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2026
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| Accesso online: | https://doi.org/10.5281/zenodo.19161151 |
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| author | Trees, Nala |
| author_facet | Trees, Nala |
| contents | <div> <div> <div> <div> <div dir="auto"> <div> <div> <p>This record contains Version 2.0 of <em>The Spectral Geometry of Coherence, Volume Two, Part Four</em>. The paper presents a compact, reproducible audit suite for testing whether capacity-horizon structure appears in canonical chaotic systems when measured through a small family of operational proxies. Across three engines, it asks whether a capacity-like scalar and related Dirichlet-style tension or roughness penalties show consistent signatures at regime boundaries, invariant structures, and transition events.</p> <p>Engine 1 evaluates horizon-style diagnostics on continuous-time chaos and a nonlinear PDE using Lorenz and Kuramoto–Sivashinsky targets, together with guarded texture variants and falsifier checks designed to rule out easy artefacts. Engine 2 provides a lightweight benchmark across three standard systems: the Lorenz flow, the Chirikov standard map, and the Hénon map. In the audited Lorenz run, a rolling-correlation-derived score shows above-chance discrimination of upcoming lobe-switch events over a short forecast horizon relative to a shuffle null; in the standard map, heatmap proxies separate the regular-island region from the surrounding chaotic sea; and in the Hénon map, the score exhibits intermittent bursts together with a stable threshold-occupancy profile.</p> <p>Engine 3 isolates the role of boundary regularity by comparing smooth, Weierstrass-type, and deterministic textured profiles under a Dirichlet energy penalty. The exported results recover the expected pattern: rough boundaries show resolution-dependent energy growth, while smooth boundaries remain stable under refinement. The overall positioning is exploratory and reproducibility-driven rather than universalist: definitions, parameters, outputs, and falsifier checks are made explicit so the suite can be rerun and inspected, and the paper does not claim preregistration or a universal law of chaos.</p> <p><strong>Keywords</strong><br>chaos diagnostics; capacity horizons; Dirichlet tension; Lorenz system; Kuramoto–Sivashinsky; Chirikov standard map; Hénon map; boundary roughness; Weierstrass-type boundaries; reproducibility</p> <p><strong>DOI</strong><br><a target="_new" rel="noopener">https://doi.org/10.5281/zenodo.19161151</a></p> <p><strong>DOI list</strong></p> <p><strong>Part 1: Capacity Geometry: REG, Dirichlet Tension, and Quasi-Local Mass, v2.0 </strong><a href="https://doi.org/10.5281/zenodo.19156067" target="_blank" rel="noopener">https://doi.org/10.5281/zenodo.19156067</a></p> <p><strong>Part 1a: The Canonical Capacity Coordinate and the Unique Quadratic Tension in the Capacity Gauge v2.0 </strong><a href="https://doi.org/10.5281/zenodo.19156067" target="_blank" rel="noopener">https://doi.org10.5281/zenodo.19156316</a></p> <p><strong>Part 2: <em>Mass as Spectral Data in Capacity Geometry: Bulk Corridors and Bubble Caps, v2.0</em></strong><br><a target="_new" rel="noopener">https://doi.org/10.5281/zenodo.19161229</a></p> <p><strong>Part 3: <em>An Operational Verification Suite for a Capacity-Field Gravity Readout: Dual-Engine Poisson-Bridge Gates, Relativity Coherence Checks, and REG Micro-Audits, v2.0</em></strong><br><a target="_new" rel="noopener">https://doi.org/10.5281/zenodo.19161141</a></p> <p><strong>Part 4 (This part): <em>Capacity Horizons as Chaos Diagnostics in Dynamical Systems: Dirichlet-Tension and Roughness Tests (including Weierstrass-type boundaries), v2.0</em></strong><br><a target="_new" rel="noopener">https://doi.org/10.5281/zenodo.19161151</a></p> </div> </div> </div> </div> </div> </div> </div> <div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19161151 