v1b_m6c_combined.md

V3 leads — combined M6c (M6a + M6b2)

Question. v3 lead 1 (M6a, common-mode partial-out) and v3 lead 2 (M6b2, per-class Mondrian) modify orthogonal axes of the M5 protocol. Do their width gains stack?

Variants

method	score	cell	params
M5	|r|	regime	12 b + 4 c (16)
M6a	|r − β·r̄|	regime	12 b + 4 c + 1 β (17)
M6b2	|r|	symbol_class	24 b + 4 c (28)
M6c	|r − β·r̄|	symbol_class	24 b + 4 c + 1 β (29)

Train β = 0.811 (R² ≈ 0.28; see v1b_m6a_common_mode_fit.csv).

Pooled OOS half-width (bps) by method × τ

target	M5	M6a	M6b2	M6c
0.7	110.2	102.8	116.1	105.1
0.8	201.0	178.3	185.3	168.0
0.9	354.5	309.0	303.7	270.7
1.0	677.5	595.6	663.9	642.7

Pooled OOS realised coverage by method × τ

target	M5	M6a	M6b2	M6c
0.680	0.680	0.681	0.680	0.680
0.850	0.850	0.850	0.850	0.850
0.950	0.950	0.950	0.950	0.950
0.990	0.990	0.990	0.990	0.990

Stacking diagnostic

Gain = (M5_width − method_width) / M5_width. Stacking-efficiency = M6c gain / (M6a + M6b2 gains). Efficiency = 1.00 means perfectly additive; > 1.00 means super-additive (rare); < 1.00 means partial overlap (the two leads are not fully orthogonal).

target	gain_m6a	gain_m6b2	gain_m6c	sum_individual	stacking_efficiency
0.680	0.067	-0.054	0.046	0.013	3.552
0.850	0.113	0.078	0.164	0.191	0.861
0.950	0.128	0.143	0.236	0.272	0.870
0.990	0.121	0.020	0.051	0.141	0.365

Reading

Read the stacking_efficiency column. If ≈ 1.0, the two leads address fully orthogonal structure and combining them is straightforward. If < 1.0, M6a and M6b2 partly capture the same residual variance. If > 1.0, there's a synergy term (uncommon).

Caveat — M6c is upper-bound. Like M6a, M6c uses the leave-one-out weekend mean residual which is Monday-derived. Deployment requires a Friday-observable proxy for r̄_w. The deployable M6c gain scales with the forward predictor's R²(r̄_w | Friday-state).

Reproducible via scripts/run_m6c_combined.py. Source data: reports/tables/v1b_m6c_combined_oos.csv.