A Calibrated Test of Internal Action Maps: State Signals Without Global Affine Closure

Behavioral accuracy, linear decodability, and successful activation interventions do not by themselves show that a model carries an operation-level structure from one symbolic domain to another. We ask a narrower question in finite isomorphic state spaces: if the hidden-state difference between two operations is estimated separately for each source input, does adding that difference to a mapped recipient input move the model toward the corresponding recipient answer? The design compares this input-specific intervention with wrong-operation, norm-matched random, and no-op controls, and separates candidate construction from an independently isolated confirmation split. On a frozen Qwen2.5-7B-Instruct model at layers 20--21, one route--domain--operation candidate from a family pre-specified and frozen before confirmation access, transparent | integer_mod16--letters16 | successor->predecessor, passed both PyVene splits; its confirmation intersection--union p-value was 0.000198 and its 36-family Holm-adjusted p-value was 0.006943. A subsequent NNsight 0.7.0 experiment, pre-specified and frozen before its confirmation access, tested only this selected prompt route, without candidate or layer reselection. It reproduced all 12 confirmation effect estimates, confidence intervals, and exact sign-flip p-values numerically; its 36-family Holm-adjusted p-value was 0.007141. The result is therefore limited to one prompt route and one candidate, replicated across two intervention implementations on one model revision and one layer interval. It does not establish cross-model generalization, full-family backend independence, domain-general transfer, or algebraic invariance.

Latent action models infer a code for the transition between two frames of action-free video. Recent methods regularise this code to compose additively and reverse antisymmetrically, and report order-of-magnitude reductions in the resulting errors as a label-free certificate that the code has captured temporal structure. We show that this conclusion does not follow. Reconstruction drives the decoded transition toward a difference of state features, for which both identities hold for any pairing, a solution the metric cannot distinguish from one encoding nuisance state or a coordinate convention. Across five source domains, a trained but unconstrained counterpart already achieves 83-97% of the reduction relative to an untrained anchor. The residual fold is governed as much by the decoder family as by what is learned. A constrained model retrained after its temporal pairing is destroyed still reaches, in each domain, a lower error than the unconstrained model on real data. Downstream, preserving the temporal pairing yields no consistent advantage on LIBERO-GOAL or LIBERO-SPATIAL, and across the tested arms the code's mean linear action decodability falls as the algebraic error improves. We also test the most direct repair, a violation-contrastive objective that requires the algebra to fail on destroyed pairings: in the tested configurations it yields only a marginal separation within the reconstruction budget, on training and test triples alike. We recommend a validation protocol that these methods currently lack: a baseline-corrected metric, retraining on destroyed pairings, and a seed-budget analysis.

What happens to information a pretrained model already encodes when post-training no longer rewards using it? The common language of representation compression conflates three fates: information may be erased, rerouted away from the decision while still represented, or rescaled to occupy less variance while still represented and used. We make these fates identifiable in models whose pretraining recovers Bayesian belief states. A reward that reads only a coarse function of the hidden state defines an exact reward-null kernel. The kernel lets us separately measure whether the information remains recoverable, whether decisions causally depend on it, and how much activation variance it occupies. Theory says what is protected: KL-anchored reinforcement learning preserves the reference policy's log-odds among equally rewarded outputs, supervised and unanchored objectives carry no such constraint, and spectral compression implies neither erasure nor loss of use. In controlled worlds, post-training mostly reroutes or rescales reward-null information and leaves it decodable. Without an anchor decisions can stop using it although the representation survives, and with one they keep using it. Erasure appears only under prolonged weight decay, for distinctions that neither reward nor next-token prediction can see. Open language models show the same dissociation: in-context belief geometry stays decodable under late-layer spectral compression, and within-class behavior depends on the anchor. Post-training thus selects a causal quotient of the pretrained belief state: the reward defines decision-equivalence, the anchor and the state update protect part of what it ignores, and optimization decides whether the rest is erased, rerouted, or rescaled.