The Inversion Error: Generator–Projection Non-Invertibility as a Cross-Domain Failure Mode (Part 1) and Human-Meaning Domain Application (Part 2)

This deposit contains two working papers that formalize and apply a single cross-domain modeling failure mode: the inversion of observable projection artifacts into the status of generator mechanisms. Part 1 (“The Inversion Error: Generator–Projection Non-Invertibility as a Cross-Domain Failure Mode”) introduces a generator–projection schema in which Ψ(x) labels generator-level dynamics, P denotes the projection pipeline (measurement, preprocessing, labeling, interpretive templates), and B(x)=P(Ψ(x)) denotes observable residues. It argues that projection pipelines are information-lossy and non-invertible in general; reconstruction of generator dynamics from observable residues alone is ill-posed without additional constraints or access channels. The inversion error is defined as the substitution Ψ̃(x):=B(x), followed by treating projection artifacts as mechanisms while suppressing correction capacity, bounded perturbation capacity, and integration of competing constraints. Part 1 provides predicted field-level signatures and explicit falsification protocols with operational definitions, procedures, and rejection criteria. � inversion_error_-_part_1_v2.6-1.docx None Part 2 (“The Inversion Error in Psychology, Psychiatry, Neuroscience, Cognitive Science, and Symbolic Systems”) applies the same schema to human-meaning domains. It specifies what counts as B(x) in these fields (symptom clusters, behavioral signatures, psychometrics, neuroimaging features, administrative categories, and symbolic templates), enumerates common inversion substitutions (symptom-as-cause, label-as-entity, correlate-as-mechanism, map-as-generator, score-as-truth, narrative-as-mechanism, identity-tag substitution, institutional convenience substitution), and provides domain-specific falsification protocols designed to be runnable using existing clinical, institutional, and neuroimaging data streams. � inversion_error_-_part_2_v2.6.docx None Keywords inversion error generator–projection non-identifiability ill-posed inverse problem measurement reification projection pipeline model failure modes taxonomy inflation comorbidity psychiatry psychology neuroscience cognitive science interpretability distribution shift multiverse analysis institutional diagnostics