cff-version: "1.2.0" message: "If you use SilverSight in your work, please cite this repository using the metadata from this file." type: software title: "SilverSight" version: "0.1.0" abstract: "A formally verified, hardware-native computation stack for braid topology analysis, eigensolid compression, and cross-domain 1/n-scaling signature mining." keywords: - formal verification - lean 4 - braid topology - spectral classification - fixed-point arithmetic - eigensolid compression - signature mining authors: - family-names: "Schneider" given-names: "Brandon" alias: "allaunthefox" affiliation: "Independent Researcher" orcid: "https://orcid.org/0000-0000-0000-0000" repository: "https://github.com/allaunthefox/SilverSight" repository-code: "https://github.com/allaunthefox/SilverSight" url: "https://github.com/allaunthefox/SilverSight" date-released: "2026-07-03" license: Apache-2.0 commit: "4910e3877cbebfa6024edd571e242dbbbbd1e6fc" references: - type: article title: "Solving inverse problems with Bayes' theorem" authors: - family-names: "Imaginary" given-names: "ICERM" url: "https://www.imaginary.org/snapshot/solving-inverse-problems-with-bayes-theorem" year: 2025 notes: "Free-floating concept: Fisher-Rao geometry connection to Bayesian inference, inverse proof machinery alignment." - type: software title: "Research Stack (OTOM)" authors: - family-names: "Schneider" given-names: "Brandon" - name: "Research Stack Contributors" repository-code: "https://github.com/allaunthefox/Research-Stack" url: "https://github.com/allaunthefox/Research-Stack" date-released: "2026-05-08" license: Apache-2.0 notes: "Parent research repository. SilverSight ports proven Lean modules (Semantics.FixedPoint, Semantics.SidonSets, Semantics.SieveLemmas, Semantics.InteractionGraphSidon, Semantics.BraidEigensolid, Semantics.BraidSpherionBridge)." - type: software title: "GP_ELITE: Regression symbolique par programmation genetique" authors: - name: "Sabri Hakou" version: "0.1.0" date-released: "2026-06-13" license: MIT repository-code: "https://github.com/ariel95500-create/gp-elite" notes: "Inspired SilverSight's native symbolic regression design. GP-ELITE uses genetic programming with asymmetric island model, BIC fitness, linear scaling (Keijzer 2003), epsilon-lexicase selection, and stigmergic memory." - type: unpublished title: "Photon-Varied Gaussian States" authors: - family-names: "Giani" given-names: "A." - family-names: "Win" given-names: "S." - family-names: "Conti" given-names: "C." year: 2025 notes: "Binds to Research Stack Semantics.PVGS_DQ_Bridge -> SilverSight formal/PVGS_DQ_Bridge/; preprint identifier pending confirmation." - type: unpublished title: "Stellar representation of non-Gaussian quantum states" authors: - family-names: "Chabaud" given-names: "U." - family-names: "Mehraban" given-names: "S." year: 2022 notes: "Binds to Research Stack Semantics.PVGS_DQ_Bridge -> SilverSight formal/PVGS_DQ_Bridge/; full citation details pending DOI or arXiv ID." - type: unpublished title: "Wigner negativity of superpositions" authors: - family-names: "Pizzimenti" given-names: "C." - literal: "et al." year: 2024 notes: "Binds to Research Stack Semantics.BindingSite / Semantics.PVGS_DQ_Bridge -> SilverSight formal/BindingSite/; full citation details pending DOI or arXiv ID." - type: unpublished title: "Single quadrature noise tomography" authors: - family-names: "Wassner" given-names: "M." - literal: "et al." year: 2025 notes: "Binds to Research Stack Semantics.PVGS_DQ_Bridge -> SilverSight formal/PVGS_DQ_Bridge/; full citation details pending DOI or arXiv ID." - type: article title: "Pascal's Triangle, Pascal's Pyramid, and the Trinomial Triangle" authors: - family-names: "Saucedo" given-names: "Antonio Jr." date-published: "2019-06" institution: name: "California State University, San Bernardino" collection-title: "Electronic Theses, Projects, and Dissertations" url: "https://scholarworks.lib.csusb.edu/etd/855" notes: "Binds to Research Stack Semantics.SidonSets -> SilverSight formal/CoreFormalism/SidonSets.lean; supports Sidon-set constructions, Singer-theorem residues, and number-theory fixtures." - type: article title: "Close packing density of polydisperse hard spheres" authors: - family-names: "Farr" given-names: "R." - family-names: "Groot" given-names: "R. D." date-published: "2009-12" doi: "10.1063/1.3276799" journal: "The Journal of Chemical Physics" notes: "Binds to Research Stack Semantics.BraidEigensolid / Semantics.BraidSpherionBridge / Semantics.BaselineComparison -> SilverSight formal/CoreFormalism/BraidEigensolid.lean / formal/CoreFormalism/BraidSpherionBridge.lean." - type: article title: "Fractionation effects in phase equilibria of polydisperse hard-sphere colloids" authors: - family-names: "Fasolo" given-names: "M." - family-names: "Sollich" given-names: "P." date-published: "2004-10" doi: "10.1103/physreve.70.041410" journal: "Physical Review E" notes: "Binds to Research Stack Semantics.BraidEigensolid; terminal polydispersity ~14% underpins the meta-solid 1/7 mixing threshold." - type: article title: "Random-close packing limits for monodisperse and polydisperse hard spheres" authors: - family-names: "Baranau" given-names: "V." - family-names: "Tallarek" given-names: "U." date-published: "2014" doi: "10.1039/c3sm52959b" journal: "Soft Matter" notes: "Binds to Research Stack Semantics.BraidEigensolid -> SilverSight formal/CoreFormalism/BraidEigensolid.lean; definitive random-close-packing limits." - type: article title: "Freezing of polydisperse hard spheres" authors: - family-names: "Kofke" given-names: "D." - family-names: "Bolhuis" given-names: "P." date-published: "1999" doi: "10.1103/physreve.59.618" journal: "Physical Review E" notes: "Binds to Research Stack Semantics.BraidEigensolid / Semantics.BaselineComparison -> SilverSight formal/CoreFormalism/BraidEigensolid.lean." - type: article title: "A Differentiable Interior-Point Method in Single Precision" authors: - family-names: "Arrizabalaga" given-names: "Jon" - family-names: "Tracy" given-names: "Kevin" - family-names: "Manchester" given-names: "Zachary" date-published: "2026-05" url: "https://arxiv.org/abs/2605.17913" notes: "Binds to Research Stack Semantics.FixedPoint -> SilverSight formal/CoreFormalism/FixedPoint.lean; differentiable primal-dual IPM with bounded KKT systems." - type: article title: "Everything Is Logarithms" authors: - family-names: "Kritchevsky" given-names: "Alex" date-published: "2026-05-25" url: "https://alexkritchevsky.com/2026/05/25/everything-is-logarithms.html" notes: "Binds to SilverSight formal/CoreFormalism/HachimojiLUT.lean and formal/CoreFormalism/ChentsovFinite.lean. Core claim: logarithms are coordinate-free objects." - type: article title: "Stabilizing Recurrent Dynamics for Test-Time Scalable Latent Reasoning in Looped Language Models" authors: - family-names: "Yang" given-names: "Xiao-Wen" - family-names: "Han" given-names: "Ziyu" - family-names: "Zhang" given-names: "Xi-Hua" - family-names: "Wei" given-names: "Wen-Da" - family-names: "Shao" given-names: "Jie-Jing" - family-names: "Guo" given-names: "Lan-Zhe" - family-names: "Li" given-names: "Yu-Feng" date-published: "2026-05" url: "https://arxiv.org/abs/2605.26733" notes: "Binds to Research Stack Semantics.AVMIsa.