fix(braid): resolve rossby_convergence_bound sorry, add rossby_energy_dissipation_rate stub

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allaun 2026-06-30 16:38:55 -05:00
parent 85141a4b94
commit 91e5bbd3d1

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