🔗 #11 Conditional MI I(f;Y|S) CHECKPOINT

Does the feature carry forward information beyond the shipped set S — including interaction-only signal with zero marginal IC? This is the question rank-IC, IC-decay, MDA and quantile-monotonicity are all structurally blind to. The KSG/Frenzel–Pompe k-NN CMI + Runge local-permutation null. Bounded slice: all 5 slice gates pass across 2 seeds; the iid/AR(1) FPR and high-dimensional-S Harden are deferred to the next firing under the compute cap.

5 / 5

slice gates pass

0.04

marginal MI (interaction ≈ blind)

z 27–33

CMI vs local-perm null

2 seeds

both 5/5 · 2 nulls deferred

Preflight (resource-only): load1 within cap · ≥8 GiB free · si/so ~0 · ClickHouse active, readonly=2. 5c/5G/no-swap capped; single-thread BLAS. Slice staged read-only at /tmp/i11_slice.parquet.

The five slice gates

Slice gate (§7 row 11)	Result (seeds 20260723 / 11)	Target
Gaussian analytic recovery	max-err 0.010 / 0.005 nats	≤ .02 nats	PASS
Admit (interaction-only)	CMI 0.312 / 0.351, z 27.5 / 33.4, p .0125 · marginal MI 0.041 / 0.049 ≈ 0	p≤α, z≥3, δ≥min · marg≈0	PASS
XOR / interaction power	1.00 / 1.00	≥ .8	PASS
Nulls FPR (2 of 4)	block-perm-target 0.000 / 0.025, latent-common-cause 0.000 / 0.000	≤ α (cc = critical no-FP)	PASS
Substitution (f≈S redundant)	not-sig 1.00 / 1.00	≥ .95	PASS

Margins are wide, not knife-edge (admit z 27–33 vs threshold 3; power 1.0; common-cause FPR exactly 0.0) → seed-robustness is structural.

The interaction archetype is the raison d'être (verify-before-report)

A conditional instrument only earns its slot if its KNOWN-POSITIVE is genuinely marginal-blind. Getting that construction right was the load-bearing fix of the slice:

First attempt (leaked). f = gaussianise(Y·sign(S) + 0.1·noise) is CMI-significant — but its marginal MI was 1.69 nats: it also carries Y's magnitude unconditionally, which rank-IC would already catch. Not a clean interaction-only case.
Fix (genuine sign-XOR). f = gaussianise(sign(Y)·sign(S) + 0.6·noise). Marginalising over S the sign-product decouples → f ⊥ Y unconditionally (marginal MI collapsed to 0.04); conditional on S, f pins down sign(Y) → I(f;Y|S) > 0 (CMI 0.31, z 27). Exactly the class flagged FNR=1 by the #4/#5/#7/#19 envelopes and routed here.

The critical no-false-positive: latent common cause. The failure that would silently invalidate a conditional instrument is a hidden state Z driving both f and Y. When S=Z captures it, I(f;Y|S) must be 0. Built from real bins (Z = a real feature; f=Z+noise, Y=Z+noise, S=Z), the local-permutation test false-positives in 0.0 of reps both seeds — because permuting f only among its S-neighbours preserves P(f|S). A global shuffle would manufacture false positives here; the Runge local null is load-bearing.

Deferred to the next firing (compute cap — resume same instrument)

The local-permutation null costs B CMI evaluations per test (each CMI = 3 cKDTree builds + n radius queries), multiplied across FPR reps and four null archetypes. Two §7 items carry forward under the frozen 5c/5G cap:

iid + AR(1) nulls FPR — the remaining 2 of the 4-null FPR battery: an independent-of-Y feature, and an AR(1)-autocorrelated feature independent of Y (confirming FPR control under time-series dependence unrelated to Y).
Imperfect / high-dimensional-S Harden — (a) curse-of-dimensionality false-negatives as dim(S) grows (does power survive a 3–5-dim conditioning set at N=1800?), and (b) the common-cause no-FP under imperfect S (partial capture of Z must not manufacture a false positive beyond α).

Only after both clear (with a seed sweep) does #11 earn a terminal GROUNDED row. This checkpoint freezes the estimator + Gaussian recovery + interaction admit + XOR power + 2 key nulls + substitution as done and reproducible.