Sensitivity Without Reproducibility: A Measurement Boundary for an Operator-Valued Representation Instrument in Qwen Models

Technical report · Not peer reviewed This study asks when an internal representation observable is reusable across fresh local presentations rather than merely sensitive to a controlled perturbation on one substrate. It evaluates a phase-indexed binary register in a frozen Qwen checkpoint panel, separating explicit transition following, demonstration-conditioned register behavior, visible-state intervention use, operator-valued representation measurement, and representation–function coupling. Qwen3.5-27B and Qwen3.6-27B passed the behavioral ladder through visible overwrite propagation; Qwen3-14B and Qwen3.8-27B failed an upstream transition gate and were not tested downstream. On Qwen3.6-27B, a rank-4 local-frame paired ridge path-operator packet qualified on one bounded substrate. A subsequent prospectively frozen 20-block requalification retained broken-square sensitivity in 59 of 60 layer-blocks, but split-half path-map spectral re-estimation passed in only 35 of 60 layer-blocks. Only 5 of 20 blocks passed jointly at all three frozen layers, below the required 16 of 20 blocks and four blocks per rollout depth. Stage E therefore remained unopened. No functional outcome, association, coefficient, predictive increment, or permutation-test result was collected. The result is a measurement boundary for this particular rank-4, three-layer, paired-map route. It does not establish the absence of hidden state, internal naturality, useful representation geometry, or a neural causal-transition operator. The record contains the 13-page DOI-bearing technical report, buildable LaTeX source, and a model-forward-free reproducibility capsule with all 60 continuous Stage M layer-block records, deterministic figure/table inputs, model/runtime bindings, provenance closure, licenses, and checksums. Scope boundary: the report is limited to the frozen Qwen checkpoints, visible-state intervention family, rank-4 paired ridge coordinate maps, layers 21/43/62, and fresh 20-block requalification described in the manuscript. Stage E, hidden intervention, internal exact naturality, and representation–function coupling remain untested.