IndisputableMonolith.Gravity.Candidates.Li

   1import Mathlib
   2import IndisputableMonolith.Constants
   3
   4/-!
   5# RS Hypothesis: Ning Li's Coherent Gravitomagnetism
   6
   7This module formalizes the core claim of Ning Li & D.G. Torr (1991) within the
   8Recognition Science framework.
   9
  10## The Claim
  11In a superconductor, the internal gravitomagnetic field B_g(z) is coupled to the
  12magnetic field B_0 via a coherence factor involving the mass/charge ratio.
  13
  14Li's Formula (from abstract):
  15  B_g(z) ≈ B_g,0 + (μ_g * m / (q * μ)) * B_0
  16
  17## RS Interpretation
  18This is a **Coherence-Gated Source Term**.
  19The "permeability" μ_g is effectively renormalized by the recognition coherence
  20of the Cooper pair condensate.
  21
  22In RS, this is not a new force, but a **restoration** of the underlying
  23gravitomagnetic coupling that is normally cancelled by phase decoherence (random walk).
  24-/
  25
  26namespace IndisputableMonolith
  27namespace Gravity
  28namespace Candidates
  29namespace Li
  30
  31open scoped Real
  32
  33/-- The fundamental coupling ratio for a Cooper pair. -/
  34def cooperPairRatio (m q : ℝ) : ℝ := m / q
  35
  36/-- Li's coupling coefficient (simplified display form).
  37    k_Li = (μ_g / μ) * (m / q)
  38    In RS, we treat (μ_g / μ) as the "Coherence Gain". -/
  39def liCoupling (mu_g mu m q : ℝ) : ℝ := (mu_g / mu) * (m / q)
  40
  41/-- The RS-modified gravitomagnetic field hypothesis.
  42    This asserts that the field B_g contains a term proportional to the
  43    magnetic field B_0, scaled by the Li coupling. -/
  44def CoherentGravitomagnetism (B_g0 B_0 : ℝ) (mu_g mu m q : ℝ) : Prop :=
  45  let B_g_internal := B_g0 + liCoupling mu_g mu m q * B_0
  46  -- The claim is that this internal field is physically realized.
  47  True -- Placeholder for field equation integration
  48
  49/-- RS Falsifier: Coherence Gating.
  50    The effect MUST vanish if the system is not superconducting (T > Tc).
  51    We model this by asserting the coupling becomes zero (or negligible)
  52    when coherence is lost. -/
  53def CoherenceGateFalsifier (T Tc : ℝ) (measured_coupling : ℝ) : Prop :=
  54  if T > Tc then
  55    measured_coupling ≈ 0
  56  else
  57    measured_coupling > 0
  58
  59/-- RS Falsifier: Sign Flip.
  60    Since B_0 is a vector field, reversing B_0 (or the current) must reverse
  61    the induced gravitomagnetic component.
  62    B_g_induced(-B_0) = -B_g_induced(B_0). -/
  63def SignFlipFalsifier (B_0 : ℝ) (induced_Bg : ℝ → ℝ) : Prop :=
  64  induced_Bg (-B_0) = -induced_Bg B_0
  65
  66end Li
  67end Candidates
  68end Gravity
  69end IndisputableMonolith
  70