Category: Computation & Complexity
Theoretical and empirical analysis of algorithms, state spaces, and computational bounds.
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Scope Theory: A Geometric Baseline for Information Scaling
Scope Theory formalizes the Information Scaling Law (ISL) across an 18-chapter geometric architecture: the Reality Manifold Ω, the 5-tuple Scope S_a, Fokker-Planck SDEs, and Shapley gap decomposition.
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Meditation with Infinity and Irrational Numbers: The Screaming Constants That Built Reality (π · e · φ · √2 · i · 0 · ∞)
A mathematical journey through π, e, φ, √2, i, 0, and ∞. Proving Hurwitz’s theorem for the golden ratio, the Hippasus diagonal crisis, and the Weyl ergodic desynchronization…
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Infinity Is a Scale Problem: The Coastline Paradox, Quantum Cutoffs, and the 10¹²⁰ Cosmological Catastrophe
The Coastline Paradox, Wilsonian Renormalization Group flows, and resolving the 10¹²⁰ vacuum energy discrepancy through the holographic Planck-to-Hubble horizon ratio.
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Infinity as Dimensional Insufficiency: When Geometry Breaks, Upgrade the Container
When geometry breaks, upgrade the dimension. Proof of hypersphere volume collapse to zero, QFT dimensional regularization poles, and holographic boundary reduction with Z3 proofs.
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A Unified Constraint-Based Framework for Algorithmic Generation of Plane Curves
The Shape Specification Triplet (SST) unifies conics, Lamé superellipses, Cassini ovals, and lemniscates via three drawing oracles, closed-form Gamma area proofs, and Z3 SMT verification.
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Geometry in Motion: Time, Energy, and Living Systems (Volume II: First-Principles Dynamics)
Deriving trajectories, Euler-Lagrange variational mechanics, Poiseuille quartic hemodynamics, Murray’s law r₀³ = r₁³ + r₂³, Turing morphogenesis, and Kleiber’s 3/4 fractal allometry.
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ISL Constraint Geometry: Derivation of the Fundamental Shapes of Reality and the Origin of Constant Φ = 120
Derivation of the 21 stable shapes across dimensions under four ISL closure layers. Explaining the sequence 1, 1, ∞, 5, 6, 3, 3…, the 24-cell anomaly, and α⁻¹…
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Fractal Approximations of Classical Curves and the Dimension Discontinuity Phenomenon
Constructive proof that fractal sequences with constant Hausdorff dimension ≈ 1.465 converge to smooth circles with dim = 1.0 at rate O(1/n²), proving Hausdorff dimension is not continuous.
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The Riemann Hypothesis as Dimensional Rigidity: Scale-Space Topology, Information Saturation, and Machine-Verified Stability
Formalizing the Riemann Hypothesis through scale-space conformal mapping |1 – 1/ρ| = 1, Li coefficient positivity wells, and Microsoft Z3 automated theorem proving.
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Code as Geometry: How 21 Universal Shapes Project to 9 Programming Languages
The GeoCode universal intermediate representation: eliminating syntactic syntax tax with 21 universal shapes and a 3-layer Graph IR projecting cleanly into Python, Rust, and C++.
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