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2026
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| Online Access: | https://doi.org/10.5281/zenodo.19189960 |
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| _version_ | 1866901732481564672 |
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| author | Trees, Nala |
| author_facet | Trees, Nala |
| contents | <p>This record contains <em>The Ledger Hamiltonian on a Capacity Background</em>, a standalone companion note within the Spectral Geometry of Coherence (SGOC) programme.</p> <p>The paper studies a distinct theorem lane from the general Schrödinger paper. Its focus is the chart-covariant first-order Hamiltonian and continuity structure induced by a fixed capacity background, rather than the density-phase forced-action classification treated in <em>The Schrödinger Equation from Capacity Geometry</em>. Working on the phase chart, the note identifies the natural first-order self-adjoint Hamiltonian representative associated with exact advection, tracks its measured-chart form, and records the corresponding continuity law, current, and falsifier structure.</p> <p>The claim is exact within its lane and no broader. This is a fixed-background, first-order transport result. It does not by itself claim the forced density-phase action theorem of the separate Schrödinger paper, and it does not claim a many-body theory, measurement theory, relativistic completion, or backreaction of the transported sector on the background geometry.</p> <p>Within the SGOC programme, this note should be read as complementary to, but distinct from, <em>The Schrödinger Equation from Capacity Geometry</em>. The present paper isolates the chart-covariant Hamiltonian generator and continuity structure on the phase chart; the Schrödinger paper addresses the separate fixed-background density-phase action lane. The note also serves as a conceptual bridge to the downstream hydrogen toy-model note, where the fixed-background framework is used as a spectral probe.</p> <p><strong>Keywords</strong><br>capacity geometry; Hamiltonian; exact advection; continuity law; phase chart; fixed background; transport generator; SGOC</p> <p><strong>Related identifiers</strong></p> <ul> <li><code>Cites</code> -> <strong>10.5281/zenodo.19156316</strong><br><em>The Canonical Capacity Coordinate and the Unique Quadratic Tension in the Capacity Gauge</em></li> <li><code>IsSupplementTo</code> -> <strong>10.5281/zenodo.19189901</strong><br><em>The Schrödinger Equation from Capacity Geometry</em></li> <li><code>IsSupplementTo</code> -> <strong>10.5281/zenodo.19191108</strong><br><em>The Hydrogen Atom on a Capacity Background</em></li> </ul> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19189960 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Ledger Hamiltonian on a Capacity Background Trees, Nala <p>This record contains <em>The Ledger Hamiltonian on a Capacity Background</em>, a standalone companion note within the Spectral Geometry of Coherence (SGOC) programme.</p> <p>The paper studies a distinct theorem lane from the general Schrödinger paper. Its focus is the chart-covariant first-order Hamiltonian and continuity structure induced by a fixed capacity background, rather than the density-phase forced-action classification treated in <em>The Schrödinger Equation from Capacity Geometry</em>. Working on the phase chart, the note identifies the natural first-order self-adjoint Hamiltonian representative associated with exact advection, tracks its measured-chart form, and records the corresponding continuity law, current, and falsifier structure.</p> <p>The claim is exact within its lane and no broader. This is a fixed-background, first-order transport result. It does not by itself claim the forced density-phase action theorem of the separate Schrödinger paper, and it does not claim a many-body theory, measurement theory, relativistic completion, or backreaction of the transported sector on the background geometry.</p> <p>Within the SGOC programme, this note should be read as complementary to, but distinct from, <em>The Schrödinger Equation from Capacity Geometry</em>. The present paper isolates the chart-covariant Hamiltonian generator and continuity structure on the phase chart; the Schrödinger paper addresses the separate fixed-background density-phase action lane. The note also serves as a conceptual bridge to the downstream hydrogen toy-model note, where the fixed-background framework is used as a spectral probe.</p> <p><strong>Keywords</strong><br>capacity geometry; Hamiltonian; exact advection; continuity law; phase chart; fixed background; transport generator; SGOC</p> <p><strong>Related identifiers</strong></p> <ul> <li><code>Cites</code> -> <strong>10.5281/zenodo.19156316</strong><br><em>The Canonical Capacity Coordinate and the Unique Quadratic Tension in the Capacity Gauge</em></li> <li><code>IsSupplementTo</code> -> <strong>10.5281/zenodo.19189901</strong><br><em>The Schrödinger Equation from Capacity Geometry</em></li> <li><code>IsSupplementTo</code> -> <strong>10.5281/zenodo.19191108</strong><br><em>The Hydrogen Atom on a Capacity Background</em></li> </ul> |
| title | The Ledger Hamiltonian on a Capacity Background |
| url | https://doi.org/10.5281/zenodo.19189960 |