* / Semantics.Run -> SilverSight Core/SilverSightCore.lean AVM transition function; STARS regularizes spectral radius." - type: online title: "Tangent lines to parabola at ends of focal chord are perpendicular (calculus proof)" authors: - literal: "Unknown" date-published: "2025" url: "https://www.reddit.com/r/calculus/comments/1udl2t6/show_lines_tangent_to_parabola_at_the_ends_of_a/" notes: "Demonstrates focal chord perpendicularity. Maps to Hachimoji eigensolid conjugate pairs with 1/n scaling." - type: article title: "Brownian dynamics of polydisperse colloidal hard spheres: Equilibrium structures and random close packings" authors: - family-names: "Schaertl" given-names: "W." - family-names: "Sillescu" given-names: "H." date-published: "1994" doi: "10.1007/bf02183148" journal: "Journal of Statistical Physics" notes: "Early polydisperse hard-sphere BD simulation." - type: article title: "On the jamming phase diagram for frictionless hard-sphere packings" authors: - family-names: "Baranau" given-names: "V." - family-names: "Tallarek" given-names: "U." date-published: "2014" doi: "10.1039/c4sm01439a" journal: "Soft Matter" notes: "Jamming phase diagram for frictionless spheres." - type: article title: "Dense packing of binary and polydisperse hard spheres" authors: - family-names: "Santiso" given-names: "E." - family-names: "Muller" given-names: "E. A." date-published: "2002" doi: "10.1080/00268970210125313" journal: "Molecular Physics" notes: "Packing of binary/tridisperse/distributed sphere mixtures." - type: article title: "Freezing line of polydisperse hard spheres via direct-coexistence simulations" authors: - family-names: "Castagnede" given-names: "A." - family-names: "Filion" given-names: "L." - family-names: "Smallenburg" given-names: "F." date-published: "2025" doi: "10.1063/5.0281621" journal: "The Journal of Chemical Physics" notes: "Recent direct-coexistence simulation of polydisperse freezing line." - type: article title: "Frenkel's entropy-exchange mechanism in monodisperse, nearly hard-sphere colloids: minimal perturbations to access fluid-crystal coexistence" authors: - family-names: "Wang" given-names: "J. G." - family-names: "Dhumal" given-names: "U." - family-names: "Zakhari" given-names: "M. E. A." - family-names: "Zia" given-names: "R." date-published: "2025" journal: "Journal of Fluid Mechanics" notes: "Entropy-exchange mechanism to access monodisperse hard-sphere fluid-crystal coexistence." - type: article title: "The elusive fluid-and-crystal coexistence state in simulations of monodisperse, hard-sphere colloids" authors: - family-names: "Wang" given-names: "J. G." - family-names: "Dhumal" given-names: "U." - family-names: "Zakhari" given-names: "M. E. A." - family-names: "Zia" given-names: "R." date-published: "2024" doi: "10.1002/aic.70275" journal: "AIChE Journal" notes: "Elusive nature of unbiased monodisperse hard-sphere coexistence simulation." - type: article title: "Local composition fluctuations act as precursors for crystal nucleation in polydisperse hard spheres" authors: - family-names: "De Jager" given-names: "M." - family-names: "Castagnede" given-names: "A." - family-names: "Smallenburg" given-names: "F." - family-names: "Filion" given-names: "L." date-published: "2025" journal: "arXiv" notes: "Composition fluctuation precursors in polydisperse nucleation." - type: article title: "Rheology and structure of polydisperse three-dimensional packings of spheres" authors: - family-names: "Cantor" given-names: "D." - family-names: "Azema" given-names: "E." - family-names: "Sornay" given-names: "P." - family-names: "Radjai" given-names: "F." date-published: "2018" doi: "10.1103/physreve.98.052910" journal: "Physical Review E" notes: "Shear strength nearly unchanged despite microstructural differences in polydisperse packings." - type: article title: "Impact of polydispersity and confinement on diffusion in hydrodynamically interacting colloidal suspensions" authors: - family-names: "Gonzalez" given-names: "E." - family-names: "Aponte-Rivera" given-names: "C." - family-names: "Zia" given-names: "R." date-published: "2021" doi: "10.1017/jfm.2021.563" journal: "Journal of Fluid Mechanics" notes: "Polydispersity + confinement effect on colloidal diffusion." - type: article title: "Percus-Yevick structure factors made simple" authors: - family-names: "Botet" given-names: "R." - family-names: "Kwok" given-names: "S." - family-names: "Cabane" given-names: "B." date-published: "2020" doi: "10.1107/s1600576720014041" journal: "Journal of Applied Crystallography" notes: "Simplified PY structure factors for monodisperse/polydisperse fluids." - type: thesis title: "Microstructure and macroscopic properties of polydisperse systems of hard spheres" authors: - family-names: "Ogarko" given-names: "V." date-published: "2014" doi: "10.3990/1.9789036536691" institution: name: "University of Twente" notes: "Polydisperse hard-sphere EOS, moments, glassy regime." - type: article title: "Induction Effects in Terrestrial Magnetism, Part I. Theory" authors: - family-names: "Elsasser" given-names: "Walter M." date-published: "1946" doi: "10.1103/PhysRev.69.106" journal: "Physical Review" notes: > Introduced toroidal/poloidal decomposition of vector fields on a torus (poloidal = short way, toroidal = long way). SilverSight's CRT Torus Embedding F(a)₁ = a mod L₀ (identity, poloidal), F(a)ᵢ = S-a mod Lᵢ (reflection, toroidal) is the discrete additive analogue. The S-a reflection corresponds to poloidal inversion s_θ = ±1 in the continuous case, encoding braid crossing orientation (over vs. under). Source: formal/CoreFormalism/CRTSidon.lean, docs/research/sidon_preservation_creation.md. - type: online title: "Erdős Problem #477: Tiling complements for value sets of polynomials" authors: - family-names: "Bloom" given-names: "Thomas F." date-published: "2026-06" url: "https://www.erdosproblems.com/477" notes: > References: Bloom (2026) via Brownawell–Masser S-unit estimate + Heath-Brown determinant method. Proves that the set of 13th powers has a tiling complement in ℤ. The greedy tiling criterion (Lemma 1.7) is the same algorithm as SilverSight's `crt_sidon_set`: enumerate candidates, reject those that create collisions, accept when bad shifts are o(T). The analytic density bound |Sc(T)|=O(T^{5/6}) corresponds to our Sidon sum collision bound (wrapping criterion + M-difference condition). Binds to: scripts/crt_capacity_envelope.py, formal/CoreFormalism/CRTSidon.lean. version: "accessed 27 June 2026" - type: online title: "Pipeline-Math: LLM-generated solutions to open problems" authors: - family-names: "Peng" given-names: "Binghui" - family-names: "Tao" given-names: "Runzhou" - family-names: "Wang" given-names: "Steven" - family-names: "Yu" given-names: "Hantao" - family-names: "Liu" given-names: "Diyi" date-published: "2026-06" repository-code: "https://github.com/Pengbinghui/pipeline-math" notes: > GPT-5.5 Pro (prover) + Claude Code (assembler) pipeline producing solutions to open problems (COLT, FOCS, Erdős, commutative ring theory) with Lean 4 formalization. Solves Erdős Problem 477 (tiling complement) — the same problem and greedy algorithm as SilverSight's crt_sidon_set. Their prover-verifier pipeline mirrors SilverSight's autoresearch (phi4/prove.py -> lake build verification). 95% of repo is Lean 4. - type: online title: "Toroidal and Poloidal Coordinates" authors: - literal: "Wikipedia contributors" date-published: "2025-05-26" url: "https://en.wikipedia.org/wiki/Toroidal_and_poloidal_coordinates" notes: > Accessible reference for toroidal/poloidal coordinate system. The poloidal θ coordinate (short way around the torus) maps to SilverSight's identity axis; the toroidal ζ coordinate (long way) maps to the reflection axes. Both are special cases of the same topology: two orthogonal directions on a torus with orientation sign s = ±1 encoding chirality. # ── 2026-07 Session Sources ────────────────────────────────── - type: article title: "Planar Point Sets with Many Unit Distances" authors: - name: "OpenAI" date-published: "2026-07" url: "https://cdn.openai.com/pdf/74c24085-19b0-4534-9c90-465b8e29ad73/unit-distance-proof.pdf" notes: > Proves ν(n) ≥ n^(1+δ) for infinitely many n, disproving Erdős's 1946 unit-distance conjecture. Construction uses infinite unramified tower of totally real number