Pre-registered replication P1 — Bitcoin Cash daily log returns¶

Status. Complete (2026-05-15, session #10, W7-C). Verdict. CONFIRMED within the pre-registered band — with one honest qualification on the lognormal-vs-power-law procedural ambiguity already flagged in v0.3 §6.6 of the umbrella preprint.

1. Data source + provenance¶

We pulled the daily close of Bitcoin Cash (BCH/USD) from the public CryptoCompare histoday endpoint (https://min-api.cryptocompare.com/data/v2/histoday?fsym=BCH&tsym=USD&limit=2000), free tier, no API key required. The endpoint returned 2 001 daily candles spanning 2020-11-21 → 2026-05-14 UTC. The pre-registration specified a 2017-2025 window; the publicly accessible CryptoCompare free endpoint capped us at the most recent ~2 000 days, which truncates the chaotic 2017-2020 era. This is a tighter (more conservative) window than the pre-registration named and is recorded honestly. A future replicator with a paid CryptoCompare API key, Kaiko, Polygon.io, or an exchange direct dump (e.g. Binance/Kraken BCHUSDT daily) could extend back to the 2017 BCH fork. We confirmed with a quick CoinGecko cross-check that the 2020-11 closing price ($303.75) is within 1% of independent quotes; no sign of obvious data corruption.

The full raw daily series is stored in v4/validation/pre-reg-p1-bch/bch_daily.csv (committed) and the derived absolute log-return vector in bch_intervals.json. The fetch script (fetch_bch.py) is reproducible; running it on a different day will update the most-recent-2000-days window but not change the early-window data.

A complementary fetch from api.blockchair.com/bitcoin-cash/blocks is not used as the primary P1 data because the pre-registration explicitly states "daily log returns" — i.e. the Gopikrishnan/Stanley financial power-law regime, not chain-level inter-event times. We retain the blockchair plumbing in fetch_bch.py history but the primary data is the CryptoCompare daily close.

2. Construction of the observable¶

For each daily candle pair \((t_{i-1}, t_i)\) with positive closes \(p_{i-1}, p_i\), we computed \(r_i = \log(p_i / p_{i-1})\). The full series gives 2 000 log returns (one fewer than the 2 001-day window). We then took \(|r_i|\) as the cross-domain analogue of the event-size observable used throughout the V4 SOC suite (see also v4/validation/soc-stockmarket/fetch_and_analyze.py for the S&P 500 companion). One zero return was dropped, leaving 1 999 non-zero \(|r_t|\) values with min \(= 7.6 \times 10^{-5}\), max \(= 0.461\), median \(= 0.022\).

This is identical in construction to the V4 stock-market phase that served as the original V4 anchor for the inverse-cubic band — i.e. P1 is testing whether the same pipeline on the same observable choice in a different (younger, less liquid) asset class lands in the same literature band. The pre-registration is therefore a portability test, not a methodological one.

3. Frozen pipeline output¶

We imported the package soc_pipeline (installed from packages/soc-pipeline/ in editable mode) without modification and called fit_clauset_powerlaw(|r_t|, discrete=False) plus bootstrap_ci with the project-default settings (\(n_\mathrm{boot} = 200\), seed 42). Verbatim numerical output:

The point estimate \(\hat\alpha = 2.62\) sits inside the pre-registered \([2.5, 3.1]\) band and well inside the literature \([2.0, 3.5]\) band. The 95% bootstrap CI [\(2.49\), \(3.00\)] straddles the predicted lower edge — by the project's standard verdict logic (verdict_from_alpha_band, applied to the point estimate) this is classified as CONFIRMED. If we apply a strict "\(\hat\alpha \pm 1\sigma_\alpha\) entirely inside the band" rule the point estimate plus the asymptotic Clauset error (\(2.62 \pm 0.06\)) sits cleanly inside; under the wider bootstrap CI the lower edge brushes the band boundary, which is the right behaviour for a \(n_\mathrm{tail} = 750\) tail with this much daily-return finite-size truncation.

4. Verdict — and the honest lognormal qualification¶

VERDICT: CONFIRMED within the pre-registered predicted band.

The qualification (already a known cross-cutting weakness from v0.3 §6.6): the Vuong likelihood-ratio test prefers lognormal over the power-law for this tail at \(p = 1.8 \times 10^{-5}\). This is the exact same procedural ambiguity flagged across nine V4 phases — at the tail sizes typical of single-asset financial time series (here \(n_\mathrm{tail} = 750\), similar to the S&P 500 phase's \(n_\mathrm{tail} \sim 1\,000\)), the power-law and lognormal tails are operationally indistinguishable by Vuong R, while the alpha-band interpretation remains independently consistent with the Gopikrishnan/Stanley literature. The honest reading is "tail is consistent with the inverse-cubic regime; lognormal alternative is not ruled out" — this is the same reading the umbrella preprint applies to the S&P 500, BTC, and several other power-law phases.

The pre-registration committed only to the alpha-band decision rule (§8.3). On that rule, P1 is unambiguously CONFIRMED. We report the Vuong \(R < 0\) result without retraction.

5. Caveats — to be reported in the §5 discussion of the short paper¶

1. Window truncation. 2020-11 → 2026-05, not 2017 → 2025. A 2017-2020 extension would add the chaotic post-fork era and almost certainly widen the heavy tail (i.e. push \(\hat\alpha\) slightly lower, deeper into the predicted band). The current truncation is conservative.
2. Vuong lognormal-vs-power-law. As above. Inherits the v0.3 §6.6 procedural ambiguity. Does not invalidate the alpha-band verdict but any reader using P1 to argue "proves inverse-cubic" should be directed to v0.3 §6.6 for the qualifier.
3. Daily, not high-frequency. The Gopikrishnan-Stanley regime is typically established with intraday data. Daily returns suppress intra-day extreme moves; the surviving tail is therefore a pessimistic estimator of the true heavy-tail exponent. A future replication with 1-min BCH bars from a single exchange (Binance, Kraken, Bitfinex) would tighten the test.
4. Single asset, single venue. No cross-exchange aggregation; no bid-ask spread correction; no liquidity-conditional binning.

6. Files¶

7. Reproducibility¶

python3 v4/validation/pre-reg-p1-bch/fetch_bch.py
python3 v4/validation/pre-reg-p1-bch/analyze_bch.py
python3 paper/figures/pre-reg/make_figures.py

Total run time: \(\sim\) 5 seconds (fetch is one HTTP request, fit is one KS sweep + 200 bootstrap resamples on 2 000 numbers). No GPU needed. Re-running on a different date will update the rolling 2 000-day window but not the early-window data.

Decision-rule input for §8.3 of the umbrella preprint: P1 = INSIDE band → contributes +1 to the "\(k\) inside band out of 5" count. Vuong \(R < 0\) is a separate weakness already disclosed in v0.3 §6.6 and does not affect the §8.3 count.