econosysmographe.com

How Three Manifolds is Produced

Methodology, data sources, AI usage, and human review process for the Three Manifolds — Weekly Market Reading.

Page target: econosysmographe.com/methodology (static, updated only when the pipeline changes — typically once per quarter).

Why this page exists: institutional readers and investors deserve to know exactly how the weekly signal is produced, where the deterministic part ends, where AI assistance begins, and what review gates apply before publication. Transparency is a feature of the deep-tech positioning, not an afterthought.

At a glance

The Three Manifolds weekly reading flows through six explicit gates. Gates 1–3 are deterministic (no AI). Gate 4 uses AI assistance for prose drafting only. Gates 5–6 are manual human steps.

DATA → COMPUTATION → READING → DRAFTING → REVIEW → PUBLICATION
 G1       G2          G3        G4          G5       G6
deterministic      deterministic   AI-assisted   human   human

Gate 1 — Data Ingestion

Inputs: end-of-day market data only, sourced from publicly available feeds:

  • US equity sector ETFs (SPDR family) — daily close prices
  • European sector indices (STOXX 600 super-sectors) — daily close
  • Spot FX rates (12 major pairs) — daily close
  • Short-term rates (3-month proxies, 10 instruments) — daily close
  • CPI series (9 country indices) — monthly, with daily forward-fill
  • Commodities and stress instruments (9 instruments) — daily close
  • US macro indicators (11 series, including industrial production) — official release cadence

No proprietary feeds. No labelled crisis dataset. No per-input tuning. Every reading is reproducible from the same public sources by any user with the same lookup window.

Universe: 77 nodes across 7 structural families on the macro panel. 11 S&P 500 sectors. 20 STOXX 600 super-sectors.

Gate 2 — Geometric Computation (deterministic, no AI)

The covariance trajectory of the universe is computed on a rolling window. The result is a sequence of points on the manifold of symmetric positive-definite matrices, denoted SPD(n).

Operations applied (same operations every reading, no per-crisis tuning):

  • Riemannian distances on SPD(n) via the Papadopoulos Distance metric (proprietary, formally specified)
  • Two-Prices framework — derives a geodesic price for each asset from the manifold attractor, compares to spot, returns the deviation σ
  • Topological Stress Score (TSS) — aggregates panel-level dispersion into a single scalar (0% = full Singularity, 100% = maximum dispersion)
  • Functional Coupling Index (FCI) and Entropy — secondary scalars for regime confirmation
  • Principal component decomposition on the contagion network — identifies the dominant variance direction
  • Contagion ring classification — sorts each node into CORE / INDUCED / PERIPHERY based on residual graph structure

No machine learning. No backtesting on labelled outcomes. The framework is geometric, not statistical.

Formal foundation: the core theorems are formally verified in Lean 4 + Mathlib. Theorems 11.1–11.3 prove Two-Price equilibrium existence and uniqueness; Theorem 12.1 proves Lyapunov suture stability of the geometric attractor.

Computation cost: 15-minute daily batch on standard infrastructure. No GPU required for the production stack.

Gate 3 — Reading Synthesis

Each daily computation produces three dashboards:

  • Macro Sysmographe — gauge, timeline, contagion network, principal-component decomposition
  • S&P 500 Sysmographe — same structure, 11 sector ETFs
  • STOXX 600 Sysmographe — same structure, 20 European super-sectors

Each dashboard exports both a visual (PNG) and a structured JSON with all numerical outputs. The JSON is the canonical record; the PNG is for human and downstream agent consumption.

Gate 4 — AI-Assisted Drafting

This is the only gate where AI is used.

What the AI does:

  • Reads the three JSON exports + the dashboard screenshots from the current week
  • Reads the previous issue’s article (for continuity)
  • Fills the canonical article and carousel templates with this week’s data
  • Writes the interpretation paragraphs in the “we observe” register

What the AI does NOT do:

  • It does not compute the signal — Gates 1–3 are deterministic and run before the AI is invoked
  • It does not decide which sectors to highlight — the dashboard JSON pre-determines that
  • It does not produce directional recommendations — the system prompt forbids “buy / sell / underweight / overweight / target price / outperform” vocabulary
  • It does not publish — Gate 6 is manual

Bounded by an explicit system prompt: the AI agent operates under a versioned instruction set that defines the canonical structure, the language register, the slug convention, the disclaimer rules, and the data-integrity rules. Any deviation by the agent is caught at Gate 5 and the system prompt is updated.

