   7/-!
   8# Flight-Gravity Bridge
   9
  10Connects the ILG (Information-Limited Gravity) weight kernel from `Gravity.ILG`
  11to the Flight/Propulsion model.
  12
  13## Key Questions This Module Addresses
  14
  151. What is `T_dyn` for a rotating lab device?
  162. What weight `w_t` does that imply?
  173. Is there any deviation from w=1 (Newtonian) at lab scales?
  184. How does the 8-tick schedule interact with ILG predictions?
  19
  20## RS Claim Structure
  21
  22The ILG weight kernel is:
  23  `w_t(T_dyn, τ₀) = 1 + C_lag * ((T_dyn/τ₀)^α - 1)`
  24
  25where:
  26- `τ₀ ≈ 7.3 fs` (recognition tick)
  27- `α = (1 - φ⁻¹)/2 ≈ 0.191`
  28- `C_lag` is a coupling constant (typically small)
  29
  30For a rotating device with period `T_rot`:
  31- `T_dyn = T_rot` (natural dynamical timescale)
  32- At lab scales, `T_rot >> τ₀` by ~10-15 orders of magnitude
  33
  34This module formalizes the prediction that `w ≈ 1` at lab scales (null result),
  35and provides falsifiers if this prediction fails.
  36-/
  37
  38namespace IndisputableMonolith
  39namespace Flight
  40namespace GravityBridge
  41
  42open Gravity.ILG
  43open IndisputableMonolith.Constants
  44
  45noncomputable section
  46
  47/-! ## Device Dynamical Timescale -/
  48
  49/-- A rotating device with angular velocity ω has period T = 2π/ω. -/
  50def rotationPeriod (ω : ℝ) (hω : ω ≠ 0) : ℝ := 2 * Real.pi / ω
  51
  52/-- The dynamical timescale of a φ-spiral rotor is its rotation period. -/
  53def deviceDynamicalTime (ω : ℝ) (hω : ω ≠ 0) : ℝ := rotationPeriod ω hω
  54
  55/-! ## ILG Weight at Lab Scales -/
  56
  57/-- Reference recognition tick τ₀ in seconds (from RS constants).
  58    τ₀ = 1/(8 ln φ) in natural units ≈ 7.3 × 10⁻¹⁵ s. -/
  59def tau0_seconds : ℝ := 7.3e-15
  60
  61/-- A typical lab rotation period (e.g., 1000 RPM = 0.06 s). -/
  62def typicalLabPeriod_seconds : ℝ := 0.06
  63
  64/-- Ratio T_dyn/τ₀ for typical lab device. This is enormous (~10¹³). -/
  65def labScaleRatio : ℝ := typicalLabPeriod_seconds / tau0_seconds
  66
  67/-- The ILG exponent α = (1 - φ⁻¹)/2 ≈ 0.191.
  68    Using the RS constant φ = (1 + √5)/2. -/
  69def ilg_alpha : ℝ := (1 - 1/phi) / 2
  70
  71/-- Lab-scale weight deviation: for α ≈ 0.191 and ratio ≈ 10¹³,
  72    the term (T_dyn/τ₀)^α ≈ (10¹³)^0.191 ≈ 10^2.5 ≈ 316.
  73
  74    However, C_lag is typically 10⁻³ to 10⁻⁵ for consistency with
  75    solar system tests. So the deviation is:
  76      w - 1 = C_lag * 315 ≈ 0.3 (at C_lag = 10⁻³)
  77
  78    This is a TESTABLE prediction if C_lag is not too small.
  79-/
  80structure LabScalePrediction where
  81  T_dyn : ℝ           -- Rotation period
  82  τ0 : ℝ              -- Recognition tick
  83  α : ℝ               -- ILG exponent
  84  C_lag : ℝ           -- Coupling constant
  85  w_predicted : ℝ     -- Predicted weight
  86  h_w : w_predicted = 1 + C_lag * (Real.rpow (T_dyn / τ0) α - 1)
  87
  88/-- Construct a lab-scale prediction for a given device. -/
  89def mkLabPrediction (T_dyn τ0 α C_lag : ℝ) : LabScalePrediction where
  90  T_dyn := T_dyn
  91  τ0 := τ0
  92  α := α
  93  C_lag := C_lag
  94  w_predicted := 1 + C_lag * (Real.rpow (T_dyn / τ0) α - 1)
  95  h_w := rfl
  96
  97/-! ## Connection to 8-Tick Schedule -/
  98
  99/-- The 8-tick window discipline divides the rotation into 8 phases.
 100    Each phase has duration T_phase = T_rot / 8. -/
 101def phaseDuration (T_rot : ℝ) : ℝ := T_rot / 8
 102
 103/-- Number of recognition ticks per phase at lab scales.
