H_1039 🟢 REDUNDANCY-CAUSAL — de-redundifying planning channels COLLAPSES the Φ sign-split

[dancinlife]

H_1039 — is the planning Φ sign-split CAUSED by redundancy? (causal ablation)

Fills the pre-registered H_1039 (merged #1939). Tests H_1017's redundancy mechanism causally.

Result: PASS (H1) — REDUNDANCY-CAUSAL 🟢

De-redundifying the planning channels (ZCA-whiten primary + Gram-Schmidt robustness, on the continuous top-variance channels before median-binarization) removes the Williams-Beer redundancy AND collapses the faithful-UP/big-Φ-DOWN sign-split, while the split holds on the matched un-orthogonalized control.

arm	faith Δ	faith	big-Φ Δ	big-Φ	Δredund	SPLIT
control	+2.3332	UP	−4.0083	DOWN	+9.3958	True
dered_zca	−0.0709	DOWN	−3.0843	DOWN	−0.2563 (97.3% cut)	False
dered_gs	+0.0023	UP	+1.2000	UP	+0.0396 (99.6% cut)	False

Frozen thresholds (pre-reg): SIGN_EPS=1e-3; redundancy removed iff |Δred_dered| ≤ 0.20·|Δred_control| (≥80% cut). Both operators clear it. ⇒ redundancy is the causal driver of the split — H_1017's correlational mechanism confirmed causally, consistent across both operators.

Discipline

• mirror ≡ stdlib RE-PROVEN at n=4 AND n=5 (h1012.prove_mirrors_at_n; big-Φ ring |Δ|=1.34e-10, faithful |Δ|≤3.75e-6) — a_phi_iit4_tool, no proxy.
• Williams-Beer I_min PID = intervention-validation variable (confirms operator removed redundancy), NOT a Φ proxy; all Φ from stdlib mirrors.
• Operator validity guard: redundant-block off-diag corr 0.9978 → 0.0000 (decorrelate), on-frac 0.500 (signal preserved), deterministic.
• TOY n=4 EXACT, 30 seeds, SERIAL CPU $0, no GPU/pod. Production scale UNVERIFIED (a_scale_honest_scope, g5/p7).

Artifacts: UNIVERSE/h1039_redundancy_causal.py · .verdicts/1039_redundancy_causal/H_1039.txt · UNIVERSE/h1039_redundancy_causal_result.json · UNIVERSE/H_1039_redundancy_causal.md (🟢 tiered).

🤖 Generated with Claude Code