Published statistic numerical reproduction
Can an independent deterministic pipeline reconstruct public raw evidence and reproduce somebody else's published number? For Kitron & Wengrowicz's BTCUSDT 15-minute kernel sign correlation, Strategy Lab reproduced the frozen oracle within 5 binary64 ULP, inside the predeclared tolerance.
Reading the result
The headline metrics answer different questions. These short definitions are the interpretation used on this page, not additional evaluation criteria.
The correlation between the current bar sign and a strictly lagged field built from the previous 12 signs, weighted by inverse lag with alpha fixed at 1. Negative values describe sign-level reversal association; this reproduction tests the published number, not a trading return.
A unit in the last place is the spacing between adjacent binary64 floating-point values at a given magnitude. The Strategy Lab result and frozen oracle differ by five such representable steps.
The predeclared absolute tolerance applies only when comparing Strategy Lab's exact deterministic result with the external published oracle, whose final bits were shown not to be portable across mathematically equivalent binary64 reduction paths.
Strategy Lab independently reconstructed the authors’ BTCUSDT 15-minute sample from public Binance evidence and reproduced the published model-free kernel sign-correlation statistic within the predeclared numerical tolerance.
The deterministic result was:
R_kernel = -0.05187475902840218
The frozen authors’ oracle was:
-0.05187475902840215
The absolute difference was 3.469446951953614e-17, equal to 5 binary64 ULP and smaller than the frozen absolute tolerance 0x1p-53 (1.1102230246251565e-16). The external conformance check therefore passed.
That is the result. It is deliberately narrower than a strategy backtest.
Nadav A. Kitron and Jonathan M. Wengrowicz study short-horizon directional dependence in Short-horizon mean reversion in cryptocurrency markets: a matched cross-market measurement. Their public reference repository includes a model-free statistic intended to measure sign-level reversal across multiple short lags.
For the fixed BTC sample, the pinned repository revision
5eb5117d353abe0569f2d98aeadddf634e044e1f
publishes R_kernel = -0.05187475902840215.
The Strategy Lab question was not whether the whole paper could be reproduced. It was much smaller:
Can we independently reconstruct the fixed BTCUSDT 15-minute sample from official public Binance archives and reproduce that one published statistic?
The Strategy Lab research classification was ORIGINAL_RESULT_REPRODUCTION.
No trading positions were opened. There is no execution model, transaction-cost model, P&L series, Sharpe ratio, or profitability criterion in this reproduction.
The object being reproduced is a statistic on a sequence of 15-minute bar signs.
That distinction also matches the source paper’s own separation between statistical reversal and economic profitability. The paper discusses whether a directional effect could clear trading costs separately from the existence of the statistical pattern. This Strategy Lab run does not reproduce or extend that profitability analysis.
A numerical pass here therefore means the fixed external number was reproduced within its predeclared numerical contract. It does not mean a tradable strategy passed.
For each 15-minute bar, the sign is defined from its open and close:
+1 when close > open-1 when close < open0 when close = openThe source statistic then correlates the current sign with a strictly lagged field built from the previous 12 signs:
R_kernel = corr(σ_t, Σ[k=1..12] σ_(t-k) / k^α)
with 12 lags and α fixed at 1.
The negative BTC value describes a negative association between the current sign and that inverse-lag-weighted recent sign history. Strategy Lab’s task was to reproduce the published number, not to infer a new economic effect from it.
The admitted evidence came from official Binance Public Data Spot kline archives.
| Field | Frozen reproduction |
|---|---|
| Market | Binance Spot |
| Symbol | BTCUSDT |
| Interval | 15 minutes |
| First bar open | 2025-01-01 00:00:00 UTC |
| Terminal bar open | 2026-02-11 00:00:00 UTC |
| Observations | 38,977 |
| Flat bars | 12 |
| Retained provider archives | 24 |
| Canonical bars SHA-256 | f57cf3cc4a110ece0e6c735209f0a74af7d12de21b27df605e7fb4d1729f4f44 |
The capture used monthly Binance Public Data archives plus daily archives for the trailing partial month. The public article does not republish those market-data files; the canonical hash identifies the normalized evidence used by the completed run.
