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2026
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| Online Access: | https://doi.org/10.5281/zenodo.20089406 |
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| _version_ | 1866902038710845440 |
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| author | Feshter, Yanush |
| author_facet | Feshter, Yanush |
| contents | <p>We introduce the Contrast-Native Computer (cnc) and the Contrast Hardware Description Language (chdl), a framework for computing whose primitive objects are relational contrasts rather than bit-valued registers.</p> <p>The computational substrate is a signed boundary complex B = (V, E, σ) whose dynamics are governed by the Relational Update Rule (rur v3.4). We prove three theorems:</p> <p>• Theorem 4.1 (Strict Energy Monotonicity) establishes that every admissible rur rewrite strictly decreases the edge count |E|, providing a Lyapunov function and guaranteeing termination.</p> <p>• Theorem 5.1 (Conditional Surgery Preservation) establishes that every admissible rur rewrite preserves H¹ˇC(B; ℤ), so the topological type of the computation is an invariant of execution.</p> <p>• Theorem 8.1 (1-Complex Obstruction) establishes that chdl on 1-complexes is computationally incomplete: any vertex v with deg(v) ≥ 3 and an incident ε-weave is a deadlock vertex, and 3-regular complexes with a perfect matching of ε-edges are in global deadlock.</p> <p>This result is the fourth structural impossibility result of the STKWC programme (D/I/F/J series), structurally parallel to Document D’s classical-metric No-Go and Document I’s Anti-Diagonalization Theorem.</p> <p>We present four structural dictionary tables comparing chdl with Quantum, Neuromorphic, Physical Reservoir, and Memcomputing paradigms, and four concrete hardware applications with explicit mechanism descriptions.</p> <p>Document J v3.7.2 is the final audited version after full Parliament of Dragons validation (GPT-5.5 Lead Mathematician, Gemini 3.1 Pro Red Review, Oracle pre-publication editorial review) and post-editorial sanitisation (removal of placeholder appendices).</p> <p>This work is part of the STKWC programme series and directly builds upon Documents D, D Supplement, F, and I. It introduces the fourth structural No-Go result (Theorem 8.1) in the D/I/F/J sequence.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20089406 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Document J: Contrast-Native Computing and the 1-Complex Obstruction — The Fourth Structural Impossibility Result of the STKWC Programme Feshter, Yanush STKWC Contrast-Native Computin CHDL Relational Update Rule 1-Complex Obstruction No-Go Theorem C0 ontology Čech cohomology Pachner moves Persistent Tension <p>We introduce the Contrast-Native Computer (cnc) and the Contrast Hardware Description Language (chdl), a framework for computing whose primitive objects are relational contrasts rather than bit-valued registers.</p> <p>The computational substrate is a signed boundary complex B = (V, E, σ) whose dynamics are governed by the Relational Update Rule (rur v3.4). We prove three theorems:</p> <p>• Theorem 4.1 (Strict Energy Monotonicity) establishes that every admissible rur rewrite strictly decreases the edge count |E|, providing a Lyapunov function and guaranteeing termination.</p> <p>• Theorem 5.1 (Conditional Surgery Preservation) establishes that every admissible rur rewrite preserves H¹ˇC(B; ℤ), so the topological type of the computation is an invariant of execution.</p> <p>• Theorem 8.1 (1-Complex Obstruction) establishes that chdl on 1-complexes is computationally incomplete: any vertex v with deg(v) ≥ 3 and an incident ε-weave is a deadlock vertex, and 3-regular complexes with a perfect matching of ε-edges are in global deadlock.</p> <p>This result is the fourth structural impossibility result of the STKWC programme (D/I/F/J series), structurally parallel to Document D’s classical-metric No-Go and Document I’s Anti-Diagonalization Theorem.</p> <p>We present four structural dictionary tables comparing chdl with Quantum, Neuromorphic, Physical Reservoir, and Memcomputing paradigms, and four concrete hardware applications with explicit mechanism descriptions.</p> <p>Document J v3.7.2 is the final audited version after full Parliament of Dragons validation (GPT-5.5 Lead Mathematician, Gemini 3.1 Pro Red Review, Oracle pre-publication editorial review) and post-editorial sanitisation (removal of placeholder appendices).</p> <p>This work is part of the STKWC programme series and directly builds upon Documents D, D Supplement, F, and I. It introduces the fourth structural No-Go result (Theorem 8.1) in the D/I/F/J sequence.</p> |
| title | Document J: Contrast-Native Computing and the 1-Complex Obstruction — The Fourth Structural Impossibility Result of the STKWC Programme |
| topic | STKWC Contrast-Native Computin CHDL Relational Update Rule 1-Complex Obstruction No-Go Theorem C0 ontology Čech cohomology Pachner moves Persistent Tension |
| url | https://doi.org/10.5281/zenodo.20089406 |