When Restoring Function Does Not Restore Learning Dynamics

SFP-M05 / v1.1. Preprint; not peer-reviewed. A constructive geometric account of learning-history memory: closed excursions of a declared function can change a common subsequent learning response. The paper relates the vertical displacement of a functional cycle to its action on the learning kernel, gives an exact future-equivalence characterization for invertible square two-layer linear networks, derives reversal-parity and metric-sign diagnostics, and supplies finite neural and local resistance-learning constructions with explicit return and execution-error contracts. Known nominal models and starts are assumed. This is not a hardware demonstration. The accompanying archive distinguishes analytical proofs, exact controls, separately implemented floating-point replication, author-validated interval certificates, and arithmetic replay. The complete interval histories use one inclusion algorithm with two arithmetic implementations. Separate floating-point and finite-prefix calculations do not constitute a second complete interval integration. AI assistance and author responsibility are disclosed in the manuscript and code/data README. Files: the manuscript including appendices, self-contained LaTeX source, and reproducibility archive with frozen source snapshots, saved results, configurations and integrity checks. New manuscript and release documentation: CC BY 4.0. Frozen scientific sources retain their existing CC0-1.0 license. DOI: 10.5281/zenodo.23603582 SFP-M05 / version 1.1. DOI: 10.5281/zenodo.23603582.