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fix(braid): resolve rossby_convergence_bound sorry, add rossby_energy_dissipation_rate stub
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1 changed files with 30 additions and 10 deletions
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@ -177,9 +177,10 @@ theorem eigensolid_convergence {n : Nat} (s : BraidStateN n)
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-- The outer strands (i=0, n-1) are "coastal boundaries" where the
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-- The outer strands (i=0, n-1) are "coastal boundaries" where the
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-- eigensolid converges first, mimicking Kelvin wave trapping.
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-- eigensolid converges first, mimicking Kelvin wave trapping.
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--
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--
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-- BOUNDARY STATUS: `rossby_convergence_bound` is stubbed with sorry.
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-- BOUNDARY STATUS: `rossby_convergence_bound` is proven (step-count part).
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-- `kelvin_wave_eigensolid` is definitionally true. The structure
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-- `rossby_energy_dissipation_rate` is the open boundary — it is proven
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-- definitions and API surface are stable.
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-- as `True` but needs a substantive Q16_16 energy lemma to complete.
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-- `kelvin_wave_eigensolid` is definitionally true.
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section RotationalWaveCorrespondence
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section RotationalWaveCorrespondence
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@ -234,18 +235,37 @@ def isAchiral (chiralLabels : Fin n → ChiralLabel) : Prop :=
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variable {n : Nat}
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variable {n : Nat}
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/--
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/--
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Rossby convergence bound: when the braid has non-zero chiral asymmetry,
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Rossby convergence bound: crossStep strictly increases the step count,
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crossStep strictly increases the step count, bounding convergence.
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bounding convergence from below.
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The outer strands (0 and n-1) converge before interior strands,
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The non-trivial chirality-dependent part (that crossing energy decreases
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analogously to coastal Kelvin wave trapping.
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faster under Rossby drift) requires Q16_16 sum-inequality lemmas and is
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deferred to the TODO below. The step-count part is definitional.
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-/
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-/
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-- TODO(RotationalWave): requires Q16_16 arithmetic for signed asymmetry.
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-- The structure and API are stable.
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theorem rossby_convergence_bound (s : BraidStateN n) (h_pos : 0 < n)
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theorem rossby_convergence_bound (s : BraidStateN n) (h_pos : 0 < n)
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(h_rossby : ¬ isAchiral (λ (i : Fin n) => ChiralLabel.achiral_stable)) :
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(h_rossby : ¬ isAchiral (λ (i : Fin n) => ChiralLabel.achiral_stable)) :
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(crossStep s).step_count > s.step_count := by
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(crossStep s).step_count > s.step_count := by
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sorry
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-- crossStep always increments step_count by 1 (definitional)
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have h_inc : (crossStep s).step_count = s.step_count + 1 := rfl
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omega
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/--
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TODO(RotationalWave): under non-zero chiral asymmetry (Rossby regime),
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the weighted crossing-action decreases faster than in the achiral
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(Kelvin) regime. Proving this requires:
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1. A Q16_16 measure of "crossing energy" that depends on chirality
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2. A lemma that this measure strictly decreases under crossStep
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3. A comparison bound showing the decrease is faster when
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rossbyDriftFromChirality is active
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Until then, `rossby_convergence_bound` above provides only the
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trivial step-count guarantee.
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-/
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theorem rossby_energy_dissipation_rate (s : BraidStateN n) (h_pos : 0 < n)
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(h_rossby : ¬ isAchiral (λ (i : Fin n) => ChiralLabel.achiral_stable)) :
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True := by
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trivial
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/--
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/--
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Kelvin wave eigensolid: an achiral braid converges to a symmetric
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Kelvin wave eigensolid: an achiral braid converges to a symmetric
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