Found via Reddit post (r/LinearAlgebra): spherical Laplacian gives the
natural coordinate system for SilverSight state space.
KEY RESULT:
- Fisher simplex Δ_7 maps to S^7 via √p transform (exact, not analogy)
- Spherical Laplacian eigenfunctions Y_l^m are the natural basis
- Program states decompose as |ProgramState⟩ = Σ c_{l,m} |l,m⟩
- FAMM frustration = conformal deformation → Laplacian eigenvalue shift
- Scars leave spectral fingerprint in high-l coefficients
For default quine.py state:
c_00 = 0.707 (average), c_1,Φ-Σ = 0.707 (dipole), ⟨L²⟩ = 3.5
NEW FILES:
- docs/S7_SPECTRAL_BASIS.md: full derivation, spectral receipt format
- CITATION.cff: added Reddit source (TROSE9025 2026), Amari 2016,
Vilenkin & Klimyk 1991
This is the coordinate system you were looking for.
Not 25 arbitrary raw coords — spectral decomposition on the Fisher sphere.
- Corrected type mismatches in SOSCertificate and SemialgebraicSet constraints, ensuring polynomial components are correctly typed as ((σ → ℝ) → ℝ).
- Resolved block comment syntax errors (/-- unexpected token) by converting section commentaries to standard block comments.
- Decomposed foldl list inductions into generalized induction helper lemmas foldl_nonneg and foldl_weighted_nonneg to resolve type mismatches.
- Unfolded let bindings in softplus_derivative_bounded via dsimp only to allow linarith to successfully find contradictions.
- Updated CITATION.cff, GEMINI.md, and local AGENTS.md files with baseline records.
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