Papers

40 research papers from the collision program. Each paper is the companion to a blog post that introduces the same material for a general audience.

Collision Calculus: Boundary Readings, Energy and RefinementOctober 2026
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The Unit Sampling Defect in Digit-Collision EnergyOctober 10, 2026
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Unity, Refinement, and Signed CaptureOctober 4, 2026
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Repetend Rigidity at the Golden ScaleSeptember 2026
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Finite Generation of Collision CapacityAugust 18, 2026
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The Stationary-to-Diagonal Transition in Collision CapacityAugust 9, 2026
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Conservation and Profinite Dynamics in Digit-Collision EnergyJuly 31, 2026
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Magnitude Decorrelation in the Collision SpectrumJuly 22, 2026
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The Secondary Term in Digit-Collision EnergyJuly 1, 2026
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The Cubic Law for Digit-Collision EnergyJune 2026
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Carry Boundaries and Bernoulli Spectra in Long DivisionMay 2026
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Additive Boundaries and Conductor Energies of Periodic Remainder OrbitsMay 2026
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The Structure That SurvivesApril 2026
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The Collision InvariantMarch 2026
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The Collision TransformMarch 2026
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The Collision SpectrumMarch 2026
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The Analytic Collision TransformMay 2025
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The Collision Spectrum and the L-Function LandscapeMarch 2025
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The Spectral RepulsionJanuary 2025
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The Double TransversalityOctober 2024
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The General Neutrality TheoremJuly 2024
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The Neutrality TheoremApril 2024
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The Collision Transform and the Critical StripJanuary 2024
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The Collision Periodic TableDecember 2023
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The Centered Collision SumOctober 2023
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The Collision Fluctuation SumApril 2023
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Silent Primes and the Variance of the Collision CountJanuary 2023
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The Character Structure of the Collision FluctuationOctober 2022
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Bin Derangements and the Gate Width TheoremJuly 2022
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Phase-Filtered Ramanujan Sums and the Spectral GateApril 2022
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The Autocorrelation FormulaJanuary 2022
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The Spectral Power of the Digit FunctionOctober 2021
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The Spectral Structure of Fractional FieldsJuly 2021
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The Cross-Alignment MatrixApril 2021
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The Coherence DecompositionJanuary 2021
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The Three-Tier TheoremOctober 2020
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The Alignment Deficit Lattice and Musical TuningOctober 2020
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The Alignment Limit for All PrimesJuly 2020
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Digit-Partitioning Primes and the Alignment FormulaApril 2020
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Why the Golden Ratio Selects the Prime ThreeJanuary 2020
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