Appendix A — Methodological Validation Script

Update I: Appendix A — Methodological Validation Supplement: The record now includes the analysis pipeline source code and the raw bitstring dataset for the worked example, enabling independent inspection and reproduction of the structural findings reported above. The tool processes SHA hash outputs and password bitstrings through identical code paths — methodological symmetry verifiable line by line in source — so any statistical asymmetry between SHA-derived and password-derived results is a property of the data, not of the analysis. Reviewers may reproduce the per-layer match patterns on the provided dataset and additionally verify on independently generated password-hash pairs that the reported structural signature does not appear in random control data. The package contains the analysis layer only; the preimage-generation engine remains outside the public record. Contents: Step₂AnalysebinärercodeₖryptoXIIJ. py — GCIS Bitstring Search Tool (Version XIII, Preprint Edition) bitstringsPassword. csv — Raw bitstring dataset for the documented worked example ____________________________ This preprint reports reproducible architectural patterns in the activation manifold of a self-organizing neural network (GCIS / ZEUS) that localize SHA-256 password preimages within prime-bit-size layers. Across eight independent runs with fresh random initialization, three methodologically distinct diagnostics converge on the same structural reading: the network organizes preimage information geometrically, and the geometry is reproducible across initializations. Key findings: - Architectural template across 8 runs: 174 layer pairs satisfy three structural conditions without exception — prime bit-sizes, layer-index gap of exactly 2 or 10, and password byte distribution symmetric within each pair to within fractions of a percent. - Partial blind byte recovery: A count-based candidate filter with frozen rules recovers 50–53% of true preimage bytes across three runs against the printable-ASCII universe (Fisher combined p = 1. 23 × 10⁻⁴, against a random expectation of 33. 7%). - Geometric mirror/gauge signal: A position-template correlation under symmetry transforms survives in 8/8 runs against random printable controls, under both permissive and strict layer-selection variants (Fisher combined p ≈ 2. 1 × 10⁻⁹). - Bypass rather than break: The findings do not algebraically invert SHA-256, MD5, or ECC, but empirically challenge the operational assumption that cryptographic outputs are structure-blind to neural geometric reading. This threat model is not addressed by the post-quantum cryptography programme.