BL-SD-043: Cross-Sectional Reversion, Fragility-Conditioned

Status: RELEASED

Classification: PUBLIC

Revision: 1

Date: 2026-09-08

Venue: Bybit perpetuals Programme: II Verdict: NOT PROVEN Blocking axis: Power Transferability: -

1. Identification

H-X2 is the test that H-X1's own withdrawal required: it is not a new idea sought after a disappointing result, it is the specific correction Rule R-10 mandates before a cross-sectional reversion verdict can be considered valid, plus the funding term the same withdrawal identified as missing.

2. Economic thesis

The mechanism is unchanged from H-X1: forced flow localised to a single symbol drives idiosyncratic moves relative to the complex, and price reverts once that local coercion is exhausted. H-X2's addition is that the intensity of that coercion is not constant. It spikes precisely when the broader market is fragile: margin runs thin across the board, books thin, and the liquidation engine works more accounts at once. In calm markets, a relative move more often carries genuine idiosyncratic information, and information does not revert.

Who is forced to lose. Leveraged holders liquidated in a specific symbol, at the moment the market is least able to absorb it. Why structural. Exchange margin rules and market maker risk limits both tighten simultaneously as volatility expands.

Fragility's role here differs from every prior use of the same variable in this record. Elsewhere it predicts width, not direction, and dies at the monetisation channel every time it is asked to (BL-SD-037, BL-SD-038). Here it is not used as a directional signal at all. It is used to time when someone else's directional signal is least distorted by common drift and most driven by the mechanism this family claims, which is a use consistent with what the variable actually measures.

The author's prior, stated before any conditioned PnL was computed: the result would likely be positive in the research era, because the characterisation map already showed it before any cost-bearing construction was built. What was stated as a risk rather than an expectation: subperiod decay, already seen in the unconditional construction and in an earlier door closure, was the biggest threat to durability, and funding, freshly confirmed as a burden in the withdrawn predecessor, might worsen under conditioning since fragile markets carry more extreme funding.

3. Falsifiable claim

Pre-registered before one conditioned PnL figure was computed:

The H-X1 construction, corrected to include funding accrual and restricted to rebalances where a causal, trailing market-fragility measure exceeds its median, produces a mean net return with a CI95 excluding zero, beating a matched permutation null, while a calm-market control shows no such effect.

Partitioning at the causal trailing median, rather than the top fragility quintile the characterisation map happened to favour, was chosen explicitly because the median is the one partition that required no judgment call after seeing the map, and it is the harder bar to clear.

4. Mathematical specification

Notation per BL-D-011. Base construction identical to BL-SD-042 (H-X1)
section 4: 24h residual signal, quintile ranking, dollar-neutral gross-1
portfolio, 24h non-overlapping rebalance, entry open[t+1], exit
open[t+1+H].
 
Change 1, correction (not a lever):
  PnL_long  += -funding_rate accrued over (ts_entry, ts_exit]
  PnL_short += +funding_rate accrued over the same window
  funding rate taken from the actual settlement series, not an as-of
  hourly fill, which would double-count between settlements
 
Change 2, conditioning (the test R-10 requires):
  frag_market[t] = cross-symbol average of composite_fragility[i,t],
                   each symbol's fragility computed causally
  condition:  trailing_percentile(frag_market, 90 rebalances) > 50
              (causal, not full-sample)
  rule:  rebalance and hold only when the condition is met; otherwise the
         portfolio is flat, zero position, zero cost. A flat rebalance is
         not counted as an observation.
 
signal, ranking, sizing, and cost model otherwise unchanged from BL-SD-042.
cost: 11.0 bps round trip x measured turnover, baseline; 5.5 and 22.0 bps
      sensitivity

Causality holds by construction for the signal, the fragility condition (trailing percentile, exclusive of the current rebalance), and the funding accrual (computed from the settlement series realised within the holding window, not projected). The condition determines only whether a rebalance trades or sits flat; it never alters the direction or weighting of a trade that does occur.

5. Operating envelope

Turnover rises under conditioning (0.949 against 0.853 unconditional) because an on/off portfolio pays to open and close positions from flat each time the fragility gate switches, a cost visible directly in the numbers rather than assumed away.

