Follow-up (2026-08-11):
We tested our own tail prediction, and half of it dies. The addendum predicted tail membership would be predictable from weights alone via distance of a net’s state-descriptor trajectory from the ensemble band. We ran that test twice — single-probe-seed on 200 nets, then the decisive version on 100 nets × 8 probe seeds with difficulty split into bias² and variance components. Results: the hard tail is real, not probe luck (single-seed vs 8-seed intrinsic difficulty, Spearman +0.82), and the mechanism claim strengthens — state-keyed corrections improve the intrinsic tail 1.32× vs 1.07× in the body. But the weights-only predictor fails: band-distance atypicality reaches only +0.24 against the bias² component and retrieves the tail at chance level.
Also tested: an ensemble version of the kink-neuron hypothesis (from Natasha Stewart’s write-up) — kink fraction correlates negatively with difficulty (−0.19), so “more boundary neurons → harder net” is wrong at net level too. A Davis–Kahan-motivated eigengap statistic (subspace sensitivity ∝ 1/gap, computed from deterministically propagated covariances) also comes back null — He-random nets at this width appear spectrally self-averaging, so the difficulty signature is not in any marginal spectral summary.
Our reconciliation: the state-keyed estimator helps the tail without ever needing to know which nets are hard — it reads state per-layer and corrects wherever the deviation is correction-relevant, while a symmetric average distance destroys exactly that direction- and depth-specific structure. So: mechanism confirmed, operationalization retracted. If someone finds a weights-only statistic that does retrieve the tail, we’d genuinely like to see it. Scripts and results committed alongside the rest: post_phase1_state_keyed/ (kink_fraction_tail_check.py, multiseed_tail_check.py).