Saved in:
| Hovedforfatter: | |
|---|---|
| Format: | Recurso digital |
| Sprog: | engelsk |
| Udgivet: |
Zenodo
2026
|
| Fag: | |
| Online adgang: | https://doi.org/10.5281/zenodo.20089406 |
| Tags: |
Tilføj Tag
Ingen Tags, Vær først til at tagge denne postø!
|
Indholdsfortegnelse:
- <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>