6. Instrument

The fragility-conditioned test and the decile map, built on the same pinned cross-sectional module as H-X1 (19 tests), extended for funding accrual and the conditioning rule.

7. Results

Every mechanism gate the pre-registration set passes: the calm-market control is negative and significant, which is the strongest form the control could take; the permutation null centres at -9.60 plus or minus 2.50 against an observed +5.00, a separation of 5.83 standard deviations, p_perm = 0.0000; subperiods run +6.93, +5.46, +3.22, three of three positive and decaying far more gently than the unconditional construction's decay; and the liquid half shows an edge stronger than the full universe. The single gate that fails is the one requiring the confidence interval to exclude zero.

Gross separation between fragile and calm regimes is 4.46 times (14.49 against 3.25 basis points), which is the clearest evidence in this dossier that fragility is not a filter that happens to split the sample well. It separates a regime where the mechanism operates from one where it works against the strategy outright.

Cost sensitivity, the row that reduces the entire finding to an executable question:

At the fee level available through a maker-oriented or lower-tier execution channel, the result is significant. At the baseline taker round trip, it is not, and the reason is not a lack of edge but a lack of statistical power at the sample size the research era can supply.

Pre-registered robustness, none surviving FDR: decile partition +5.27, CI [-6.26, +16.21]; short-leg-only versus market +3.98, CI [-1.03, +8.84], t = +1.58, a higher t-statistic than the primary despite a lower point estimate because its standard error is smaller (2.52 against 4.01); 12-hour rebalance -3.95, CI [-7.93, -0.12], negative significant, because turnover cost doubles as fast as the gross that a characterisation map suggested was already fully realised within 12 hours. That last result is recorded explicitly as a discipline example: the characterisation map suggested doubling PnL by rebalancing twice as often, and the pre-registered exact test rejected it outright.

Statistical power: standard error is 4.01 basis points on n = 569. Reaching t = 1.65 requires approximately 1,157 fragile rebalances, roughly 7.1 years of research-era-equivalent data; reaching t = 2.00 requires roughly 1,700, about 10.5 years. Held-out B would add only about 160 observations, moving t from 1.25 to approximately 1.42, not enough to settle the question.

8. Verdict, blocking axis, and transferability

Verdict: NOT PROVEN. Axis: power. Transferability: not applicable.

The pre-registered kill criterion (CI95 contains zero) is technically met by the letter of the original pre-registration, but Rule R-9 governs exactly this situation and its own author applies it here against the outcome that would otherwise have been convenient to accept: a death verdict requires power, meaning a confidence interval narrow enough to exclude an edge large enough to matter. The upper bound of this interval is +12.67 basis points, larger than the entire round-trip cost this operator pays. An edge that size cannot be excluded, and the minimum detectable effect at 80 percent power is 11.2 basis points; this instrument can only kill an edge larger than that. Declaring FALSIFIED here would repeat, in the opposite direction, the exact error Rule R-9 exists to prevent.

The comparison that establishes this classification is principled rather than opportunistic, and is stated as such: BL-SD-039's capped-notional result carried an upper CI bound of +2.45 basis points against a 22 basis point cost, a best case that remains useless regardless of where the true value sits, and that dossier's CLOSED verdict stands. Here the best case consistent with the data is a genuinely good strategy. The same rule applied in both directions produces different labels because the evidence is different, not because the label was chosen to fit a preferred outcome.

No transferability classification applies to a NOT PROVEN verdict, since an unresolved hypothesis has nothing yet to transfer.

9. Cost and capacity analysis

Gross, primary (fragile)          +14.49 bps per traded rebalance
Cost, measured turnover 0.949      -9.49 bps
Net                                +5.00 bps, CI [-3.05, +12.67]
Net at 5.5 bps cost                +9.74 bps, CI [+1.70, +17.40], significant
Standard error                      4.01 bps, n = 569
Minimum detectable effect, 80pct    11.2 bps

The capacity gate passes directionally: net on the liquid half (+5.66) is higher than on the full universe (+5.00), which rules out the common failure mode of an edge concentrated in untradeable names.