Gate 5 — Human Editorial Review

Every draft is reviewed by the author (Evangelos Papadopoulos, Independent Researcher) before publication.

What the review covers:

  • Cross-check every numerical value in the article against the JSON exports from Gate 3
  • Verify the register stays “we observe” — no predictive or directional language
  • Verify all factual claims requiring external sources (e.g. DAX composition, STOXX weights) against publicly available references
  • Verify continuity sentences vs the previous issue (no contradictions, no stale framing)
  • Validate the carousel images match the slide narrative
  • Approve or revise

Time budget: approximately one full day per week (typically Saturday afternoon and Sunday morning). The human time is the quality bottleneck — and that bottleneck is intentional.

Gate 6 — Manual Publication

Publication is never automated.

  • Article uploaded to WordPress by hand
  • Carousel exported to PDF and posted to LinkedIn by hand
  • Cluster posts to LinkedIn groups staggered by hand
  • Inbound institutional inquiries handled via the contact form at econosysmographe.com/contact

Publication window: Sunday 12:00–14:00 Paris time, weekly.

The manual step is deliberate — the friction forces a final read-through, prevents auto-publication of a flawed draft, and creates an audit trail at the publication moment.

What this means in practice

  • The signal you see in the dashboards is 100% deterministic. No AI, no labelled training, no per-crisis tuning. Reproducible by any user with the same data window.
  • The prose you read in the article is AI-drafted, human-reviewed. The writing is assisted; the analytics are not. The author retains editorial accountability.
  • Publication is human-gated. Nothing reaches the public surface without explicit human approval.

On AI disclosure

We use AI in Gate 4 because that is what allows a one-person research operation to maintain a 26-week weekly cadence at institutional quality. We disclose this here, on a public methodology page, rather than on every article footer — because the AI is bounded to drafting and the signal itself does not depend on it. Hiding the AI usage would be dishonest. Mentioning it on every article would be misleading the other way (it would suggest the analytics are AI-generated, which they are not).

The deep-tech positioning of Econosysmographe™ is built on three pillars: formally verified geometric methodology, AI-assisted production discipline, and human editorial accountability. We treat the three as inseparable.

Beyond the weekly reading — the URF business application

The deterministic geometric stack described above (Gates 1–3) also powers a separate institutional application currently in private staging. This application allows authorised users to interact with their own portfolio readings through a conversational analytical layer, ask the dashboards specific questions, and stress-test allocations against the manifold structure in real time.

The application is not publicly accessible at this stage. It is used internally to extract the geometric indices that feed the weekly reading and to develop the institutional product. Q2 2026 institutional POC access is available on request to risk officers and asset managers who want to evaluate the system on their own portfolio. Contact: contact@econosysmographe.eu.

Reproducibility

Every reading is reproducible from end-of-day public data using the published methodology. The full URF specification is documented in the SSRN papers:

  • URF-1: The Universe Risk Framework
  • URF-2: Crisis Detection on the SPD Manifold
  • URF-3: Two-Price Equilibrium and Geodesic Convergence
  • URF-4: Lorentzian Signature of the Manifold (in preparation)

Lean 4 + Mathlib formal proofs available on request for institutional due-diligence.

Educational positioning

The Three Manifolds Weekly Market Reading is educational material. SmartGreenInvest Ltd (Reg. England & Wales No. 14636473) is not an FCA-authorised firm and does not provide investment advice, recommendations, or solicitation to invest. The structural readings are research outputs intended to inform institutional risk-management discussions, not to substitute for them.

For institutional POC discussions or investor conversations, contact: contact@econosysmographe.eu.

Page maintained by Evangelos Papadopoulos. Last reviewed: 3 May 2026. Next scheduled review: 1 August 2026 (Q3 update) or earlier if the pipeline changes.