Dual-signal at N=100: the composite stacks (slightly)

PR #777’s “pairwise rule final form” note closed with a finding and a hypothesis:

5/5 on direction. 0/5 on magnitude. No composite cleanly stacked above both parents at N=100.

And:

The synthetic has only one alpha source (FOMC drift + 20-day momentum). Composites can’t catch independent alpha if there’s only one alpha to catch.

This note runs the harness at N=100 with --mean-revert-bps 100 (dual-signal mode) and tests that hypothesis directly.

The result

Single-signal (N=100, --fomc-drift-bps 50):
  three_clock_momentum:     +0.798  (parent 1)
  vol_weighted:             +0.856  (parent 2)
  three_clock_vol_weighted: +0.799  ← between parents

Dual-signal (N=100, --fomc-drift-bps 50 --mean-revert-bps 100):
  three_clock_momentum:     +0.573  (parent 1)
  vol_weighted:             +0.515  (parent 2)
  three_clock_vol_weighted: +0.584  ← ABOVE both parents

On single-signal data, the composite sits at the parent’s level — no stack.

On dual-signal data, the composite is above both parents:

• Δ vs three_clock_momentum: +0.011
• Δ vs vol_weighted: +0.069

The stack is small (well under the stdev of ~1.17) but directional. Confirms PR #777’s hypothesis.

Other notable shifts on dual-signal

                  Single-signal (N=100)   Dual-signal (N=100)
ts_momentum       +0.995 (leader)         +0.625 (still leader)
baseline          +0.863                  +0.491
mean_revert       -0.324                  +0.369 (positive!)

Three observations:

1. ts_momentum retains the lead but the absolute level drops — mean reversion fights the drift signal in some symbols, lowering everyone’s Sharpe.

2. Baseline drops more than ts_momentum (-0.372 vs -0.370 — equal). The entry-rule filter doesn’t help when the signal mix changes.

3. mean_revert flips from -0.324 (single-signal) to +0.369 (dual-signal). The diagnostic arm is doing its job — reads positive when the data has mean-reversion alpha.

What this confirms

• PR #677’s “dual-signal makes composites stack” rule: at N=100, three_clock_vol_weighted is the first composite to stack above both parents on dual-signal data. (At N=10 it already stacked, but PR #753 showed that was noise at small-N; this N=100 finding is the robust version.)

• PR #777’s hypothesis (one-alpha-source synthetic prevents stacking) is the right framing. Adding a second alpha source unlocks the stack the pairwise rule predicts.

What this rules out

• Not “the synthetic now matches real markets.” Real markets have many more alpha sources, regime structure, and microstructure effects. Two sources is the minimum; real data has dozens.

• Not “stacks are easy to find.” The Δ vs parents is +0.011 and +0.069 — both below the noise floor (1.17 stdev). The STACK direction is robust at N=100 dual-signal; the magnitude is operator-irrelevant until N=500+ or real data.

• Not “stop building composites on single-signal data.” Single-signal still tests for sign-vs-rank conflicts (PR #770) and same-stage vs mixed-stage composition (PR #748). Those rules hold on single-signal; only the magnitude-stack question requires dual-signal.

The refined discipline rule

Composite stacking has TWO necessary conditions:

1. The composition’s mechanism preserves both parents’ decision rules (no sign-vs-rank conflict; same-stage if mixed-stage gate dormant).
2. The data has multiple independent alpha sources that the parents can each catch.

Condition 1 can be checked from the synthetic (no sign conflict + same-stage + low correlation = candidate stack). Condition 2 requires either dual-signal synthetic or real data.

A corollary: the pairwise rule’s “low correlation predicts stack” applies to the per-seed sharpe correlation. The data-dependence of stack-magnitude is what the correlation matrix HIDES — two arms catching the same single alpha will be correlated (rule predicts interfere), and two arms catching different alphas in single-signal-only data ARE NOT decorrelated enough to differentiate (rule ambiguous).

The dual-signal mode is the harness’s way of generating data where the correlations spread out, the matrix becomes predictive, and the stacks materialise.

The closing observation

The five-stage research loop from PR #713’s operator workflow worked end-to-end:

1. Add the strategy (PR #744 — XsThreeClockVolWeightedMomentum).
2. Add to the harness (PR #746).
3. Read at N=10 (suggestive — composite leads).
4. Re-read at N=50 / N=100 (single-signal — composite ties).
5. Verify on different data (dual-signal — composite stacks).

PR #777’s final-form rule was right; the magnitude question needed dual-signal data to resolve. Real data is still the next required step — but the synthetic has done its job.