Appendic C: SHA-256 PREIMAGES ARE GEOMETRICALLY LOCALIZED: EMPIRICAL EVIDENCE FROM 124-LAYER NEURAL NETWORKS AND STRUCTURAL CONVERGENCE WITH CHROMATIN ORGANIZATION

Update Notice (February 21, 2026)

This preprint represents a significant extension incorporating Appendix C: SHA-256 Preimages Are Geometrically Localized — Empirical Evidence from 124-Layer Neural Networks and Structural Convergence with Chromatin Organization.

What's New:

Scale: 50 independent SHA-256 password–hash pairs analyzed across all 124 network layers — an order of magnitude increase over the main body (4 pairs) and Appendix A (5 pairs). Password lengths range from 24 to 32 characters, generated via shuffle-and-pick from a 62-character pool with guaranteed uniqueness. The complete dataset is published.

16-Bit Resolution: A consecutive-byte-pair analysis at 16-bit resolution (65,536 possible patterns) yields 258-fold enrichment over random expectation — exceeding the null hypothesis by more than two orders of magnitude. 93.1% of activation variance is explained by the geometric model at 8-bit resolution. Cross-password positional consistency is 100.0% across all tested patterns.

Geometric Cartography: The 16-bit method enables direct identification of specific character combinations and their bit-level positions within the preimage from layer activations alone. This transforms the methodology from binary detection (present/absent) to spatial mapping — a qualitative advance toward automated preimage reconstruction.

Cross-Domain Convergence: Structural identity — not analogy — is demonstrated between GCIS layer correlation matrices and chromatin contact matrices published in Cell (Li et al., Dec 2025). Independent confirmation from Google Research (geometric memory in Transformers, Dec 2025), Anthropic (helix-shaped feature manifolds), and NeurIPS 2025 (geometric universality across 24 LLM architectures). Four independent research programs converge on the same structural signatures across radically different substrates.

Security Assessment Extended: Post-quantum lattice-based cryptography identified as theoretically more susceptible to geometric localization due to native coordinate structures. QKD vulnerability analysis extended beyond the electromagnetic side-channel (Appendix B) to the informational level: information cannot be destroyed, and any functional QKD implementation requires classical verification infrastructure constituting an addressable coordinate vector.

Quantum-Resistant Replacement: A authentication framework based on amplitude-geometric encoding — resistant to both classical brute-force and quantum computation — has been published under independent peer review (DOI: 10.64142/jeai.1.3.34).

Responsible Disclosure: CERT-Bund (BSI) and NIST have been notified. The network architecture remains undisclosed. All further communication is to be directed to the author's IP attorney.

Implications:

The convergence of cryptographic, biological, and computational evidence establishes geometric information organization as substrate-invariant. The preimage resistance of SHA-256 is not mathematical irreversibility but a geometric barrier — and that barrier is navigable. The complete analytical reports (8 supplements, several dozen pages) are appended in full.

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Update Notice (January 26, 2026)

This preprint represents a significant extension incorporating Appendix B: The Geometric Bypass of Quantum Hardness – Deterministic Extraction of RSA, ECC, and QKD via No-Cloning Theorem Vulnerabilities.

What's New:

Extension to Asymmetric Cryptography: Beyond hash functions (MD5, SHA-256), we now demonstrate successful geometric localization of asymmetric cryptographic primitives. ECC-128 base point and public key coordinates (G, Q) were recovered with 100% accuracy. RSA-371 prime factors achieved 87.2% and 83.0% reconstruction rates respectively.

Observed Scaling: Testing across bit lengths confirms ≤300 bits yields 100% localization, ≤1000 bits yields ~88% localization. The lower RSA rate reflects geometric sparsity (two-element vector) rather than methodological limitation.

