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arXiv · 2608.13626

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

Dekun Yang
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Abstract

A hidden state signal can be decodable or causally usable without supporting a reusable action map. We test whether action maps fitted without a source reach its natural post-action activation and compose. We organize the tests as an evidence lattice and validate the geometric branch on a known affine S_5 carrier: all held-source folds pass one-step, composition, inverse, decoding, and commutativity gates. Structured curvature and held-domain conjugacy raise error monotonically, but only 23/30 strongest cells flip a closure gate, bounding rather than universalizing calibration. In post-trained Qwen/Qwen3-4B, frozen final-token h28 affine maps have mean held-entity error .519, versus .398 for within-test-domain cross-fit. Seven randomized entity splits and map geometry do not support a purely entity-specific account. Earlier h4/h16 layers fit one-step transitions better, but h4 conflict-state decoding is weak and lexical controls remain unresolved. Three matched intervention datasets regenerated from one frozen checkpoint show causal effects only at h28/h36. Outcome-aware refitting improves h28 one-step error to .474 (.469 with weighting), yet no refit passes composition. Learned finite worlds likewise preserve relative algebraic signals or shared charts without held-source affine closure. Within the tested carriers, state availability, causal use, local geometry, and reusable closure are separable. The result is limited to one pretrained model, sampled final-token layers, two finite worlds, and the tested affine or diagnostic function classes.

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Dekun Yang. 2026-08-13. A Calibrated Test of Internal Action Maps: State Signals Without Global Affine Closure. https://arxiv.org/abs/2608.13626

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