Dynamical Information Geometry, Part XI: Front-Response Non-Reconstruction as a Structural No-Go Result within the Twin-Test Framework

Preprint: This work is a preprint, has not undergone peer review, and is made publicly available to establish a public scientific record. This preprint constitutes Dynamical Information Geometry (DIG), Part XI: Front-Response Non-Reconstruction as a Structural No-Go Result within the Twin-Test Framework. The work establishes a principled non-reconstruction limit for front-response information within the audit-fixed DIG Twin-Test protocol. It shows that categorical Twin-Sign and front-response PASS/FAIL classifications, even when available for arbitrarily many non-collinear projection directions and exhibiting regime-stable behavior, do not permit reconstruction of internal dynamics, ontology, state-space representation, or response geometry. The result is purely logical and structural. It follows from the categorical, projection-based nature of front-response information in the Twin-Test framework and does not arise from finite statistics, noise, or insufficient data. No new observables, datasets, intervention classes, audit rules, or interpretive principles are introduced. No reconstructive, ontological, or explanatory claims are made. All statements are strictly restricted to the audit-fixed Twin-Test protocol space defined in DIG Parts IV–X. Part XI serves as a structural closure result, delineating the intrinsic limits of inference within the Twin-Test framework, even after all trivial, representational, and protocol-internal alternative explanations have been eliminated. All results are qualitative, sign-based, and independent of numerical parameter tuning. For reference and context, related DIG manuscripts include: DIG Part I (Theoretical framework):https://doi.org/10.5281/zenodo.17983399 DIG Part II (Positive information curvature and acceleration):https://doi.org/10.5281/zenodo.17982058 DIG Part III (Hardware validation):https://doi.org/10.5281/zenodo.18100057 DIG Part IV (Regime structure and operational necessity):https://doi.org/10.5281/zenodo.18202656 DIG Part V (Multidimensional formulation):https://doi.org/10.5281/zenodo.18210315 DIG Part VI (Scaling 1D hardware validation):https://doi.org/10.5281/zenodo.18226369 DIG Part VII (2D Twin-Sign validation):https://doi.org/10.5281/zenodo.18313460 DIG Part VIII (Multidimensional front-response structures):https://doi.org/10.5281/zenodo.18395775 DIG Part IX (Regime structure and adversarial stability):https://doi.org/10.5281/zenodo.18422925 DIG Part X (Intervention-based killshot closure):https://doi.org/10.5281/zenodo.18451913 Companion documents: DIG — N1 (Definitions and scope):https://doi.org/10.5281/zenodo.18001179 DIG — N2 (Definitions, interpretation rules, non-equivalences):https://doi.org/10.5281/zenodo.18380514 DIG — No-Derivation Claim and scope delimitation:https://doi.org/10.5281/zenodo.18392928 Related dataset (transpiler killshot):https://doi.org/10.5281/zenodo.18451716 Correspondence regarding this work may be directed to:[email protected]