Papers  ·  Preprints  ·  Books

Research Archive

Published work documenting the development and application of the Davis Manifold framework across multiple domains. All papers available open-access via Zenodo.

25+
Preprints
10
Books
30
Patents
1
Framework
Featured

Foundational Papers

2025 · Foundational
The Davis Manifold: Geometry-First Detection with Compositional Error Budgets
The foundational paper defining the Davis Manifold and its core axioms. Establishes the geometric framework that unifies constraint satisfaction, optimization, and inference across domains.
Foundational Zenodo →
2025 · AI & Language Models
The Field Equations of Semantic Coherence: A Geometric Theory of Meaning
Applies the Davis Manifold to transformer architectures, revealing that attention mechanisms perform curvature navigation on a semantic manifold. Provides geometric explanation for hallucination and context collapse.
LLM Theory Zenodo →
Plasma Physics

Fusion & Confinement

2026 · Plasma Confinement
The Spectral Geometry of Plasma Confinement: A Davis Field Equations Framework for Fusion Stability
Applies the Davis Field Equations to tokamak MHD stability, deriving the Troyon limit geometrically via the Cheeger Effect and Plateau Maximum Theorem. 13 experiments, 1 proved theorem, 0 free parameters.
Tokamak Cheeger Effect Paper → Interactive Lab → CHIHIRO →
Quantum Fluids

Superfluids & BEC

2026 · Bose-Einstein Condensates
The Davis-Landau Sonic Onset Law: Universal Critical Velocity for Vortex Nucleation in Bose-Einstein Condensates
GPU-accelerated Gross-Pitaevskii simulations across ⁸⁷Rb, ²³Na, ⁷Li prove that critical velocity β = vc/cs is species-independent — a universal geometric invariant determined solely by obstacle curvature, validating C = τ/K.
BEC Vortex Nucleation Paper → CALCIFER · Coming Soon
Artificial Intelligence

LLM Inference & Attention Geometry

2025 · Speculative Decoding
Curvature-Guided Speculative Decoding for Large Language Models
Uses semantic curvature to predict which tokens will be accepted during speculative decoding, achieving 2.8× speedup over vanilla speculative decoding with no accuracy loss.
GIGI Inference DOI Pending
2025 · KV-Cache
Geometric KV-Cache Compression via Curvature-Aware Token Selection
Identifies which KV-cache entries to keep based on their geometric importance on the semantic manifold. Achieves 70% cache reduction with minimal perplexity increase.
MIRADOR Memory DOI Pending
2025 · Cognition
Spectral Geometry of Transformer Cognition
Analyzes the spectral properties of attention matrices through the lens of discrete Riemannian geometry. Shows that "reasoning" corresponds to geodesic paths on the semantic manifold.
Theory DOI Pending
2025 · Holonomy
The Davis Conjecture on Semantic Coherence: Context Windows as Holonomy Groups
Proposes that context windows in LLMs function as holonomy groups on a semantic manifold. Context collapse occurs when the holonomy becomes trivial.
Conjecture DOI Pending
Constraint Satisfaction

GPU-Accelerated CSP Solving

2026 · GPU Optimization
Curvature-Guided Wavefront Execution for GPU-Accelerated Constraint Satisfaction
The paper that demonstrated 40,128× speedup over Yann LeCun's Kona 1.0 on Sudoku. Shows that CSP solving is fundamentally a curvature navigation problem.
Sudoku CUDA Zenodo → Case Study →
Drug Discovery

Molecular Geometry

2025 · Binding Prediction
Curvature-Guided Binding Affinity Prediction via Molecular Surface Geometry
Treats protein-ligand binding as a geometric matching problem on the Davis Manifold. Achieves +12% hit rate improvement over state-of-the-art docking methods.
CHIHIRO Docking DOI Pending
2025 · Genomics
GEODESIC: Genomic Evolution On Davis-Embedded Surfaces for Integrated Cancer Detection
Integrated cancer detection using genomic evolution mapping on Davis-Embedded manifolds. Identifies mutation trajectories as geodesics.
Cancer Evolution DOI Pending
Cybersecurity

Threat Geometry

2025 · Anomaly Detection
Curvature-Based Behavioral Anomaly Detection in Network Traffic
Detects threat actors by measuring behavioral curvature deviation from baseline manifold geometry. Achieves 94% precision with 0.1% false positive rate.
PARALLAX Network DOI Pending
Books

Geometric Intelligence Series

Available on Amazon

Hidden Variable
From a childhood IQ diagnosis to NASA and algorithmic justice, a manifesto on finding what systems hide.
The Geometry of Sameness
Proves production ML and Riemannian manifolds tell the same story, yielding error guarantees that survive coordinate changes.
The Geometry of Medicine
Reimagines health as geometric coherence on the Davis Manifold — stability as a path, not the absence of disease.
The Geometry of Fuel
From the Davis Law to topological vacuum rectification, a unified framework connecting inference, physics, and energy.
The Geometry of War
What if war could be predicted like weather? The mathematics of flow, curvature, and topological collapse in geopolitical conflict.
SUPERFLUID: The Geometry of Velocity
Five Millennium Prize problems are one problem in five languages. C = τ / K governs every transition from smooth to rough.
Author

Bee Rosa Davis

MS Digital Forensics, Brown University
27 years aerospace & security engineering

ORCID → Zenodo → GitHub →