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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.
67 lines
2.2 KiB
YAML
67 lines
2.2 KiB
YAML
cff-version: "1.2.0"
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message: "If you use this software, please cite it as below."
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type: software
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title: "SilverSight: Deterministic Equation Search via Fisher Geometry"
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authors:
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- family-names: "Allaun"
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given-names: ""
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repository-code: "https://github.com/allaunthefox/SilverSight"
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license: MIT
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references:
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- type: article
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authors:
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- family-names: "Giani"
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given-names: "A."
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- family-names: "Win"
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given-names: "S."
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- family-names: "Conti"
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given-names: "C."
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title: "Photon-Varied Gaussian States"
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year: 2025
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journal: "arXiv:2505.XXXXX"
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- type: article
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authors:
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- family-names: "Chabaud"
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given-names: "U."
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- family-names: "Mehraban"
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given-names: "S."
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title: "Holomorphic representation of quantum states"
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year: 2022
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- type: article
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authors:
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- family-names: "Pizzimenti"
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given-names: "C."
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- family-names: "et al."
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title: "Wigner negativity of superpositions"
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year: 2024
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- type: article
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authors:
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- family-names: "Wassner"
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given-names: "M."
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- family-names: "et al."
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title: "Single quadrature noise tomography"
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year: 2025
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- type: software
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authors:
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- family-names: "TROSE9025"
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title: "From Spherical Gradients to Dirac Kets: The Hidden Linear Algebra of the Laplacian"
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year: 2026
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url: "https://www.reddit.com/r/LinearAlgebra/comments/1ucglpd/"
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notes: "Reddit post connecting spherical Laplacian to angular momentum operators and Dirac kets. Key insight for SilverSight: Fisher simplex maps to S^7 under sqrt(p) transform, giving spherical harmonics Y_l^m as the natural spectral basis for program state embedding."
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- type: book
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authors:
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- family-names: "Amari"
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given-names: "S."
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title: "Information Geometry and Its Applications"
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year: 2016
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publisher: "Springer"
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- type: book
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authors:
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- family-names: "Vilenkin"
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given-names: "N.J."
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- family-names: "Klimyk"
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given-names: "A.U."
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title: "Representation of Lie Groups and Special Functions"
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year: 1991
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publisher: "Kluwer"
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notes: "Volume 3: Classical and Quantum Groups and Special Functions. Spherical harmonics on S^n."
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