New Release The Geometry of War by Bee Davis
72 days.

The Geometry of War

On December 14, 2021, a mathematician in Sacramento watched a number cross a threshold. She wasn't in a government situation room. She had a laptop, a theory borrowed from fluid dynamics, and a metric no one else was measuring. Seventy-two days later, Russian tanks crossed the border.

The warning was there. The math was right. This book reveals the geometry that predicts when nations slide toward conflict — and when they don't.

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One Framework  ·  Every Hard Problem

When the Math
is Right,
Domains Become Details

The Davis Manifold — a unified geometric framework that rewrites the rules across plasma physics, drug discovery, finance, autonomous systems, and AI. Not a collection of tools. A singular mathematics that solved 30 patent-worthy problems because it solved the right problem first.

9
Products
30
Patents
10
Books
1
Math
Bee Rosa Davis
Brown University (MS) · 27 Years Aerospace
ORCID: 0009-0009-8034-4308
Independent Researcher · Davis Geometric
Pre-Seed · $175K
Invest in Davis Geometric
One math. 18 products. 30 patents. $200B+ TAM.
View Pitch Deck →
Domain Coverage
Plasma Physics5 patents
Drug Discovery5 patents
Finance & Markets4 patents
AI & LLM Inference6 patents
Cybersecurity5 patents
Autonomous Systems5 patents
Geometry Unifies
What Looks Different · Is the Same Problem

Every hard problem is a manifold. Protein folding, market regime detection, plasma confinement, neural network inference — they're all curvature navigation in disguise. Domain experts hallucinate separate disciplines. The Davis Manifold sees one thing: the shape of constraint.

01 — The Domains

Six Frontiers, One Math

These aren't metaphors. These are production systems, each powered by the same curvature-guided architecture. The Davis Manifold doesn't "apply to" different fields — it reveals that they were never different to begin with.

Ψ
Plasma Physics
Fusion confinement geometry, MHD stability analysis, magnetic field topology. CHIHIRO platform.
Δ
Drug Discovery
Binding affinity prediction, molecular conformation search, pharmacokinetic modeling. 5 patents. CHIHIRO platform.
Σ
Finance & Markets
Regime detection, portfolio curvature optimization, non-Gaussian risk geometry. 4 patents. PRISM & MARCELLA platforms.
Ω
AI & LLM Inference
KV-cache compression, speculative decoding, attention geometry, hallucination detection. 6 patents. MIRADOR & GIGI platforms.
Λ
Cybersecurity
Behavioral anomaly detection, threat graph traversal, encryption key geometry. 5 patents. PARALLAX platform.
Π
Autonomous Systems
Path planning on curved terrain, sensor fusion geometry, multi-agent coordination. 5 patents. DHOOM & PSYCHOHISTORY platforms.

Classical heuristics in each field — Monte Carlo, gradient descent, constraint propagation, MCTS — all emerge as degenerate cases of curvature-guided scheduling when specific geometric weight components are set to zero.

02 — The Theory

The Davis Manifold

Every decision space forms a manifold — not as metaphor, but as literal Riemannian geometry with metric tensor, connection, and holonomy. The Davis Manifold theory provides a coordinate-free language that makes the "hard parts" of any problem visible as curvature, and the solution path apparent as a geodesic.

The Core Insight
$$V(x) = \frac{K_{\text{loc}}(x) + \displaystyle\sum_{y \sim x} K_{\text{loc}}(y)}{\left|\mathcal{A}(x)\right|}$$
Information Value: identifies where to invest compute for maximum global constraint reduction. Works identically across all domains — the only thing that changes is what $x$ represents.
Symbol Breakdown
V(x)Information Value at point x — how much solving here helps everywhere
KlocLocal curvature — how "bent" or constrained this spot is
y ~ xPoints y that neighbor x — connected decisions
|A(x)|Available actions at x — how many choices remain
In Plain English

Imagine you're solving a jigsaw puzzle. This formula tells you which piece to try next. It looks at how constrained a spot is (few pieces fit there) plus how constrained its neighbors are, divided by how many options you have. High score = solve this first because it will make everything else easier. The magic: this same formula works for drug molecules, plasma control, financial portfolios — anything.

Derives From
C = τ / KThe Davis Law

V(x) is an instantiation of the Davis Law: Capacity (C) equals tolerance (τ) divided by curvature (K). The information value at any point is exactly what remains when you divide how much variation the system can tolerate by how curved (constrained) that region is.

