Watching 24 calendar-rule hypotheses daily for an unadjusted p below 0.05 produces a winner in 94.5% of simulated worlds with no edge. Benhamou, Ohana, Guez, Setrouk, Saadi and Jacquot reduce that count to 0 of 3,000 paths with their promotion gate (upper bound 0.128%). Detection takes years, though, even with a 14.4% annualized edge injected into returns. I think the gate gives a research process sound accounting. It yielded nothing deployable, and the authors largely acknowledge that.
What PROMOTE keeps on the ledger
The paper sets a rule for when a trading idea earns promotion. A candidate is an executable package whose asset, direction, rebalance convention and cost model are frozen. At registration, called its birth, the authors fingerprint the package with SHA-256. Altering any field creates a new candidate.
Testing starts the next session. The rule's return after a predictable cost is divided by a predictable scale, then clipped to [-1, 1]. The null says that this clipped score has a conditional mean at most zero on every post-birth date. Each session multiplies test wealth by (1 + λY). Evidence comes from an equal-weight average of five e-processes, using constant bets of 0.025, 0.05, 0.10, 0.20 and 0.35. Relative to the best bet on that path, averaging costs at most log 5 of log evidence. The product under the null is a nonnegative supermartingale. Ville's inequality therefore limits the probability of ever reaching 1/u to u, regardless of how long the researcher watches.
PROMOTE adds a spending constraint to that test. At birth, each candidate receives testing mass π from a lifetime budget of one. Promotion occurs when evidence first crosses 1/(απ). The union bound caps the probability of ever promoting any null rule at α.
Abandoning an idea returns nothing to the budget.
A restart or tweak requires a new candidate and fresh funding. Trading starts the session after a crossing. For 24 equally funded candidates at α = 0.05, the boundary is 480 for each.
The authors test eight calendar rules: turn of month, first three days, last three days, Monday, Friday, quarter end, January and third Friday. The three panels contain six equity ETFs, five defensive ETFs and the ten Fama-French value-weighted industries. Daily data run from March 2006 to May 2026. They fix direction, activation frequency and scale using 2006 to 2010, then use 2011 to 2014 for diagnostics. Testing covers January 2015 to May 2026, a total of 2,868 sessions. Costs are 5 bp per dollar of one-way turnover.
Our run covered only the two ETF panels, or 16 rule-panel hypotheses. We excluded the ten Fama-French industries because we cannot trade them. Reducing the family lowers the boundary. Our run thus exercises the same promotion gate on a subset of the paper's instruments; it does not replicate the 24-hypothesis experiment.
How much does the 94.5% versus 0.0% comparison tell us?
Much of that contrast comes from a strawman, as the authors acknowledge. They describe the repeated z test as "intentionally common rather than defensible." On zero-shift paths, that same naive test declares the target in 23.2% of cases. The authors also explain that freezing positive costs makes their shared-sign null strict. Some of the 0.0% result (Wilson upper bound 0.128%) therefore comes from slack.
The more useful comparison is an e-process with a per-stream anytime boundary of 20 and no wealth split. Across the fixed family, its 0.7% rate looks nearly safe: 21 crossings. The separate adaptive audit gives a different picture.
In that audit, an agent watches 32 iid Rademacher streams over 768 sessions. It registers whichever stream has the largest trailing-64 sum when that sum reaches 20, allowing up to 12 births. All post-birth scores have mean exactly zero. Across 3,000 programs, the unfunded boundary crosses in 18.40%. Funded PROMOTE crosses in 1.77% [1.35, 2.30]; repeated p tests reach 93.07%.
The distinction is clear. Any e-process handles optional stopping on its own. Adaptive selection adds multiplicity, which requires the budget. How the budget is spent also affects results at the margin. On the same 3,000 adaptive null programs, allocating half the remaining wealth at each birth yields 2.37%. Equal 12-slot reserves yield 1.17% and consume an average 82.36% of the budget. The authors call these differences "a design trade-off rather than a ranking theorem," so the comparison of 2.37% with 1.17% establishes no ranking.
A 14.4% edge waits nine years
For the power experiment, the authors add a fixed shift to every equity ETF return each session, following the direction of the equity turn-of-month rule. A constant shift in every session is about as easy an alternative as one could choose. The paper warns that weak or intermittent effects often never reach the boundary.
Power is 0.00% at 5 bp, equivalent to 4.8% annualized target gross alpha. It rises to 7.73% at 10 bp. With 15 bp, or 14.4% annualized, PROMOTE detects 70.1% of paths. Among those that cross, the median crossing arrives at session 2,327 of 2,868, roughly nine years into the test. That median excludes paths that never cross. At 20 bp, power reaches 99.27%, and the median is 1,743 sessions. Even a 30 bp shift, 28.8% annualized, takes a median 1,049.
The authors acknowledge the wait. Their conclusion says a valid gate "may wait for weak effects" and describes the delay as "the cost of an optional-stopping guarantee." It is a substantial price. Reaching 70% power within the 2,868-session test takes an injected gross annualized edge of 14.4%. Even then, the detected paths need a median nine years.
Continuous monitoring adds little power. A matched terminal rule checks only at session 2,868, using the same boundary. At 15 bp its power is 67.1% [64.7, 69.5], compared with 70.1% [67.7, 72.3] for PROMOTE. The authors note the overlapping intervals. Earlier decisions are the real benefit: at 20 bp, the median anytime crossing precedes the terminal decision by 1,125 sessions.
Eleven years of market data, no promotions
None of the 24 candidates earns promotion in the market replay. The highest e-value reached by any rule is 1.93, far short of 480. Of the 24 shadow paths, only two have positive means. The larger is 0.087% annualized. Taken together, the sleeves return -1.341% a year with a Sharpe of -0.85 and finish at 0.858 after costs.
The naive gate promotes one candidate: the reversed industry January rule, on 13 January 2016. Over its 2015 to 2026 path, that rule loses 0.90% a year, with Sharpe -0.18. The 1/24 sleeve ends at 0.992 after costs. Industry sleeves cannot be traded directly. The paper also cautions that these figures "do not prove that the crossing was a statistical false positive."
The authors describe the result as "a weak library after the retrospective split, not evidence that the gate suppresses profitable rules," and acknowledge designing both the split and the library in hindsight. I agree with both readings. We still never see PROMOTE approve a real rule.
Their disclaimer sets the terms for what follows: "The certificate controls historical false promotion under the declared null; it is not a certificate that an earlier edge remains profitable at deployment." They propose funded revalidation. Each epoch e receives mass ω_h q_e, for example q_e = 6/[π²(e+1)²]. Later renewals therefore face quadratically higher boundaries and rely exclusively on post-restart data. Stale certificates become expensive. This cannot shorten the nine-year median required by a 14.4% edge.
I would classify PROMOTE as a governance tool.
The injected-edge experiments already demonstrate that it can pass a known effect: power is 99.27% at 20 bp and 100% at 30 bp. The authors acknowledge what remains untested. A fixed market replay cannot demonstrate adaptive births; those are tested only with iid Rademacher scores. An adaptive library tested on market data, with a rule that crosses the boundary, would change my view of its usefulness as a deployment gate.