A geometry of belief for reading market regimes.
Root systems, Coxeter groups, and a local AI architecture built to diagnose — not predict — how markets change their story.
EST treats the market's active narratives as generators of a reflection group, and asks a precise, checkable question: is the current regime bounded and self-correcting, drifting at the edge of stability, or breaking into something genuinely new. It runs on EQUI Technologies' local, user-controlled AI infrastructure — never as a black box, never as a promise of prediction.
A root system: the finite structure a regime is built from.
The Theory
Markets don't drift uniformly. They pass through regimes.
Traders call it a regime. Economists call it a structural break. Risk managers call it correlation breakdown. All of these name the same intuition, without ever making it precise enough to measure while it's happening.
Epistemic Symmetry Theory (EST) starts from a different question: not what is a regime, but what kind of mathematical object could support the number and variety of regimes we actually observe — one that accounts for regimes replacing one another, distinguishes an ordinary wobble from a genuine break, and does so from data we can actually collect.
The answer is geometric. EST borrows a branch of pure mathematics — root systems and the Coxeter groups they generate — and treats a market's active narratives as the generators of one such group. The structure that results is finite, precisely classified, and checkable: bounded and self-correcting, flat and drifting, or unbounded and diverging.
This is a deliberate offshoot of EQUI Technologies' broader Geometry of Meaning research line, which applies the algebra of the exceptional Lie group E₈ to semantic structure in general. EST takes a narrower slice of that machinery — root systems and their Coxeter groups, independent of any particular embedding — and gives it its own axioms, applied to one well-defined domain: the dynamics of narrative and belief in financial markets.
The result is not a forecast. It is a diagnosis: a statement of what kind of change occurred, how confidently that diagnosis can be made, and what the finite set of structurally reachable next states looks like from here.
The Architecture
One coherent stack, three layers.
EST is not a standalone tool bolted onto a data feed. It is the applied layer of an architecture EQUI Technologies has been building for longer: a deterministic operating kernel, a semantic-measurement infrastructure, and, on top of both, domain-specific reasoning like EST's market-regime geometry.
AXION AI OS
A deterministic operations algebra for AI agents: a partial-action monoid over atomic, idempotent operators, with formal closure over what is and isn't currently executable. It replaces probabilistic tool-calling with a structure that can be checked.
Quantalia
A semantic-indexing infrastructure for local AI appliances: content is measured along named, interrogative axes rather than blind embedding similarity — so the system can say what it found, and just as importantly, report when it doesn't know.
Epistemic Symmetry Theory
The geometric layer built on top: axis measurements become roots, roots generate a Coxeter group, and the group's structure becomes a diagnosis of the market regime — reachable states, drift, and structural breaks.
Philosophy
Local by design, not as an afterthought.
Every layer of this stack is built to run on hardware you own, with models you choose — never as a hosted black box you have to trust blindly.
Your hardware, your models
Designed for local AI appliances — from a single powerful workstation to purpose-built AI box hardware — with no requirement to send data anywhere it doesn't already live.
Mixture-of-Experts, applied locally
Different models for different jobs — measuring, routing, generating, verifying — assigned per task rather than forced through one general-purpose model, including sparse MoE architectures running on-device.
Vendor-neutral by principle
No data source, model vendor, or hardware platform is assumed on your behalf. You choose what feeds the system and where it runs.
The Book
The full theory, stated precisely.
SYMMETRY
THEORY
Root Systems · Mixture-of-Experts
Local AI Box Intelligence
Epistemic Symmetry Theory
A Geometry of Belief for Reading Market Regimes: Root Systems, Mixture-of-Experts, and Local AI Box Intelligence
The complete mathematical development — axioms, root extraction, the Root Admissibility Condition, Coxeter classification, orbits, curvature, and elasticity — alongside a conceptual account of the infrastructure a working system needs, and two full worked examples on real historical market data, reported with their actual limitations.
- Full mathematical core, built for a mathematically literate reader
- Two worked examples on real historical data, honestly reported
- A practical guide to setting up your own epistemic space
- Templates for extending the same geometry beyond finance
IP & Patents
Disclosure
Several of the architectural components referenced on this page — the AXION operating layer, the Quantalia measurement infrastructure, and related mechanisms — are, in whole or in part, the subject of pending patent applications filed by EQUI Technologies International LLC.
Nothing on this page constitutes investment advice, and no part of it should be read as a recommendation to buy, sell, or hold any financial instrument. Epistemic Symmetry Theory describes a theoretical framework and a family of measurement methods; readers who wish to apply it to real decisions should do so with independent professional advice and at their own risk.