What is ESER™ (Enterprise Statistical Exploration Report)?

ESER™ is an exhaustive finite-domain parameter enumeration report. It sweeps every valid indicator parameter configuration across your specified asset universe at native 1-minute resolution. Unlike optimization, ESER delivers the complete solution set — every configuration that meets your statistical thresholds — so you can assess robustness rather than relying on a single optimized result.

How does Student One handle data security?

Student One operates under an ephemeral compute paradigm. Client data transits through cryptographically isolated compute boundaries with zero persistent storage. Upon completion, deterministic purge operations eliminate all intermediate artifacts. Every engagement includes a compute lifecycle certificate and data-use attestation as cryptographic proof of data destruction.

Who is Student One for?

Student One serves funds managing $50 million to $1 billion that need institutional-grade quantitative research without building internal supercomputing infrastructure. Our clients include hedge funds, multi-strategy desks, family offices, endowments, registered investment advisors (SEC, FCA, SEBI), and proprietary trading firms.

What is the difference between Student One and a backtesting platform?

Backtesting platforms optimize signal, position sizing, and risk simultaneously — joint optimization with maximum degrees of freedom that maximizes overfitting risk. Student One separates signal discovery entirely: we enumerate 1M+ parameter configurations through advanced robustness gates (walk-forward survival, permutation null with BH-FDR, auto OOS split) and deliver only statistically validated anomalies. Your quants then apply position sizing and risk to vetted signals — not curve-fitted backtest outputs. The backtest should not be the research.

Does Student One offer a Machine API for trading bots and AI agents?

Yes. Our machine-native API serves trading bots, AI agents, LLM platforms (Claude, GPT, Gemini via MCP tool definitions), and data pipelines. Authenticate with X-Api-Key, submit OHLCV via presigned S3 URLs, and receive exhaustive results via polling or webhooks. OpenAPI 3.1 spec available. Croissant ML-compliant datasets for ML pipeline interop. No human interaction required.

What are the statistical robustness gates?

Foundation: Win-Rate Gate, Recurrence Gate, Excursion Gate (MFE), Per-Regime MFE Gate. Differentiators: Time-of-Day Buckets, Day-of-Week Mask, Volume Confirmation, Volatility Regime, Third-Indicator Regime Gate (Bonferroni-corrected). Advanced: Walk-Forward Survival (Pardo 2008), Permutation Null with Benjamini-Hochberg FDR (Hansen 2005, Romano-Wolf 2005), Cluster Stability (DBSCAN), Auto OOS Split with zero re-optimization (López de Prado 2018). Each gate carries its academic citation and produces auditable metadata.

GEMINA

gemina, -ae — twins; a pair — Latin

Cross-Asset Pair Convergence Enumeration Engine

SUPERCOMPUTED ON DEMAND • ZERO COPIES RETAINED • EMPIRICAL

LIVE SIMULATIONETH/BTC × SOL/BTC1440m

Try it in Dojo→

Shut Up and Calculate+

Gemina does not model. It does not assume. It does not predict. It enumerates.

Gemina does not model. It does not assume. It does not predict.

It enumerates.

STEP 1

Start with two price series

Pick any two assets. Any pair. Gemina ingests their minute-by-minute closing prices across the entire trading day. Two lines. Two prices. Nothing else.

Raw prices. Minute by minute. This is all Gemina starts with — two time series, same frequency, same timestamps.

STEP 2

Pick a reference minute — the “anchor”

Choose one minute from the day. Call it the anchor. At the anchor, both assets’ returns are reset to 0%. Every minute after the anchor, compute a simple percentage return:

return at minute t = (price_t − price_anchor) ⁄ price_anchor × 100

This gives you two return lines, both starting at zero, diverging in real time.

Both return lines start at 0% at the anchor. No hedge ratio. No rolling mean. Just the raw percentage change from one reference price.

STEP 3

Every minute is an anchor — not just market open

This is the critical insight. Market open is just the first anchor. Gemina repeats the identical procedure at minute 2, minute 3, minute 4 … all the way to the last minute of the session. Every single minute becomes its own reference point, producing its own pair of return lines.

Session lengths range from 240 (SSE/SZSE) to 510 (LSE/Euronext) minutes for equities. A crypto or forex pair with 1,440-minute days has 1,440 anchor points. Each anchor produces a unique pair of return lines — and every pair is checked independently.