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Capacity Horizons as Chaos Diagnostics in Dynamical Systems: Dirichlet-Tension and Roughness Tests (including Weierstrass-type boundaries) Trees, Nala <div> <div> <div> <div> <div dir="auto"> <div> <div> <p>This record contains Version 2.0 of <em>The Spectral Geometry of Coherence, Volume Two, Part Four</em>. The paper presents a compact, reproducible audit suite for testing whether capacity-horizon structure appears in canonical chaotic systems when measured through a small family of operational proxies. Across three engines, it asks whether a capacity-like scalar and related Dirichlet-style tension or roughness penalties show consistent signatures at regime boundaries, invariant structures, and transition events.</p> <p>Engine 1 evaluates horizon-style diagnostics on continuous-time chaos and a nonlinear PDE using Lorenz and Kuramoto–Sivashinsky targets, together with guarded texture variants and falsifier checks designed to rule out easy artefacts. Engine 2 provides a lightweight benchmark across three standard systems: the Lorenz flow, the Chirikov standard map, and the Hénon map. In the audited Lorenz run, a rolling-correlation-derived score shows above-chance discrimination of upcoming lobe-switch events over a short forecast horizon relative to a shuffle null; in the standard map, heatmap proxies separate the regular-island region from the surrounding chaotic sea; and in the Hénon map, the score exhibits intermittent bursts together with a stable threshold-occupancy profile.</p> <p>Engine 3 isolates the role of boundary regularity by comparing smooth, Weierstrass-type, and deterministic textured profiles under a Dirichlet energy penalty. The exported results recover the expected pattern: rough boundaries show resolution-dependent energy growth, while smooth boundaries remain stable under refinement. The overall positioning is exploratory and reproducibility-driven rather than universalist: definitions, parameters, outputs, and falsifier checks are made explicit so the suite can be rerun and inspected, and the paper does not claim preregistration or a universal law of chaos.</p> <p><strong>Keywords</strong><br>chaos diagnostics; capacity horizons; Dirichlet tension; Lorenz system; Kuramoto–Sivashinsky; Chirikov standard map; Hénon map; boundary roughness; Weierstrass-type boundaries; reproducibility</p> <p><strong>DOI</strong><br><a target="_new" rel="noopener">https://doi.org/10.5281/zenodo.19161151</a></p> <p><strong>DOI list</strong></p> <p><strong>Part 1: Capacity Geometry: REG, Dirichlet Tension, and Quasi-Local Mass, v2.0 </strong><a href="https://doi.org/10.5281/zenodo.19156067" target="_blank" rel="noopener">https://doi.org/10.5281/zenodo.19156067</a></p> <p><strong>Part 1a: The Canonical Capacity Coordinate and the Unique Quadratic Tension in the Capacity Gauge v2.0 </strong><a href="https://doi.org/10.5281/zenodo.19156067" target="_blank" rel="noopener">https://doi.org10.5281/zenodo.19156316</a></p> <p><strong>Part 2: <em>Mass as Spectral Data in Capacity Geometry: Bulk Corridors and Bubble Caps, v2.0</em></strong><br><a target="_new" rel="noopener">https://doi.org/10.5281/zenodo.19161229</a></p> <p><strong>Part 3: <em>An Operational Verification Suite for a Capacity-Field Gravity Readout: Dual-Engine Poisson-Bridge Gates, Relativity Coherence Checks, and REG Micro-Audits, v2.0</em></strong><br><a target="_new" rel="noopener">https://doi.org/10.5281/zenodo.19161141</a></p> <p><strong>Part 4 (This part): <em>Capacity Horizons as Chaos Diagnostics in Dynamical Systems: Dirichlet-Tension and Roughness Tests (including Weierstrass-type boundaries), v2.0</em></strong><br><a target="_new" rel="noopener">https://doi.org/10.5281/zenodo.19161151</a></p> </div> </div> </div> </div> </div> </div> </div> <div> </div> |
| title | Capacity Horizons as Chaos Diagnostics in Dynamical Systems: Dirichlet-Tension and Roughness Tests (including Weierstrass-type boundaries) |
| url | https://doi.org/10.5281/zenodo.19161151 |