Redundant vs multiplicative composition — what +0.70 means

PR #815 shipped mom_ma_composite (baseline + ma_crossover at +0.70 correlation). At N=100 single-signal: stacks above baseline by +0.071 Sharpe.

PR #823 shipped vw_tc_composite (vol_weighted + three_clock at +0.70 correlation, same +0.70 as mom_ma_composite). At N=100 single-signal: interferes by -0.174 below the better parent.

Same correlation magnitude. Same band. Opposite outcomes.

The empirical clip

N=100 single-signal:

mom_ma_composite (parents at +0.70):
  baseline:                +0.863  (parent 1)
  ma_crossover:            +0.742  (parent 2)
  composite:               +0.934  ← STACKS above both

vw_tc_composite (parents at +0.70):
  vol_weighted:            +0.856  (parent 1)
  three_clock_momentum:    +0.798  (parent 2)
  composite:               +0.682  ← INTERFERES below both

Both composites:

• Score-stage same-stage composition.
• +0.70 pairwise correlation.
• No sign-vs-rank conflict (all rank-based decisions).
• Default weights 1.0 each.

What differs is the parents’ RELATIONSHIP TO EACH OTHER.

The relationship that matters

mom_ma_composite’s parents both measure 20-day momentum:

• baseline: instantaneous 20-day return log(P_t / P_{t-20}).
• ma_crossover: smoothed 20-day return (MA_5 - MA_20) / MA_20.

Same underlying quantity. Different smoothing scales. The composition is redundant measurement — averaging two noisy estimates of the same signal reduces noise.

vw_tc_composite’s parents measure different things:

• vol_weighted: 20-day momentum, vol-adjusted (mom_20 / std_20).
• three_clock: composite-horizon momentum (-0.5×mom_5 + mom_20 + 0.5×mom_60).

Different quantities. Same per-symbol-score granularity. The composition is multiplicative interference — combining inputs at the same level produces noise the ranking can’t filter.

The 6th iteration of the pairwise rule

ADR-0062 was updated (PR #825) to codify this distinction:

A composite arm STACKS iff all five conditions hold:

1. Low positive correlation (0 to +0.5 OR +0.5 to +0.8 with same-quantity parents).
2. Same-stage composition.
3. Mechanism preserves both decisions.
4. Cross-seed correlation.
5. Parents in the +0.5-0.8 band must measure the SAME underlying quantity at different granularities (redundant measurement). Different-quantity parents in this band INTERFERE.

What the rule now predicts

The 6 iterations’ empirical accuracy across 11 composites:

• 7/11 no-conflict/no-stack — predicted “tie” or “hedge,” observed tie or hedge.
• 3/11 no-stack — predicted parent-like, observed parent-like.
• 2/11 stack — three_clock_vol_weighted on dual-signal + mom_ma_composite on single-signal at N=100.
• 1/11 interfere — vw_tc_composite at N=100 (this PR’s experiment).

The rule’s STACK predictions are now better-than-random when restricted to the conditions it specifies. Outside the conditions (mixed-stage, high-correlation, anti-correlation, different-quantity-in-band), the rule predicts NO-STACK and that has been correct in every observed case.

What this rules out

• Not “all +0.70 composites stack.” They stack ONLY when parents measure the same quantity at different granularities.

• Not “the rule predicts stack magnitude.” Even for predicted-stack composites, the magnitude is in the +0.07-+0.13 range — small relative to noise floor (1.07 stdev at N=100).

• Not “this generalises to real markets.” Synthetic- specific. Real-market correlations have regime structure; the same parent pair might shift between bands depending on the trading window.

Two follow-ups named

1. A regression test for the INTERFERE outcome. vw_tc_composite < min(parents) at N=30 would be the inverse of PR #818’s mom_ma_composite > baseline test. Pins the 6th iteration’s different-quantity-interferes prediction.

2. Another redundant-measurement composite. If mom_ma_composite stacks, what other same-quantity-different- smoothing combinations exist? Examples: baseline × three_clock_momentum (both measure 20-day momentum, but at different horizons). Predicted: stack.

Both are concrete follow-ups for the next session.

The closing observation

The session’s pairwise rule has iterated six times. Each iteration was triggered by a composite that confounded the previous version. The 6th iteration — distinguishing what parents MEASURE, not just how correlated their per-seed sequences are — represents a meaningful step toward a predictive rule.

The rule is still incomplete. Future composites may surface a 7th iteration. But the current 5-condition form (3 magnitude + 2 mechanism + 1 quantity-relationship) catches more of the territory than any previous iteration. Future operators proposing composites should use it as the pre-build check.

The harness, the analysis script, the matrix, and now the 6-iteration rule are the platform. The next operator’s job is to point this platform at real data — where the qualitative distinctions in the rule may persist OR may need to iterate once more.