 104    For T_rot = 0.06 s, T_phase = 7.5 ms, so n_ticks ≈ 10¹².
 105    This is far above the 8-tick threshold. -/
 106def ticksPerPhase (T_rot τ0 : ℝ) : ℝ := phaseDuration T_rot / τ0
 107
 108/-- The 8-tick schedule is well-separated from the recognition tick
 109    when the number of recognition ticks per phase >> 8. -/
 110def scheduleWellSeparated (T_rot τ0 : ℝ) : Prop :=
 111  ticksPerPhase T_rot τ0 > 64  -- At least 8² ticks per phase
 112
 113theorem lab_schedule_well_separated :
 114    scheduleWellSeparated typicalLabPeriod_seconds tau0_seconds := by
 115  unfold scheduleWellSeparated ticksPerPhase phaseDuration
 116  unfold typicalLabPeriod_seconds tau0_seconds
 117  -- 0.06 / 8 / 7.3e-15 = 0.0075 / 7.3e-15 ≈ 10¹² >> 64
 118  norm_num
 119
 120/-! ## Null Hypothesis and Falsifiers -/
 121
 122/-- The null hypothesis: at lab scales, w ≈ 1 (no ILG deviation). -/
 123def nullHypothesis (P : LabScalePrediction) (tolerance : ℝ) : Prop :=
 124  |P.w_predicted - 1| < tolerance
 125
 126/-- If C_lag < tolerance / (ratio^α - 1), the null hypothesis holds. -/
 127theorem null_holds_if_C_lag_small (T_dyn τ0 α C_lag tolerance : ℝ)
 128    (hτ : 0 < τ0) (hT : τ0 < T_dyn)
 129    (hα : 0 < α) (hC : 0 ≤ C_lag)
 130    (hbound : C_lag * (Real.rpow (T_dyn / τ0) α - 1) < tolerance) :
 131    nullHypothesis (mkLabPrediction T_dyn τ0 α C_lag) tolerance := by
 132  unfold nullHypothesis mkLabPrediction
 133  simp only
 134  have hratio_pos : 0 < T_dyn / τ0 := div_pos (lt_trans hτ hT) hτ
 135  have hpow_ge_one : 1 ≤ Real.rpow (T_dyn / τ0) α := by
 136    have hge1 : 1 ≤ T_dyn / τ0 := by
 137      rw [one_le_div hτ]
 138      exact le_of_lt hT
 139    exact Real.one_le_rpow hge1 (le_of_lt hα)
 140  have hdiff_nonneg : 0 ≤ Real.rpow (T_dyn / τ0) α - 1 := sub_nonneg.mpr hpow_ge_one
 141  have hprod_nonneg : 0 ≤ C_lag * (Real.rpow (T_dyn / τ0) α - 1) :=
 142    mul_nonneg hC hdiff_nonneg
 143  -- Simplify |1 + x - 1| = |x| = x (since x ≥ 0)
 144  have hsimpl : 1 + C_lag * (Real.rpow (T_dyn / τ0) α - 1) - 1 =
 145                C_lag * (Real.rpow (T_dyn / τ0) α - 1) := by ring
 146  rw [hsimpl, abs_of_nonneg hprod_nonneg]
 147  exact hbound
 148
 149/-- Falsifier: if measured thrust is nonzero at lab scales,
 150    either ILG is wrong or there's a non-gravitational effect. -/
 151structure GravityFalsifier where
 152  measured_thrust : ℝ
 153  predicted_thrust_from_ILG : ℝ
 154  discrepancy : ℝ := |measured_thrust - predicted_thrust_from_ILG|
 155
 156def falsifierTriggered (f : GravityFalsifier) (threshold : ℝ) : Prop :=
 157  f.discrepancy > threshold
 158
 159/-! ## RS-Specific Predictions -/
 160
 161/-- The RS prediction: C_lag is derived from φ, not a free parameter.
 162    Specifically, C_lag = φ⁻⁵ ≈ 0.0902 in the time-kernel formula. -/
 163def C_lag_RS : ℝ := Real.rpow phi (-5)
 164
 165/-- With C_lag = φ⁻⁵ and typical lab scales, the predicted deviation is:
 166    w - 1 = φ⁻⁵ * ((0.06 / 7.3e-15)^0.191 - 1)
 167          ≈ 0.09 * 315
 168          ≈ 28
 169
 170    This would be a LARGE effect if true! The null hypothesis would fail.
 171-/
 172def rsLabPrediction : LabScalePrediction :=
 173  mkLabPrediction typicalLabPeriod_seconds tau0_seconds ilg_alpha C_lag_RS
 174
 175/-- The RS prediction yields w ≈ 29, not w ≈ 1.
 176    This is either:
 177    (a) A falsifiable prediction (test it!)
 178    (b) Evidence that C_lag is suppressed at lab scales
 179    (c) Evidence that T_dyn ≠ T_rot for a non-gravitationally-bound system
 180-/
 181def rs_lab_prediction_value : Prop :=
 182  25 < rsLabPrediction.w_predicted ∧ rsLabPrediction.w_predicted < 35
 183
 184/-! ## Interpretation Options -/
 185
 186/-- Option A: ILG applies at lab scales → large deviation → testable. -/
 187def optionA_testable : Prop :=
 188  rsLabPrediction.w_predicted > 10
 189
 190/-- Option B: ILG only applies to gravitationally-bound systems.
 191    For a rotating device, T_dyn = ∞ (not bound), so w = 1. -/
 192def optionB_bound_only : Prop :=
 193  ∀ (device : LabScalePrediction), ¬(device.T_dyn > 0 ∧ device.T_dyn < 1e10) →
 194    device.w_predicted = 1
 195
 196/-- Option C: C_lag is scale-dependent (runs with energy/length).
 197    At lab scales, C_lag → 0, preserving w ≈ 1. -/
 198structure RunningCoupling where
 199  C_lag_of_scale : ℝ → ℝ  -- C_lag as function of length scale
 200  h_galactic : C_lag_of_scale 1e20 = C_lag_RS  -- Galactic scale
 201  h_lab : C_lag_of_scale 1 < 1e-10  -- Lab scale (1 meter)
 202
 203end
 204
 205end GravityBridge
 206end Flight
 207end IndisputableMonolith
 208