STEP 4

Divergence — the two return lines spread apart

From any given anchor, if the gap between the two return lines exceeds a threshold (e.g., 0.20%), Gemina records a divergence event. The threshold is a fixed percentage in return space — 0.20% means 0.20% regardless of volatility regime.

Once the gap crosses the threshold, a divergence is flagged. The question then becomes: do they come back together?

STEP 5

Convergence — the lines meet again

After divergence, Gemina watches for a cross — the moment the two return lines touch or pass through each other again. Binary outcome: cross, or no cross. Gemina checks for this within a configurable convergence window — from 3 market hours up to multiple trading days.

The convergence window intentionally extends beyond a single session — the overnight gap is part of the measurement.

STEP 6

Count everything. Assume nothing.

For every anchor minute, of every trading day, across every lookback period (30–510 trading days): did divergence happen? Did convergence follow? The result is a single number: win rate = days converged ⁄ total days.

But not all divergence is the same. The gap can open in different ways — one asset up and the other down, A leading or B leading. Gemina partitions every divergence event into six mutually exclusive non-discretionary conditions.

THE 6 CONDITIONS

Given two return lines anchored at any minute, Gemina classifies every divergence into one of these six conditions — then checks each for convergence independently.

θ — THE NOISE FLOOR IS YOURS TO SET

Every condition below requires the gap to exceed a threshold θ. This is not a fixed rule — you choose it. 0.10%0.20%…0.80% and more. A lower θ catches smaller divergences (more signals, more noise). A higher θ ignores minor moves (fewer signals, cleaner dataset). Gemina enumerates every threshold level — the full set is available inside.

OPPOSITE-SIGN DIVERGENCE (EITHER DIRECTION)

One asset is above 0%. The other is below 0%. The gap between them ≥ your chosen threshold (θ). Tunable from 0.10% upward. Either asset can be the one above — this test is symmetric.

Question: A is above zero, B is below zero, gap ≥ θ. How often do they meet again within the convergence window?

T1 = T2 ∪ T3. It is the union of the next two directional tests.

A POSITIVE, B NEGATIVE

Specifically: Asset A > 0% and Asset B < 0%, gap ≥ threshold. The directional version — A is the one that moved up first.

Isolates the case where A leads upward while B lags downward — a directional lead-lag signal.

B POSITIVE, A NEGATIVE

The mirror: Asset B > 0% and Asset A < 0%, gap ≥ threshold. B leads up, A lags down.

Mirror of T2. Together, T2 ∪ T3 = T1. Comparing T2 and T3 win rates tells you which asset leads.

GROUP 2 — ABSOLUTE GAP

Now: both assets can be moving in the same direction. Both up. Both down. The only thing that matters is the gap between them.

ABSOLUTE GAP DIVERGENCE (EITHER DIRECTION)

|gap| ≥ threshold, regardless of whether either asset is above or below zero. Both can be up +2% and +2.3% — that 0.3% gap qualifies.

Key insight: Both assets are trending up. But A is outrunning B. Does B catch up? How often? That is what C4 measures.

T4 = T5 ∪ T6. The union of the two directional gap tests.

A ABOVE B, GAP DIVERGENCE

Asset A’s return is above Asset B’s return, gap ≥ threshold. Both can be positive, both negative, or mixed — only the gap direction matters. When T5 converges consistently, A is leading B.

Directional: A outperforming B by ≥ θ. Asymmetry between T5 and T6 reveals which asset leads and which follows.

B ABOVE A, GAP DIVERGENCE

The mirror: Asset B’s return is above Asset A’s return, gap ≥ threshold. When T6 converges more often than T5, B is the one leading.

Mirror of T5. Together, T5 ∪ T6 = T4.

CONVERGENCE CRITERION

After divergence is detected, one question: do the return lines cross again?

Binary: cross or no cross. The convergence window deliberately extends beyond a single trading session. The overnight gap is part of the measurement. If a pair survives earnings, macro shocks, and correlated news events overnight and still converges — that is empirical data.

180minutes~3 market hours

540minutes~1.5 trading days

… extended windows up to multiple trading days

full range available inside Convergence windows span from intraday to multi-day horizons. The complete set of configurable windows is available when you run a scan.

