BL-SD-042: Cross-Sectional Residual Reversion

Status: SUPERSEDED

Classification: PUBLIC

Revision: 1

Date: 2026-09-08

Venue: Bybit perpetuals Programme: II Verdict: WITHDRAWN Axis of death: Procedure Transferability: -

1. Identification

This dossier records a withdrawal, not a settled verdict. The original measurement is preserved in full below because the number itself was not wrong and the instrument that produced it passed its own sanity check. What is withdrawn is the verdict drawn from it, on two procedural grounds disclosed by the author against their own prior conclusion.

2. Economic thesis

When a perpetual moves sharply relative to the crypto complex, rather than relative to itself, most of that idiosyncratic move is driven by forced flow localised to that symbol: liquidation of leverage holders in that name, and a market maker pulling quotes because inventory risk has spiked in that name specifically. The party pushing price has no choice, and price reverts relative to the complex once the local coercion is exhausted. Movement shared across the whole complex carries macro information and does not revert.

Who is forced to lose. Leveraged holders liquidated in a specific symbol, and anyone who must execute while that symbol's book depth is thin. Why structural. The coercion is written into exchange margin rules and market maker risk limits, both of which tighten independently of any single participant's preference.

This construction differs from the family's prior directional attempts (BL-SD-039 through BL-SD-041) in one deliberate respect: it removes the common cross-symbol component by dollar-neutral construction rather than measuring an absolute, per-symbol move. That removal is the entire structural lever this hypothesis exists to test, and it is the lever whose correct measurement the withdrawal in section 8 turns on.

3. Falsifiable claim

Pre-registered before one cross-sectional PnL figure was computed:

A dollar-neutral portfolio, long the lowest quintile and short the highest quintile of 24-hour cross-sectional residual return, rebalanced daily, produces a mean net return whose CI95 excludes zero, beats a within-timestamp rank-permutation null at p below 0.05, and holds on the liquid half of the universe.

As drafted and as executed, this claim was tested unconditionally, which section 8 identifies as one of two procedural defects in how the resulting verdict was drawn.

4. Mathematical specification

Notation per BL-D-011. All rolling statistics causal, trailing, exclusive
of bar t.
 
signal:  resid_L[i,t] = log_change(close_i, L) - mean_cross_symbol(
                          log_change(close, L), t)
         L = 24h
 
ranking: per timestamp, across all symbols with a valid signal
entry:   LONG the lowest-residual quintile, SHORT the highest-residual
         quintile, equal-weight within each leg, dollar-neutral, gross
         notional = 1 unit of capital
         return = 0.5 * mean(LONG leg return) - 0.5 * mean(SHORT leg return)
rebalance: every H hours, non-overlapping
horizon H: 24h primary, 72h reported as robustness only
execution: open[t+1] entry, open[t+1+H] exit
minimum bar condition: at least 20 symbols with a valid signal, else skip
 
cost:    11.0 bps round trip x measured turnover per rebalance (baseline)
         AS ACTUALLY MEASURED: price return only. Funding accrual over the
         24-hour holding period, which crosses three 8-hour settlements,
         was not included in the reported PnL. This omission is the first
         of two defects identified in section 8 and is stated here rather
         than silently corrected, because the original specification and
         the original result must remain legible together.
 
sizing:  none required. A dollar-neutral, gross-1 portfolio is fully
         specified by construction; there is no equal_weight versus
         equal_notional ambiguity of the kind found in BL-SD-039, because
         no per-timestamp collapse across a variable number of signals is
         needed here.

Causality holds by construction for the signal, the ranking, and the turnover-weighted cost. The specification omits a term that should have been present under the programme's own accounting standard for a perpetual position: funding is a real cash flow on any position held across a settlement boundary, and the mechanism memo (section 2) predicted no funding effect one way or the other, so its omission was not a deliberate simplification stated in advance. It is recorded here as a specification gap rather than reconstructed as though it had been anticipated.

5. Operating envelope

6. Instrument

The cross-sectional reversion test and the cross-sectional primitive (19 pinned tests) computed the demeaning, quintile assignment, dollar-neutral return, and turnover convention. The instrument's own sanity check is worth recording independent of the withdrawal: a within-timestamp rank-permutation null returned -8.87 basis points against a theoretical prediction of -(turnover x cost) = -8.53, confirming the instrument does not manufacture edge from its own construction.

7. Results (as originally reported, price return only)

Null-adjusted significance: observed net of +1.66 against a permutation null of -8.87 plus or minus 1.56, a separation of 6.75 standard deviations, p_perm = 0.0000. The mechanism, in the narrow sense of beating a rank-randomised null, is confirmed more decisively here than in any other entry in this family.

Cost sensitivity: at 5.5 bps round trip, net +5.9, CI [+1.1, +10.8], positive and significant; at 22.0 bps, net -6.9, CI [-11.7, -2.1], negative and significant. Subperiods: +4.4, +1.1, -0.5, decaying monotonically.

These figures, exactly as measured, are the ones the original document used to conclude CLOSED on cost, axis turnover: a real, 6.75-sigma mechanism consuming 84 percent of its gross edge to transaction cost. Section 8 explains why that conclusion, however arithmetically correct on its own terms, cannot stand as issued.

