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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.
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|---|---|---|
| .. | ||
| architecture | ||
| assets/css | ||
| concepts | ||
| famm | ||
| research | ||
| roadmaps | ||
| speculative-materials | ||
| _config.yml | ||
| COEVOLUTION_MODEL.md | ||
| compression_signal_shaping_synthesis.md | ||
| FAMM_BAKER_ANALOGUE.md | ||
| math-first-tooling.md | ||
| optional-science-toolbelt.md | ||
| PROOF_SELFSIGHT.md | ||
| rainbow_raccoon_compiler_integration.md | ||
| README.md | ||
| rrc_equation_classification.md | ||
| rrc_logogram_projection_bridge.md | ||
| rrc_logogram_projection_formalism.md | ||
| S7_SPECTRAL_BASIS.md | ||
| STATE_SPACE_EMBEDDING.md | ||
| transfold_couch_data_magnetic_domain_comparison.md | ||
| transfold_enwiki8_magnetic_domain_generator.md | ||
| WEIRD_MACHINE_SPEC.md | ||
| WIKI.md | ||
NOTE: This directory is a legacy alias. The authoritative documentation tree is 6-Documentation/docs/. See ARCHITECTURE.md for the full doc map.
Files here are retained as stable references. New documentation should be added to 6-Documentation/docs/.