EXHAUSTIVE ENUMERATION

Every condition is checked at every anchor minute of every trading day across every lookback period (30–510 trading days).

Anchor minutes per day390

Maximum lookback days510

Divergence test types6

Individual checks1,193,400

No sampling. No approximation. Every minute, every day, every condition, every lookback. The output is a flat table: win rate = days converged / total days. Raw frequency.

Accelerate your quantitative research.

Why Gemina Is a Paradigm Shift+

Finds what others find — plus what others systematically miss. 7 comparisons vs. Engle-Granger, Johansen, Z-Score, Kalman, Copula, Distance Method, and VECM.

vs. ENGLE-GRANGER COINTEGRATION

Engle-Granger estimates a long-run equilibrium via OLS regression, then checks the residual for stationarity. It assumes a linear, time-invariant relationship and requires the spread to be I(0).

Gemina makes no distributional assumption, does not estimate a regression, and does not require stationarity. It counts convergence events directly.

vs. JOHANSEN COINTEGRATION

Johansen extends Engle-Granger to multivariate settings using VAR models. It requires choosing lag order and deterministic trend specifications.

Gemina operates on raw returns with no model structure — there is nothing to mis-specify.

vs. SPREAD Z-SCORE TRADING

Standard pairs trading computes a spread, estimates rolling mean and standard deviation, and enters/exits at z-score thresholds. The z-score threshold changes meaning as volatility changes.

Gemina’s threshold (θ) is a fixed percentage in return space — you choose from 0.15% to 0.90%, and it means the same thing regardless of regime. No hedge ratio. No rolling statistics.

vs. KALMAN FILTER PAIRS

Kalman filter approaches estimate a time-varying hedge ratio and spread mean. They require specifying state transition and observation noise covariance matrices.

Gemina has no state to estimate and no filter to tune.

vs. COPULA-BASED APPROACHES

Copula methods model the joint dependence structure between two return series, often assuming a specific copula family (Gaussian, Clayton, Gumbel).

Gemina does not model dependence — it measures convergence frequency through direct enumeration.

vs. DISTANCE METHOD (GGR 2006)

The classic distance method selects pairs based on minimum sum of squared deviations of normalised price series. It uses daily prices and checks one entry per deviation event.

Gemina uses 1-minute prices and checks every minute of every day — 330–1,440× the resolution per session.

vs. VECM-BASED STRATEGIES

Vector Error Correction Models estimate speed-of-adjustment coefficients parametrically. They require lag selection and assume Gaussian errors.

Gemina does not estimate reversion speed — it counts how often reversion occurred within a fixed window. The window is the parameter, not a model coefficient.

What You Receive+

Enumerated convergence dataset in JSON, Parquet & human-readable formats. Filter by win rate, lookback, threshold, condition.

A fully explainable, quantitative, enumerated, non-discretionary dataset. Not a strategy. Not a recommendation. A structured body of empirical measurements you use to design your own financial models.

ENUMERATED CONVERGENCE DATASET

One row per (condition × anchor × lookback × threshold) configuration. Every combination checked. Every result recorded. No sampling, no discretion.

WIN RATE PER CONFIGURATION

For each configuration: how many past windows saw convergence vs. how many did not. That is the win rate — a simple empirical ratio. Filter by it. Sort by it. Build on it.

MEAN CONVERGENCE LATENCY

Average minutes from divergence to convergence across all converging windows. Measures how quickly the return differential reverted — not whether it will again.

DELIVERY FORMATS

{ }JSON

▦Parquet

☰Human-Readable

Machine-ingestible. Pipeline-ready. Build your own novel strategies from these enumerations.

HOW YOU READ THIS DATA

No matter how large the enumeration — hundreds of thousands of checks — every row carries a win rate. That is your filter.

Win rate is simply: given N past windows (30, 60, 90… up to 510 trading days), in how many of those windows did the condition meet? That ratio lets you filter by strength or weakness of any condition, for any pair, at any threshold.

LOOKBACK WINDOWS

306090…510ALL

DIVERGENCE THRESHOLDS (θ)

0.10%0.20%…0.80%+ more

TEST TYPES

T1 Opposite SignT2 A>0 B<0T4 Absolute GapT5 A Above B…6 types

As comprehensive as you want it to be. Every combination available. Some research needs conditions that rarely meet — others anticipate conditions that frequently meet. Both are valid. Both are in the dataset. Filter accordingly, based on your own research and internal controls.

