🔬 Research Category Hub
Tag: Scale-Space Topology
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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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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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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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