10. Envelope sensitivity and reopening conditions

Binding parameter: statistical power, not cost or capital in the usual sense, though cost determines what power would need to achieve.

At 11.0 bps (baseline)   : net +5.00, CI spans zero, upper bound +12.67
At 5.5 bps               : net +9.74, CI excludes zero
Reversal condition        : execution at or below approximately 5.5 to 7.5
                             bps round trip removes the need for additional
                             power, since the point estimate itself clears
                             cost with room; short of that, roughly 1,157
                             to 1,700 fragile rebalances are needed at the
                             current cost to resolve significance, which
                             exceeds the entire research era at the
                             realised trade rate

The path to resolution runs through execution cost rather than through more data on this substrate. Opening the sealed held-out era was considered and explicitly rejected as a way to gain power: it would add only approximately 160 observations, moving t from 1.25 to approximately 1.42, not enough to change the classification, while spending the programme's one-shot verification asset on a result already predictable to remain inconclusive.

What would reopen it: a measured, realistic execution cost at or below roughly 7.5 basis points, verified against adverse selection on the liquid half of this specific universe rather than the wide-spread names a separate door's adverse-selection measurement covered, or a variance-reduction construction of the kind the short-leg-only robustness variant hints at (higher t from a smaller standard error rather than a larger point estimate), pursued deliberately rather than reported as an incidental sensitivity.

What would not reopen it: firing the sealed held-out era at the current sample size, and rebalancing more frequently, both tested directly and both shown to fail or to be uninformative.

11. Reference implementation

The conditioning layer is published as 05_INSTRUMENTS/strategies/python/src/fragility_conditioning.py, with 37 tests, and the portfolio arithmetic beneath it as 05_INSTRUMENTS/src/cross_sectional.py, shared with BL-SD-042 and unmodified. The decile map and the test driver that orchestrate them remain scheduled.

Two properties of the published gate decide whether this hypothesis was tested honestly, and both are pinned rather than asserted.

The gate reads a trailing percentile, not a full-sample median. A full-sample median would put look-ahead directly into the decision path: the question is whether to trade at this rebalance, and that has to be answerable from what has already printed. One test changes a late bar and confirms no earlier percentile moves.

The threshold is 50, and it is 50 because that is the median. It was fixed before the decile map was drawn, not chosen as a quintile after looking at one. BL-D-003 is the article on why that ordering is what makes a conditioning variable pre-registered rather than discovered.

The percentile itself is a midrank rather than a plain empirical distribution function, and that choice is the most consequential detail in the layer. It was found before a single forward return had been computed, which is why it is a design note here instead of an incident. Perpetual funding is clamped to a one-basis-point baseline whenever the premium index sits inside the interest-rate band, and between 43 and 68 percent of bars on our panel sit at exactly that value depending on the symbol. Under a plain distribution function the modal value scores near zero despite being the median, and a threshold written as "at or below 10" was measured capturing 24 percent of the sample. The threshold had stopped meaning what it was written to mean, which is an instrument failure rather than a hypothesis failure. The published test suite reproduces that substrate condition and pins the fixed definition against it.

12. Evidence register

13. Lessons extracted

This is the first hypothesis in the archive to pass every mechanism gate the programme knows how to write, calm-market control, permutation null, subperiod consistency, capacity, and fail only on statistical power. It is recorded as the clean, principled application of Rule R-9 rather than as a near-miss to be regretted: the instrument does not have enough resolution to certify a genuinely good outcome, and saying so honestly is worth more than rounding either up to PASS or down to FALSIFIED.

The variance-reduction finding in the short-leg-only robustness (higher t from a smaller standard error, at a lower point estimate) is flagged as an unexplored lever distinct from every other lever this programme pulled, which sought a larger edge rather than a tighter one, and is carried forward as an open direction rather than a closed one.

14. Cross-references

BL-SD-042 for the withdrawn predecessor this hypothesis corrects. BL-SD-039 for the contrasting, principled application of Rule R-9 in the other direction. BL-D-002 on power versus falsification. BL-SD-000 ledger row H-X2 and section 6's discussion of what remains open.

Copyright (c) 2026 Bijective Labs. All rights reserved.