Thursday close above the weekly open: a pre-registered six-asset test

Summary

Over 1,892 complete Monday-to-Sunday weeks on six Binance markets, a Thursday close strictly above the Monday open was followed by a weekly close strictly above that open in 82.6% of the 936 event weeks (773 of 936). All six assets clear the pre-registered one-sided exact binomial test at the Bonferroni-adjusted threshold; the pooled all-week unconditional rate over the same 1,892 weeks is 49.6%.

The verdict below is the mechanically correct application of the pre-registered decision rule in CHARTER.md §9, as re-derived independently in VALIDATION.md. It is a statement about a conditional frequency under stated definitions, not about a tradable edge, and this note does not upgrade it to one.

Key figures

The claim and definitions

Claim under test. Per asset, does a Thursday close strictly above the week's Monday open imply that the week closes strictly above that open more often than chance? The pre-registration fixes every parameter before the run: no tuning, no weekday scan, one six-asset Bonferroni family.

Definitions (all times UTC, Binance 1d bars). Week = Monday 00:00:00.000Z → Sunday 23:59:59.999Z. WO = Monday bar open, TC = Thursday bar close, WC = Sunday bar close. Condition TC > WO (strict); outcome WC > WO (strict). Only weeks with the Monday, Thursday and Sunday bars present are used. The incomplete week (any week with Monday ≥ 2026-09-14) is excluded by construction, so the last outcome bar is Sunday 2026-09-13 for every asset.

Decision rule (charter §9). SUPPORT requires 6/6 per-asset passes at Bonferroni α/6 ≈ 0.00833 with ≥ 30 event weeks, out-of-sample direction consistent, and a pooled net-20-bps mean above zero with t ≥ 2. The verdict returned by the analysis is SUPPORT, with the conditioning caveat above carried into the reading.

Source: analysis/results.json (data.*, panel.*); data/DATA.md. 13,304 daily bars parsed; the only drops are the leading partial listing week of each asset, so every asset clears the 2% drop gate (worst: HYPE 1.47%). Each archive is verified against its sibling .CHECKSUM (SHA-256); no checksum mismatch, no 404, no interior gap and no duplicate day is recorded for any of the six symbols.

Per-asset primary results

One-sided exact binomial on event weeks, H0: p ≤ 0.5, against the six-test Bonferroni threshold α/6 = 0.00833. Verdicts are per the pre-registered rule; the smallest sample is HYPE at 32 event weeks, which clears the 30-week minimum gate as written.

Source: analysis/results.json (primary.*.full, pooled.full.primary). The pooled row is descriptive only and never substitutes for a per-asset verdict (charter §4).

In-sample and out-of-sample

IS = Sunday bar on or before 2022-12-31; OOS = Sunday bar on or after 2023-01-01. TAO and HYPE list after the split and are OOS-only by construction; IS and OOS rows are never pooled silently.

Source: analysis/results.json (primary.*.is / primary.*.oos). OOS direction is consistent on all six assets (p̂ > 0.5 throughout), which is one of the three SUPPORT conditions.

Conditional vs unconditional

The unconditional rate is P(WC > WO) over all complete weeks of the asset. Every asset shows a positive lift over its own unconditional rate, tested with a one-sided two-proportion z (pooled variance). The pre-registered Fisher trigger (any expected cell below 5) never fires here: the smallest expected cell in the family is 15.76 for HYPEUSDT, so the z-test is used throughout, as the rule is written.

Source: analysis/results.json (lift.*, pooled.full). Because the conditional set is a subset of the all-week set the two proportions are dependent, which makes the pooled-variance z mildly conservative; the direction of every conclusion is unaffected. The formal z-statistic contrasts conditional against non-event weeks; the printed lift column uses the all-week rate — the two signs agree by construction.

Observed conditional, unconditional, and the random-walk baseline, by asset

Source: analysis/results.json (primary.*.full.phat, primary.*.unconditional.full.phat, post_hoc.random_walk_benchmark.*.implied_conditional_rate). The baseline marker is the post-hoc driftless reference discussed in "The conditioning caveat" below; it is not part of the pre-registered test and carries no inference.

The simple long backtest (gross / 10 / 20 / 40 bps)

The backtest leg is an accounting of the same event weeks under stated cost assumptions: long at the Thursday bar close whenever TC > WO, exit at the Sunday bar close, 1× unlevered, r = WC/TC − 1, all figures USDT-denominated. Costs are 0 (gross), 10 (one maker side / fee discount), 20 (retail spot taker both sides) bps round trip. The 40-bps column is a 2× slippage stress run labelled exploratory/post-hoc; it is not part of the pre-registered table.

Source: analysis/results.json (backtest.POOLED.full.scenarios). Pooled rows weight each event week equally, not each unit of capital. The 40-bps scenario survives double the retail-cost assumption; it changes no part of the reading above.

Per asset, net 20 bps

Source: analysis/results.json (backtest.*.full.scenarios[20], scenarios[40]). Only ETH (t = 2.088) and SOL (t = 3.118) individually clear t ≥ 2 at the 20-bps cost scenario; the pooled SUPPORT economics leg is met, per-asset economics are not established and must not be read as such.

Pooled net-20-bps mean per event week, by Sunday-bar year

Source: analysis/results.json (regimes.by_year_pooled[*].backtest_net20bps). Same event weeks as the tables above, sliced by Sunday-bar year; the conditional rate stays above 0.5 in every year while the cost-adjusted mean does not.

Source: analysis/results.json (regimes.by_year_pooled). 2022 is negative and 2025 is flat: the conditional rate is stable through time, the cost-adjusted expectancy is not.

Robustness

R1–R4 are pre-registered diagnostics and carry no inference; the primary verdict stands on the base specification. R2 reproduces the primary panel exactly, because no week has TC exactly equal to WO on any asset.

Source: analysis/results.json (robustness.R1–R4, robustness.pooled). R3's removed weeks map to BTC/ETH/XRP 104 each, SOL 71, TAO and HYPE none. Full per-asset R1/R3 rows and the complete R4 grid are in analysis/RESULTS.md §5.

The conditioning caveat (random-walk benchmark)

This subsection is post-hoc and not pre-registered; it is the binding caveat on how the verdict may be read. The pre-registered null (p ≤ 0.5) is not the only reference point available for this design: conditioning on a positive Monday-open→Thursday-close move mechanically raises the probability that the week closes above its open. For independent zero-mean legs with standard deviations s₁ and s₂, P(WC > WO | TC > WO) = 0.5 + atan(s₁/s₂)/π — already 0.75 when the legs have equal volatility. Feeding in each asset's empirical leg volatilities gives the reference below.

Source: analysis/results.json (post_hoc.random_walk_benchmark). The pooled observed rate sits 3.5 points above the driftless baseline; adding the observed positive drift in both legs raises the pooled mechanical baseline to ≈0.82 (post-hoc extension recorded in VALIDATION.md), leaving an excess of ≈0.6 point against a binomial standard error of ≈1.2 points at n = 936 — within sampling noise.

The practical consequence is stated plainly and without softening: most of the distance between 0.5 and the observed ≈0.83 is a mechanical property of conditioning on a positive move, not a discovered late-week effect. Nothing in the pre-registered panel is changed by this diagnostic, and no inferential claim is drawn from it.

Caveats and residual risk