8. Verdict, axis of death, and transferability

Verdict: WITHDRAWN. Axis: procedure. Transferability: not applicable.

Two defects, both disclosed by the author against the interest of the conclusion already reached, void the original verdict rather than merely qualify it.

Defect one: the PnL omitted funding. A position held 24 hours on a perpetual crosses three 8-hour settlements, and funding is a real cash flow, not a modelling nicety. Recomputing the identical construction with funding accrued from the actual settlement series rather than assumed away moves the unconditional net return from +1.66 basis points to +0.17 basis points, and the direction of the correction is adverse: the top decile, symbols rising sharply, carries funding around -4.5 basis points, meaning shorts pay longs there, and this construction is short exactly those names. The mechanism memo did not anticipate this cost in either direction, so its absence was an omission, not a stated simplification.

Defect two: the verdict was drawn from unconditional statistics alone. Rule R-10, written earlier in this same programme after an identical gap closed a branch of BL-SD-039 prematurely, states plainly that a dead verdict is not valid on unconditional statistics alone when a conditioned variant implied by the mechanism has not been tested. The mechanism memo in section 2 explicitly names market fragility as the variable that should modulate the intensity of forced, localised flow. That conditioned test was never run before H-X1's verdict was issued. Closing this branch without running it repeats the exact procedural violation R-10 exists to prevent, on the rule's own author's part.

Neither defect changes the arithmetic in section 7, which stands as correctly computed. Both defects invalidate the inference drawn from that arithmetic: a verdict is not merely a number, it is a number combined with a complete and rule-compliant procedure for interpreting it, and this one was neither complete (missing funding) nor rule-compliant (missing the mandated conditioning test). No transferability classification is assigned because no verdict stands to classify.

9. Cost and capacity analysis

Gross, primary                +10.19 bps per rebalance
Turnover, measured             0.776
Cost, price-only                -8.53 bps
Net, price-only                 +1.66 bps
Net, with funding accrued       +0.17 bps

The capacity gate passed in the original measurement (edge stronger on the liquid half than the full universe) and is not reopened by the withdrawal; it is reported here as a fact about the substrate that survives regardless of what happens to the funding-corrected, conditioned successor test.

10. Envelope sensitivity and reopening conditions

No binding parameter is named here, because this dossier does not carry a settled verdict to attach one to.

Reversal condition: not applicable to a withdrawn verdict.

The question this hypothesis asked, whether cross-sectional dollar-neutral construction lifts a real reversion signal above transaction cost, remains open. It is answered, under the procedurally corrected specification, in BL-SD-043.

What reopened this branch: funding accrual added to the PnL model, and the fragility conditioning Rule R-10 required. Both are executed in the successor hypothesis rather than retrofitted into this one, preserving the distinction between a hypothesis and its correction.

What would not reopen this specific verdict: nothing. It is withdrawn, not reversible by further sensitivity analysis on the same unconditional, funding-blind construction.

11. Reference implementation

The cross-sectional primitive is published as 05_INSTRUMENTS/src/cross_sectional.py, specified by BL-IS-001 and BL-IS-015, and is retained and reused unmodified in its core portfolio arithmetic by the successor hypotheses BL-SD-043, BL-SD-044 and BL-SD-045. The fragility-conditioned test drivers built on it remain scheduled.

No separate implementation exists for the withdrawn, funding-blind, unconditional variant beyond what already produced the numbers in section 7.

The source suite holds 19 pinned cases, and that figure is correct. The published suite carried 16 of them plus one new guard, arriving at 17 without recording the three it left behind. They are restored, and two of the three had no counterpart anywhere in the published file: the rounding rule that keeps at least one name per leg when a fractional quantile count falls below one, and the portfolio return with a negative short-leg mean. The second is the one that mattered. Every other portfolio-return case in the published file used two positive leg means, which is exactly the configuration in which a sign error on the short leg is invisible. All three pass against the published implementation unchanged, so the arithmetic was right and only the coverage was thin.

12. Evidence register

13. Lessons extracted

This is the second time Rule R-10 has been invoked against this programme's own work, following its origin in BL-SD-039's retracted first closure. Its recurrence here, on a different signal, a different construction, and a different author judgment, establishes it as a structural discipline rather than a one-off correction: any hypothesis whose mechanism memo names a conditioning variable must have that variable tested before a death verdict is issued on unconditional statistics, without exception for how confident the unconditional result appears.

The funding omission adds a narrower, instrument-specific lesson: any position held across a perpetual funding settlement must carry funding in its PnL model from the first specification, not as a robustness check added after a favourable-looking unconditional result invites scrutiny. The programme's cost model checklist was updated to require an explicit funding term or an explicit, pre-registered justification for its absence, for every future cross-sectional or multi-day directional construction.

14. Cross-references

BL-SD-043 (H-X2) for the procedurally corrected, fragility-conditioned successor this withdrawal produced. BL-SD-039 for the earlier origin of Rule R-10. BL-D-002 and BL-D-007 for the doctrine on procedural validity and marginal contribution. BL-SD-000 ledger row H-X1.

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