| Quantity | Value |
|---|---|
| Frozen authors’ oracle | -0.05187475902840215 |
| Strategy Lab | -0.05187475902840218 |
| Absolute error | 3.469446951953614e-17 |
| Difference | 5 ULP |
| Predeclared absolute tolerance | 0x1p-53 = 1.1102230246251565e-16 |
| Oracle conformance | PASS |
The two decimal strings are not bit-identical. They were not required to be.
The frozen comparison rule anticipated the narrow floating-point portability issue described below. Strategy Lab preserved its own deterministic result exactly and compared that result to the external oracle under the predeclared tolerance.
Before the Strategy Lab implementation, the external calculation was reproduced separately. The authors’ current implementation and an independent implementation both reported:
-0.0518747590284022
A diagnostic on the same operands then compared mathematically equivalent binary64 reduction paths:
| Reduction path | Result |
|---|---|
| Authors’ matrix-multiplication path | -0.0518747590284022 |
| NumPy sum path | -0.05187475902840217 |
High-accuracy math.fsum path | -0.05187475902840218 |
Those differences are only a few ULP. Floating-point addition is not associative, so different reduction order and numerical backends can legitimately produce different final bits even when they implement the same mathematical expression.
That is why the external oracle comparison used a narrowly predeclared absolute tolerance.
It does not mean Strategy Lab uses approximate equality for its own result integrity. The completed run, evidence identities, artifact hashes, and offline re-entry remain exact. Only the comparison to the externally produced oracle allows the demonstrated binary64 portability envelope.
The final-bit difference is therefore not scientific disagreement.
The external numerical reproduction passed because the absolute error was below the frozen tolerance and oracle_conformance_ok is true.
Changed-evaluator replay was NOT_APPLICABLE_REDUNDANT, not a replay failure. The current numerical implementation identity was the same as the source run’s implementation identity, so running the identical evaluator again would not test a changed implementation.
Terminal offline re-entry did succeed without provider or network access, without invoking the evaluator, and without rewriting the completed artifacts. The publication handoff was produced after completed-run verification and did not recalculate the research.
The numerical implementation identity recorded in the handoff is:
c72e540b21e7e1faac2160f67342456e7a4264a63edca566976362fd6caaaa3e
This reproduction supports one narrow statement:
Strategy Lab independently reconstructed the authors’ BTCUSDT 15-minute sample from public Binance evidence and reproduced the published model-free kernel sign-correlation statistic within the predeclared numerical tolerance.
It does not establish:
That scope is a feature of the result, not a weakness. A numerical reproduction is most useful when it says exactly what matched and stops there.
The Strategy Lab research identity is:
48928be708ccd4517eb9b53f149521c38e4d0a7c40f73a025ff378248556a476
The frozen source-material SHA-256 is:
50385a1f9d6f2490d747f7d7ed17064fba3928e418406d2e9d64430b44909e75
The canonical normalized-bars SHA-256 is:
f57cf3cc4a110ece0e6c735209f0a74af7d12de21b27df605e7fb4d1729f4f44
The public reference repository at the pinned commit preserves the external source used for the oracle. The selected public Strategy Lab handoff below preserves the completed reproduction’s exact numerical result and identities without republishing raw provider data or private runner material.
Predeclared conformance rule
The comparison used the exact Strategy Lab result and frozen oracle. Headline cards may use compact display values; exact values below and in the evidence are unchanged.
Inspect the evidence
The public handoff below is a byte-identical copy of the authoritative Strategy Lab publication handoff supplied for this article. It contains the research identity, exact statistic, oracle, tolerance, dataset identity, implementation identity, and preserved result-artifact hash. Raw Binance archives, normalized bars, binaries, and private runner material are not republished.
These excerpts support inspection of the reported work; they are not a complete package for independently rerunning the experiment. Read the evidence policy.