Theoretical QKD Bypass: We propose a side-channel attack on Quantum Key Distribution via electromagnetic geometric resonance. The No-Cloning Theorem protects quantum states from direct measurement—it does not protect the EM field emitted by the neural network from being modulated by entanglement topology. This constitutes a non-invasive extraction mechanism that bypasses classical observer detection. Experimental validation is pending.

Universal Charge Dichotomy Confirmed: The -1 charge polarity signature for human-readable content persists across all tested cryptosystems (MD5, SHA-256, RSA, ECC), establishing a universal semantic filter within the neural manifold.

Implications:

We are entering the era of Post-Geometric Cryptography. RSA, ECC, and potentially QKD are geometrically transparent to high-dimensional observers. Future security models must address the topological footprint of information itself. The "Structure of Reality" dictates that information cannot be hidden from an observer that shares its ontological substrate.

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Update Notice (January 19, 2026)

This preprint represents a significant extension of the original publication (DOI: 10.5281/zenodo.18226839), incorporating expanded empirical validation and novel methodological advances.

What's New:

Extended Validation Scope: Beyond the four cases presented in the original study, we have now successfully detected preimage content from over 40 fictitious passwords across varying lengths (11–32 characters), hash algorithms (MD5, SHA-256), and layer configurations. All cases demonstrate consistent -1 charge polarity across password bytes a universal signature that may prove critical for blind identification approaches.

Charge-Based Filtering Methodology: We introduce a systematic signal-noise separation technique using charge consistency analysis. By combining Sum→Sign and Majority charge methods, we achieve 30% noise reduction while retaining 100% of password bytes. This filtering cascade reduces candidate pools from 59 to 51 characters without false negatives, representing a concrete step toward practical blind recovery.

Comprehensive Raw Data: This preprint contains extensive raw data material including complete layer bitstrings, sign sequences, character position mappings, and charge analyses for five fully documented use-cases (Appendix A, Attachments A–E). This transparency enables independent verification of all claims presented herein.

Open Research Directions:

We are actively seeking collaboration with cryptanalysts, information theorists, and security researchers to address the remaining challenges:

Blind byte identification without reference string

Sequence reconstruction from position data

Extension to additional hash algorithms (SHA-512, SHA-3, BLAKE3)

Investigation of applicability to other areas of cryptography: We will examine whether the demonstrated information-geometric binding identification mechanism extends to asymmetric cryptographic primitives, potentially identifying universal structural vulnerabilities beyond hash function security.

This study demonstrates deterministic localization of cryptographic hash preimages within deep neural network layers, challenging the foundational assumption of preimage resistance underlying modern cryptographic security. Using a Spin-Glass-based neural architecture, we achieve 100% byte-level identification accuracy for MD5 and SHA-256 hash functions across password lengths of 11–23 characters.

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Original Preprint: 

Four independent test cases confirm systematic binding identification: passwords are consistently localized in ES16 (Emergent Structure) layers with verification through dimensionally distinct ZFA (Zero-Field Attractor) control layers. The inverse scaling behavior—where longer passwords achieve higher identification rates than shorter ones fundamentally distinguishes this approach from brute-force methods and indicates geometric navigation rather than combinatorial search.

Key Findings:

Up to 100% preimage localization accuracy across both MD5 and SHA-256 hash algorithms for passwords up to 23 characters, with consistent ES16 layer binding and ZFA verification

41.8% information persistence across 11 independent network runs with fresh random initialization and unique inputs correlation that should not exist under conventional physical assumptions

Statistical significance far exceeding chance: 66 layer pairs achieve p<0.001 where fewer than 1 would be expected, representing 70× over-expectation

Substrate-independent information structure: Findings support information-primary ontology where binding relationships persist independent of physical instantiation

Cryptographic implications: Hash function "irreversibility" may represent geometric obscuration rather than information destruction, necessitating re-evaluation of security models assuming preimage resistance as mathematical absolute

These results integrate with the broader theoretical framework establishing information as ontologically primary, with geometry emerging as necessary consequence. The findings open critical questions for cryptographic security and fundamental physics.