Overlapping windows that satisfy a condition across consecutive days (day 23, 24, 25… through day 102) reveal a spectral phase — persistent structural behaviour. Apply White’s Reality Check or Hansen’s SPA to these overlapping observations to control for data-snooping bias. The dataset gives you the raw material. The statistical controls are yours to apply.

THE POINT IS NOT THE EXACT MINUTE

Patterns do not repeat at the same minute every day — expecting that would be irrelevant. The purpose of exhaustive per-minute enumeration is what emerges after you apply White’s Reality Check, Hansen’s SPA, or your own filtering criteria across thousands of anchor points.

Researchers can look for session phase clusters — convergence frequencies that concentrate in recognisable intraday regimes:

Opening PhasePost-Open PeriodMidday NullLate SessionClose Phase

Individual minutes are noise. Clusters of adjacent minutes that survive your filters may indicate structure — or may not. The dataset provides the raw material; the interpretation is yours.

Gemina outputs measurements, not recommendations. The interpretation of these measurements is entirely the responsibility of the researcher.

For the complete mathematical framework including formal definitions, see Policies → Gemina™ Mathematical Framework.

WHAT GEMINA IS

A fully explainable, enumerated, non-discretionary dataset
An exhaustive enumerator over a defined parameter space
Raw material for designing your own quantitative models
Supercomputed — each dataset is generated the moment you request it; nothing is cached, nothing is stale, nothing is retained once delivered

WHAT GEMINA IS NOT

Not a trading strategy or advisory service
Not a prediction engine — no forward-looking claims
Not a substitute for independent research or due diligence
Past convergence does not imply future convergence

Try it: filter a Gemina convergence report

Click any column header ▾ to filter — just like a spreadsheet. Filter by strong win rates for convergence signals, or by weak win rates for normalisation baselines. Win rate does not imply performance — it is a frequency measure for quantitative research.

Showing 200 of 1,428 checks (244,800 total for SOL / ETH)