The Energy Functional
$$E[\gamma] = \lambda_1 \int_\gamma ds + \lambda_2 \int_\gamma K(s)\, ds + \lambda_3 \int_\gamma \left\| \mathrm{Hol}_\gamma(s) - I \right\| ds$$
Path length + curvature load + holonomy deficit. The geodesic of this functional is the optimal traversal through any constraint space.
Symbol Breakdown
E[γ]Total energy cost of path γ — what we minimize
λ1,2,3Tuning weights — how much each factor matters
∫ dsPath length — total distance traveled
K(s)Curvature at point s — how "hard" that spot is
HolγHolonomy — accumulated "twist" along the path
IIdentity — the "no twist" reference state
In Plain English

Think of navigating a city. The first term is distance. The second is "avoid traffic" — don't go through congested areas. The third is "stay oriented" — don't take so many turns you get lost. The best route minimizes all three, weighted by what matters to you. The path that minimizes this energy is the optimal solution to any problem — finding a drug, stabilizing plasma, optimizing a portfolio. Same equation, different interpretations of "distance" and "twist."

Proves Via
S + d² = 1The Davis Identity

Any geodesic satisfying E[γ] = minimum also satisfies the Davis Identity: Sameness (S) plus squared deviation (d²) equals unity. This isn't just optimization — it's proof. The identity guarantees that every optimal path is verifiably optimal, with a certificate.

→ How It All Connects — The Full Mathematical Framework
σ
Saturation
Boundary curvature — how constrained is this point? High saturation = forced decisions = resolve early.
ρ
Scarcity
Fiber dimension — how rare is this resource? Low scarcity = bottleneck = prioritize before starvation.
κ
Coupling
Connection rigidity — how tightly linked to neighbors? High coupling = cascading effects = resolve for maximum propagation.
03 — The Proof

Not Theory. Deployed Systems.

These aren't proposals or prototypes. These are production platforms, each demonstrating the Davis Manifold's ability to outperform domain-specific solutions built by experts who spent decades in their fields. The math doesn't care about your PhD — it cares about the geometry.

Sample Performance Gains
Transaction Matching (PRISM)99.97%
Language Model (MARCELLA)3.85×
Plasma Diagnostics (CHIHIRO)<10ms
Conflict Prediction (PSYCHOHISTORY)72 days
Data Compression (GIGI)54-84%
Benchmarks measured against domain-leading competitors. Full methodology in individual product documentation.
Intellectual Property
U.S. Patents (Pending)30
Production Products9
Published Books10
Peer-Reviewed Papers12
DOI-Registered Preprints25+
View all products and patents →
The Portfolio
AI & LLM
6 patents
Plasma Physics
5 patents
Drug Discovery
5 patents
Cybersecurity
5 patents
Autonomous
5 patents
Finance
4 patents
The Heresy

Why Domain Experts Hate This

"You can't solve plasma confinement with the same math as drug binding."

Except you can. The objection confuses encoding with structure. Different variables, same curvature. Different constraints, same geodesic. The Davis Manifold doesn't ignore domain complexity — it reveals that domain complexity is a coordinate artifact. The hard part was always the same: navigating constraint manifolds efficiently. Everything else is notation.

The Old Way
Learn one domain deeply. Build bespoke solutions. When problems shift, start over. Guard expertise jealously. Publish incrementally. Career as a moat.
The Davis Way
Learn the shape of constraint. Build once, deploy everywhere. Problems shift — the manifold stays. Share the math. Publish the architecture. Domains become details.
The Architect
Bee Rosa Davis

Bee Rosa Davis

MS Digital Forensics, Brown University
27 years aerospace & security engineering
ORCID: 0009-0009-8034-4308
Independent researcher who stopped asking "how do we solve this problem?" and started asking "what shape is this problem?" The Davis Manifold is the answer. Nine products, thirty patents, ten books later — still finding new applications of the same math. Overall Mother of the House of Diwa.
The full story →
Foundational Papers
The Davis Manifold — The framework that started it all
The Field Equations of Semantic Coherence — LLM inference as geometry
Geometric Intelligence Series
Hidden Variable — From NASA to algorithmic justice
The Geometry of Sameness — ML as Riemannian geometry
The Geometry of Medicine — Health as geometric coherence
The Geometry of Fuel — From inference to physics
Start Here

Explore the Framework

View All Products → Research Papers → GitHub →
9
Products
MIRADOR, GIGI, DHOOM, PRISM, CHIHIRO, PSYCHOHISTORY, HELICITY, PARALLAX, MARCELLA
30
Patents
U.S. Provisional Patent Applications across plasma physics, drug discovery, finance, AI, cybersecurity, and autonomous systems
10
Books
The Geometric Intelligence Series: from algorithmic justice to topological vacuum rectification
Licensing: The Davis Manifold framework and its domain-specific applications are protected by 30 U.S. Provisional Patent Applications filed 2025-2026. Contact bee_davis@alumni.brown.edu for licensing inquiries.