Research
The methods behind the readings, documented and citable — and the weekly analyses where they are applied to live markets, in public.
Portfolio methodology and case study
The conceptual and mathematical foundations of the measurement, in a seven-minute note — and the same measures applied to a fund, page by page.
Methodology
Same weights, same securities — and yet not the same portfolio. How the journey from one market state to another is measured.
Portfolio case study
54 securities, but only 13 effective market directions. A complete review of a ten-mandate demonstration fund.
The Three Manifolds — weekly analyses
Every week since April 2026, we publish our structural reading of the market: what the manifolds show, against which thresholds, and what the reading cannot tell us. Every reading is dated and stays on public record as published.
- Chip Stocks Fell 11%. Our S&P 500 Panel Flagged an Epicenter for One Day.
- Brent Spot Jumped 18%. Our S&P Sector Panel Has Gone Six Weeks Without a Decline in Diversification.
- The Ten-Year Hit 5.29% and Credit Spreads a Six-Month High. Our S&P 500 Sector Panel Is the Most Diversified Since Marc
- Cybersecurity Rose 21% and Moved as One
- The Fed Raised Rates to 3.75%–4.00%. Stocks Held. The Fast Regime Changed.
Working papers
The research background of the framework is documented in five working papers available on SSRN (not peer-reviewed). Where a definition on this site differs from a paper, the methodology page is the reference.
- The Geometry of Risk: Predicting Financial Crises 332 Days Early Across a 26-Year Sample — SSRN 6566658, April 2026.
- Why Martingales Cannot Predict Markets — And What Riemannian Geometry Can Do Instead — SSRN 6400438, March 2026.
- Beyond Portfolio Death: Geometric Rupture Detection and the Cone de Evangelos — A Riemannian Critique of Lifecycle Investing and the 100% Equity Illusion — SSRN 6140809, February 2026.
- The Minsky Singularity: A Geometric Discovery of the Economic Termination Signal — SSRN 6212120, January 2026.
- The Universe Risk Framework: Geometric Foundations of the EconoSysmographe — SSRN 6055375, January 2026.
The framework explained
Three short videos: what the instrument measures, how a single model produces every view, and how the reading behaves through a correlation crisis.
Methodology in brief
The universe of listed instruments is read as a daily sequence of correlation states on SPD(n), the space where correlation matrices live, computed deterministically from public price data. On this structure, the platform measures each block’s diversification score (the Topological Survival Score) and its zone, redundancy measures that locate concentration, and a System reading across blocks that measures whether they still move independently. The same inputs always produce the same reading; every historical reading can be re-run and verified.
The Eratosthenes test
Around 240 BC, Eratosthenes of Cyrene measured the circumference of the Earth without leaving Egypt, by asking what the geometry of the Earth allows. The Eratosthenes test asks the same kind of question of a stress scenario: does it remain a possible market state?
Risk teams often build a correlation stress by taking an observed shock ‚Äî COVID 2020, the 2022 rate shock ‚Äî and scaling it in a straight line to a larger severity. Beyond a certain amplification, the resulting matrix is no longer a valid correlation matrix: no market could produce it. The test computes that point for each scenario, s* = 1 / (1 ‚àí Œªmin), where Œªmin is the smallest generalised eigenvalue of the scenario against today’s state, and reports the remaining headroom as a number.
What it answers that a backtest cannot. A backtest asks whether a model matched history, and needs out-of-sample data. The admissibility of a scenario is a mathematical property of the scenario itself: a model-validation team can check it today, on the stresses already in production, with no forecast involved.
What it does not do. It does not say whether a scenario is likely, it does not forecast, and it does not build better scenarios. It rules out one specific failure — a stress that describes a market that cannot exist — and states how close each existing scenario is to that boundary. See it applied in the Socrate II case study. The test is run as a scoped engagement rather than as a product tier — contact us to discuss whether it applies to your scenarios.
Glossary
Manifold — SPD(n), the space of correlation matrices of a market universe, built from public price data, on which all measures are computed.
TSS (Topological Survival Score) — the diversification score of the correlation structure, expressed as a percentage: 100 when every direction carries the same variance, lower as the spectrum becomes uneven, whether because one common direction dominates or because some assets become near-duplicates. Descriptive, not a forecast.
TSS zone — a descriptive band fixed in advance on the normalised scale TSS*: Singularity below 0.50, Tension from 0.50 to 0.80, Isotropic at 0.80 and above. It is not a probability and not a signal.
Atlas — the market read through its economically coherent blocks: each block measured as a structure of its own, a System reading across them, and an attribution module locating where alarms concentrate. Two-Prices was retired on 25 August 2026.
Epicentre ‚Äî the resolved direction of the structure with the most abnormal reading against its own history; it locates the week’s largest deviation, not a cause. Surrounding directions are classified as core, induced or periphery.
FCI (Flash Condition Index) — a composite of four geometric components of the structure; a high reading means the four are high together. Descriptive, not a forecast of any market event.
Entropy — the dispersion measure of the structure, tracked alongside the FCI on the daily timeline.
Deterministic computation — no stochastic or machine-learning step: identical inputs always yield identical readings, making every reading independently verifiable.
See the research applied, live.
In a 30-minute discovery session, we demonstrate the platform on current market data — the same measures described on this site, running on this week’s market.