#	Lookback (d) ▾	Anchor (min) ▾	Condition ▾	Win Rate % ▾
1	30d	min 1	T1	66.0%
2	30d	min 1	T2	25.7%
3	30d	min 1	T3	70.6%
4	30d	min 1	T4	46.2%
5	30d	min 1	T5	76.3%
6	30d	min 1	T6	79.8%
7	30d	min 2	T1	65.7%
8	30d	min 2	T2	71.7%
9	30d	min 2	T3	60.8%
10	30d	min 2	T4	58.9%
11	30d	min 2	T5	15.6%
12	30d	min 2	T6	50.4%
13	30d	min 3	T1	56.4%
14	30d	min 3	T2	82.0%
15	30d	min 3	T3	68.8%
16	30d	min 3	T4	69.5%
17	30d	min 3	T5	46.5%
18	30d	min 3	T6	41.5%
19	30d	min 4	T1	34.3%
20	30d	min 4	T2	35.5%
21	30d	min 4	T3	44.0%
22	30d	min 4	T4	37.7%
23	30d	min 4	T5	64.1%
24	30d	min 4	T6	76.8%
25	30d	min 5	T1	80.2%
26	30d	min 5	T2	64.7%
27	30d	min 5	T3	53.6%
28	30d	min 5	T4	48.8%
29	30d	min 5	T5	70.8%
30	30d	min 5	T6	81.1%
31	30d	min 6	T1	34.3%
32	30d	min 6	T2	53.4%
33	30d	min 6	T3	72.8%
34	30d	min 6	T4	44.4%
35	30d	min 6	T5	52.1%
36	30d	min 6	T6	83.9%
37	30d	min 7	T1	62.6%
38	30d	min 7	T2	20.5%
39	30d	min 7	T3	51.2%
40	30d	min 7	T4	48.9%
41	30d	min 7	T5	50.8%
42	30d	min 7	T6	48.1%
43	30d	min 8	T1	34.0%
44	30d	min 8	T2	78.1%
45	30d	min 8	T3	70.7%
46	30d	min 8	T4	61.5%
47	30d	min 8	T5	21.9%
48	30d	min 8	T6	66.9%
• • •rows omitted for example purposes — delivered report contains every minute from 1 to 390
49	30d	min 195	T1	72.2%
50	30d	min 195	T2	16.2%
51	30d	min 195	T3	64.9%
52	30d	min 195	T4	67.2%
53	30d	min 195	T5	58.1%
54	30d	min 195	T6	53.3%
55	30d	min 196	T1	69.9%
56	30d	min 196	T2	19.7%
57	30d	min 196	T3	83.1%
58	30d	min 196	T4	83.5%
59	30d	min 196	T5	36.6%
60	30d	min 196	T6	35.8%
61	30d	min 197	T1	81.2%
62	30d	min 197	T2	59.1%
63	30d	min 197	T3	36.7%
64	30d	min 197	T4	43.9%
65	30d	min 197	T5	73.1%
66	30d	min 197	T6	61.3%
• • •rows omitted for example purposes — delivered report contains every minute from 1 to 390
67	30d	min 388	T1	44.6%
68	30d	min 388	T2	53.7%
69	30d	min 388	T3	82.1%
70	30d	min 388	T4	40.8%
71	30d	min 388	T5	77.9%
72	30d	min 388	T6	36.5%
73	30d	min 389	T1	33.0%
74	30d	min 389	T2	42.7%
75	30d	min 389	T3	32.0%
76	30d	min 389	T4	42.8%
77	30d	min 389	T5	47.2%
78	30d	min 389	T6	39.3%
79	30d	min 390	T1	66.6%
80	30d	min 390	T2	29.6%
81	30d	min 390	T3	57.4%
82	30d	min 390	T4	35.1%
83	30d	min 390	T5	83.1%
84	30d	min 390	T6	76.9%
85	60d	min 1	T1	54.6%
86	60d	min 1	T2	43.5%
87	60d	min 1	T3	59.9%
88	60d	min 1	T4	53.8%
89	60d	min 1	T5	15.5%
90	60d	min 1	T6	79.6%
91	60d	min 2	T1	69.2%
92	60d	min 2	T2	54.6%
93	60d	min 2	T3	33.2%
94	60d	min 2	T4	55.4%
95	60d	min 2	T5	54.0%
96	60d	min 2	T6	74.9%
97	60d	min 3	T1	55.2%
98	60d	min 3	T2	22.7%
99	60d	min 3	T3	83.0%
100	60d	min 3	T4	45.2%
101	60d	min 3	T5	83.4%
102	60d	min 3	T6	85.0%
103	60d	min 4	T1	80.1%
104	60d	min 4	T2	57.6%
105	60d	min 4	T3	23.6%
106	60d	min 4	T4	69.4%
107	60d	min 4	T5	77.7%
108	60d	min 4	T6	57.8%
109	60d	min 5	T1	77.4%
110	60d	min 5	T2	18.1%
111	60d	min 5	T3	82.1%
112	60d	min 5	T4	38.7%
113	60d	min 5	T5	17.5%
114	60d	min 5	T6	11.1%
115	60d	min 6	T1	80.2%
116	60d	min 6	T2	17.5%
117	60d	min 6	T3	43.0%
118	60d	min 6	T4	54.4%
119	60d	min 6	T5	12.8%
120	60d	min 6	T6	44.7%
121	60d	min 7	T1	66.5%
122	60d	min 7	T2	15.7%
123	60d	min 7	T3	10.8%
124	60d	min 7	T4	66.9%
125	60d	min 7	T5	18.2%
126	60d	min 7	T6	66.3%
127	60d	min 8	T1	72.5%
128	60d	min 8	T2	43.2%
129	60d	min 8	T3	21.4%
130	60d	min 8	T4	47.0%
131	60d	min 8	T5	42.8%
132	60d	min 8	T6	51.3%
• • •rows omitted for example purposes — delivered report contains every minute from 1 to 390
133	60d	min 195	T1	66.7%
134	60d	min 195	T2	55.0%
135	60d	min 195	T3	20.1%
136	60d	min 195	T4	74.0%
137	60d	min 195	T5	35.3%
138	60d	min 195	T6	55.1%
139	60d	min 196	T1	73.2%
140	60d	min 196	T2	57.6%
141	60d	min 196	T3	41.7%
142	60d	min 196	T4	69.6%
143	60d	min 196	T5	14.2%
144	60d	min 196	T6	31.0%
145	60d	min 197	T1	55.8%
146	60d	min 197	T2	56.1%
147	60d	min 197	T3	66.8%
148	60d	min 197	T4	30.8%
149	60d	min 197	T5	83.9%
150	60d	min 197	T6	71.3%
• • •rows omitted for example purposes — delivered report contains every minute from 1 to 390
151	60d	min 388	T1	67.1%
152	60d	min 388	T2	61.5%
153	60d	min 388	T3	42.0%
154	60d	min 388	T4	67.9%
155	60d	min 388	T5	17.5%
156	60d	min 388	T6	61.5%
157	60d	min 389	T1	59.5%
158	60d	min 389	T2	44.4%
159	60d	min 389	T3	58.1%
160	60d	min 389	T4	68.6%
161	60d	min 389	T5	82.1%
162	60d	min 389	T6	61.9%
163	60d	min 390	T1	59.7%
164	60d	min 390	T2	56.2%
165	60d	min 390	T3	56.1%
166	60d	min 390	T4	38.6%
167	60d	min 390	T5	48.0%
168	60d	min 390	T6	34.7%
169	90d	min 1	T1	70.6%
170	90d	min 1	T2	75.8%
171	90d	min 1	T3	17.9%
172	90d	min 1	T4	58.4%
173	90d	min 1	T5	62.3%
174	90d	min 1	T6	67.0%
175	90d	min 2	T1	43.7%
176	90d	min 2	T2	73.0%
177	90d	min 2	T3	60.0%
178	90d	min 2	T4	56.9%
179	90d	min 2	T5	63.8%
180	90d	min 2	T6	18.2%
181	90d	min 3	T1	59.2%
182	90d	min 3	T2	81.0%
183	90d	min 3	T3	39.8%
184	90d	min 3	T4	74.5%
185	90d	min 3	T5	41.1%
186	90d	min 3	T6	48.9%
187	90d	min 4	T1	33.0%
188	90d	min 4	T2	16.9%
189	90d	min 4	T3	19.7%
190	90d	min 4	T4	43.8%
191	90d	min 4	T5	43.9%
192	90d	min 4	T6	72.5%
193	90d	min 5	T1	60.4%
194	90d	min 5	T2	30.8%
195	90d	min 5	T3	80.5%
196	90d	min 5	T4	40.2%
197	90d	min 5	T5	31.2%
198	90d	min 5	T6	79.5%
199	90d	min 6	T1	81.2%
200	90d	min 6	T2	35.3%

