Identifiability of Noise Sources in Bodily Judgments

Changes in temporal response curves after brain stimulation do not by themselves locate the changing variability within a sensory or decision process. We examine this distinction in the public body-ownership and simultaneity experiment of D'Angelo et al. (2026; 30 participants, 12,600 binary judgments). Recomputing the released Bayesian causal-inference likelihoods reproduces all saved objectives within 2×10⁻⁹. An information-criterion sign discrepancy is traced through the public code and all 30 source-data rows; correcting it preserves the aggregate preference for the noise-varying model. A parameter-free conditional test nevertheless rejects a mandatory zero-centered symmetry constraint of both released model families under their independent-binomial observation law (deviance 984.304; 19,999 conditional simulations; plus-one $p=.00005$). Adding task-specific centers improves prediction under a fixed five-fold within-cell partition; the noise-varying family with task-specific centers has lower held-out NLL than its prior-varying counterpart by 60.885 (mean participant difference −2.029; descriptive 95% interval −3.268 to −0.791). Building on established sensory/criterion-noise models, we construct a constant-sensory-variance, variable-criterion implementation that preserves every marginal probability of the released noise-varying observer, including its condition-specific threshold policy. All 1,260 fitted count-cell probabilities agree within 2.23×10⁻¹⁶. We then derive a conditional repair: with calibrated marginal parameters, one shared internal sensory draw, and independent decision and lapse processes, one additional population joint-response probability identifies shared variance. Allowing bounded criterion correlation yields a sharp interval instead; near zero total correlation, centered observations have only second-order sensitivity. Exact binomial confidence-set projection propagates finite-sample uncertainty. All 240 prespecified valid synthetic scenarios meet nominal 95% coverage, while their often-wide intervals and 240 assumption-violation controls expose the practical limits. The contribution is a source-specific, reproducible separation of model comparison, model adequacy, and implementation identification, with an explicit additional-measurement contract. It does not identify an anatomical mediator or validate a theory of subjective experience. Methods preprint and retrospective secondary analysis of published bodily-judgment data, with conditional identification results and finite-sample model calculations. Reanalysis of existing human data is distinguished from new data collection and from prospective paired-report predictions. Substantial ChatGPT assistance under the author's direction is disclosed. Not peer reviewed. No new human or animal data were collected; no new pretrained language-model experiment is reported, and C1 is not claimed to be empirically validated. The CC BY 4.0 license applies to newly authored material to the extent rights are held. Included third-party materials retain their own rights and source-specific terms; no new blanket license is applied to the original data workbooks. See the reproducibility archive's THIRD_PARTY_NOTICES.md and provenance records.