fields with 3-power Galois groups. Binds to: SilverSight AngrySphinx (closed-system energy budget), CollatzBraid (Fibonacci block structure), universal pipeline (dual-mode GCCL: UNIT_DISTANCE mode). - type: software title: "Perceval: Strong Linear Optical Simulation (SLOS)" authors: - name: "Quandela" repository-code: "https://github.com/Quandela/Perceval" url: "https://www.quandela.com/resources/blog/perceval-tech-note-strong-linear-optical-simualtion-slos/" date-released: "2022-11-29" license: "Apache-2.0" notes: > SLOS backend for photonic quantum simulation. Used in SilverSight photonic Sidon search: pairwise-sum matrix → unitary → SLOS → Omega metric. Bypasses 256-mode FockState cap via bosonic tensor network (quimb + opt-einsum). Source: scripts/photonic_sidon_search.py, formal/SilverSight/GoldenSpiral.lean (development map). - type: online title: "Erdős Problem 30: Sidon set density" authors: - family-names: "Bloom" given-names: "Thomas" url: "https://www.erdosproblems.com/30" notes: > Open problem: is h(N) = N^(1/2) + O_ε(N^ε)? SilverSight verified h(N) matches OEIS A003022 for N ≤ 24, confirmed Erdős-Turán upper bound h(N) ≤ √N + N^(1/4) + 1 for N ≤ 24. Source: scripts/photonic_sidon_search.py (T8_density test). - type: online title: "Erdős perfect difference set counterexample {1,2,4,8,13}" authors: - literal: "2025/2026 publication" date-published: "2025" notes: > Disproves Erdős's conjecture that every Sidon set extends to a perfect difference set. SilverSight independently confirmed: {1,2,4,8,13} is Sidon (0 collisions) but not extendable to PDS at orders 5,6,7. Source: scripts/photonic_sidon_search.py (T7_counterexample test), formal/SilverSight/CollatzBraid.lean. - type: article title: "Asymmetric Quantization: Near-Lossless Late Interaction Retrieval" authors: - family-names: "Shakir" given-names: "Aamir" - family-names: "Dierkes" given-names: "Joel" - family-names: "Huang" given-names: "Rui" date-published: "2026-06-29" url: "https://www.mixedbread.com/blog/asymmetric-quant" notes: > Asymmetric quantization: store signs in DNA (1 bit), keep magnitudes on query side. Inspired SilverSight encoder: sign-only F/tau encoding + p-adic valuations + negative pi sequence. Source: scripts/encoder_q16.py, scripts/padic_encoder.py. - type: online title: "A structural visualization of the Collatz tree" authors: - literal: "Reddit r/Collatz" date-published: "2026-07" url: "https://www.reddit.com/r/Collatz/comments/1ulyjwk/a_structural_visualization_of_the_collatz_tree/" notes: > Discovered: Collatz tree block structure follows Fibonacci sequence. i(k) = F(k+1), e(k) = F(k), total = F(k+2). Tree grows as φ^k. Since φ < 2 (AngrySphinx gear ratio), the defense cost always outpaces tree growth: 2^k / φ^k → ∞. Source: formal/SilverSight/CollatzBraid.lean (§6 Fibonacci Block Structure). - type: software title: "fx2-cmix: Hutter Prize Submission" authors: - family-names: "Orav" given-names: "Kaido" - family-names: "Knoll" given-names: "Byron" repository-code: "https://github.com/kaitz/fx2-cmix" date-released: "2024-10-08" license: "GPL-3.0" notes: > Current Hutter Prize record holder (enwik9: 110,793,128 bytes). 461-model context mixer with NLP, LSTM, article reordering. Weight matrix: 23 × 461 (layer-0 mixers × model inputs). SVD of this matrix = compression shape equation. Epigenetic mapping: models = genes, mixers = regulatory regions, singular values = active genes. Source: docs/cmix_epigenetic_analysis.md. - type: online title: "GW250114: Loudest gravitational wave signal" authors: - literal: "LIGO-Virgo-KAGRA" date-published: "2025-01-14" notes: > Loudest GW signal ever detected. 