This is a simplified illustration. A delivered Gemina convergence report contains the complete exhaustive enumeration — every lookback, every anchor minute, every condition — which you can filter, sort, and analyse with any tooling of your choice. Both strong and weak win rates carry research value: strong rates highlight convergence candidates; weak rates serve as normalisation baselines.

Equities—Forex—Crypto—Commodities

Any pair. Any exchange. 1-minute resolution.

LOADRR™

Drop your data. We handle the rest.

ANY FORMAT

CSV, TSV, JSON, Parquet, TXT. No conversion needed.

AUTO-DETECT

Finds your datetime and close columns automatically.

SESSION CLIP

Mismatched sessions aligned bar-for-bar.

DATE ALIGN

Only overlapping trading days kept. Gaps handled.

N-ASSET PAIRS

Load N assets, get every pair. Aligned and ready.

ZERO COPIES

Processed in memory. Nothing stored. Nothing retained.

.csv.tsv.json.parquet.txt

Bloomberg • Refinitiv • Yahoo Finance • Binance • any OHLCV export

SANDBOX

Try Gemina in a browser-based workbench. Upload your data, configure, and run scans directly.

OPEN DOJO

ENTERPRISE

Sovereign compute. Encrypted delivery. Full SLC tiers. Dedicated throughput.

CONTACT SALES

NOTICE: Gemina is a historical data analysis tool. All outputs are derived exclusively from observed market data and describe past statistical relationships. Gemina does not generate predictions, forecasts, trading recommendations, or investment advice. The enumeration of divergence–convergence events is a measurement, not a recommendation. Past convergence frequency does not guarantee, imply, or suggest future occurrence. Users are solely responsible for any interpretation or application of Gemina outputs. Student One Causal Networks Private Limited accepts no liability for decisions made using this data.