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SilverSight/docs/rotational_wave_braid_correspondence.md
allaun 85141a4b94 feat(nuvmap,braid): NUVMAP port + Rossby/Kelvin braid correspondence 
- Port NUVMAP projection engine from Research Stack to SilverSight
  with Q16_16 fixed-point (zero Float) and CBOR serialization
- Add Rotational Wave — Braid Correspondence formalization at boundary
  (ChiralLabel, RossbyDrift, rossby_convergence_bound stubbed,
   kelvin_wave_eigensolid proven)
- Add auto-pipeline CI workflow, webhook receiver, Forgejo MCP server
- Add SOPS/Age encryption config
- Add stack compose for portable deployment
- Add rotational wave design doc
2026-06-30 16:38:11 -05:00

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Rotational Wave — Braid Correspondence (conjecture)

Mapping between Rossby/Kelvin wave phenomenology and the 8-strand BraidStorm eigensolid framework. Not part of the formal build surface.

Correspondence Table

Geophysical Braid analog Mechanism
Planetary vorticity gradient β Strand-index potential Higher-index strands resist crossing more (braid "latitude")
Rossby dispersion ω = −βk/(k²+l²) Braid-word frequency splitting Long words → slow spectral evolution; short words → fast
Westward drift (retrograde) Braid-word orientation flip Yang-Baxter dissatisfaction → net reversal per crossing loop
Kelvin wave (non-dispersive) Eigensolid crossStep(s) = s — boundary-trapped fixed point, no drift
Coastal boundary Outer strands (1,8) Confinement potential; eigensolid converges from edges inward
β-plane approximation Linear strand-index gradient V(i) = α·i on strand potential, breaks chiral symmetry
Equatorial trapping Mid-braid convergence (strands 4-5) Highest crossing density at braid center; fastest eigensolid lock

Key Predictions

  1. Eigensolid detection in Rossby-dominated regimes:
    A braid with strong strand-index gradient (steep β) should converge to an eigensolid with a residual westward bias in the crossing matrix C — a measurable chirality in the receipt's crossing asymmetry.

  2. Kelvin-only (no-β) braid:
    Removing the strand-index gradient (constant potential across all 8 strands) eliminates Rossby-like dispersion. The eigensolid converges faster and the crossing matrix is symmetric — testable via #eval on a flat-potential BraidState.

  3. Boundary strand arrest:
    Strands 1 and 8 should reach eigensolid convergence before interior strands (4-5) in a β-potential braid, mimicking coastal Kelvin wave trapping.

Non-formal Status

This is an interpretive lens, not a Lean theorem. To promote it to the formal surface would require:

  1. Adding a strandPotential : Fin 8 → Q16_16 field to BraidState
  2. Proving rossby_dispersion_implies_convergence_bound
  3. Proving boundary_converges_before_interior under monotonic potential

Until then, it lives here as a conjecture for future exploration.