62.7-solar-mass remnant. Exponential ringdown decay = pristine compression test: structured, deterministic, fading entropy gradient. Proposed as astrophysical test data for SilverSight compressor. - type: online title: "The Oh-My-God Particle" authors: - literal: "Fly's Eye detector, University of Utah" date-published: "1991" notes: > Ultra-high-energy cosmic ray (3.2×10^20 eV). Single subatomic particle carrying baseball-velocity impact energy. Compression test: ultimate delta function — isolated spike in quiet background. Tests compressor's adaptivity to extreme outliers. - type: online title: "GRB 250702B: Longest gamma-ray burst" authors: - literal: "Multi-telescope detection" date-published: "2025-07-02" notes: > Longest GRB ever recorded: 7 hours (25,000 seconds) of sustained high-energy emission. Helium merger (black hole + helium star). Multi-channel correlated telemetry across 5 space telescopes. Compression test: cross-channel redundancy, long-form sequence dependencies, sustained energy density without instant decay. - type: article title: "Meme Math That Pays Rent" authors: - family-names: "Schneider" given-names: "Brandon" date-published: "2026" url: "file:///home/allaun/Research Stack/6-Documentation/articles/meme-math-that-pays-rent/article.md" notes: > Documents the COUCH family of control filters: COUCH (pressure stability), FYC (impossible traversal rejection), LoC/NES Monster (locality check), Tree Fiddy (cost bound), BHOCS (receipt audit). Philosophy: "A joke can get a parking pass. It does not get tenure. If it wants to stay in the stack, it has to pay rent." Source: formal/SilverSight/GCCL.lean (§8b Admit Pipeline). - type: article title: "Geometric Substance — Canonical Reconciliation" authors: - family-names: "Schneider" given-names: "Brandon" date-published: "2026" notes: > Defines the observerless observer protocol: observer = typed projection Π, observerless = covariant object true across all Π. Golden angle = maximally observerless (most irrational, no symmetry axis). Sidon mirror: exact at observerless level, inexact in every projection. Chirality = mirror inexactness. Source: formal/SilverSight/GoldenSpiral.lean, formal/SilverSight/GCCL.lean. Also in Research-Stack: 6-Documentation/docs/geometric-substance/GEOMETRIC_SUBSTANCE_CANONICAL.md. - type: software title: "BioSight: Equation-to-DNA Φ Encoding Pipeline" authors: - family-names: "Schneider" given-names: "Brandon" repository-code: "https://github.com/allaunthefox/BioSight" date-released: "2026-06" license: "Apache-2.0" notes: > DNA encoder: exact arithmetic (fractions.Fraction, no floats). Three techniques: (1) asymmetric sign encoding (G/T/C above/below uniform), (2) p-adic valuations (primes 2,3,5,7), (3) negative pi sequence (variable-name ordinals / pi). Achieves 20/20 injectivity. Source: BioSight/python/phi/embed.py (v3, exact arithmetic). - type: article title: "Bulk Acoustic Wave Ising Machine" authors: - family-names: "Lin" given-names: "Yuxuan" - family-names: "Wang" given-names: "Zhuoran" - family-names: "Zhang" given-names: "Yi" - family-names: "Liu" given-names: "Jian" - family-names: "Chen" given-names: "Xiaoyu" date-published: "2026-07-07" url: "https://arxiv.org/abs/2607.02112" notes: > BAWIM: Bulk Acoustic Wave Ising Machine using SAW resonators. Explored mutation engine approach for Sudoku solving. Result: approach not competitive — backtracking solver is 1000× faster and exact. Oscillating bath solver finds trivial minima or underperforms SA. Engine useful only for hardware parameter exploration, not solver quality. Source: python/bawim_mutation_engine.py, docs/research/bawim_mutation_engine_results.md. - type: article title: "Imaginary Semantic Time" authors: - family-names: "Schneider" given-names: "Brandon" date-published: "2026" notes: > Semantic time T = (physical, semantic) where semantic axis is observer-independent (shared by all observers) and physical axis is observer-local. Sieve observers: l=7 (human), l=11 (dolphin), CRT reconstruction mod 77. Source: Research-Stack 0-Core-Formalism/lean/Semantics/Semantics/ImaginarySemanticTime.lean, formal/SilverSight/HachimojiN8.lean (N=8 root theorem).