| _version_ | 1866901827540221952 |
|---|---|
| author | BALL, ALAN |
| author_facet | BALL, ALAN |
| contents | <p>This paper specifies voxel gearing: a 1:1:4 rotational register for geared bodies on a cubic balanced-ternary substrate.</p> <p>The register is motivated by the dimensional packet π + π² + 4π³, read as axial circular closure, precessional surface sweep and four coupled body gears. The cubic host is the face-centred six-orbit of the 3×3×3 voxel neighbourhood under the octahedral group O_h.</p> <p>A geared body is treated as a local burdened body carrying a centred balanced-ternary register: one axial channel, one precession channel and four internal body channels. The four body channels are not ordinary spatial axes. They are internal centred gears whose field expression can flatten into a thin slab or distribute through deeper shallow volumes without changing the register identity.</p> <p>The paper defines the body-field-contact mechanism by which register state, field load, signed drive and contact work interact. It also reports browser-prototype validation results using live x:x:x controls, Full 1:1:4 geared drive, fixed four-body layouts, random eleven-body layouts and slab depths n_z = 1, 3, 7 and 11.</p> <p>The reported results support a narrow interpretation: Full 1:1:4 separates from the live x:x:x baseline in the random-register test, and deeper slabs carry larger body-channel loads without replacing the six-channel register. The work is presented as an instantiation and falsifier framework, not as a completed derivation of the local substrate law.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19917920 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Voxel Gearing: A 1:1:4 Rotational Register for Geared Bodies on the Cubic Substrate BALL, ALAN CAELIX voxel gearing balanced ternary cubic lattice discrete substrate rotational register 1:1:4 gearing π + π² + 4π³ integer field dynamics bounded integer Laplacian thin slab dimension uniformity body-field-contact mechanism signed drive contact work projection parity octahedral symmetry O_h 3×3×3 stencil face-centred orbit emergent field physics computational physics Discrete mathematics Mathematical physics Dynamical systems Theoretical physics <p>This paper specifies voxel gearing: a 1:1:4 rotational register for geared bodies on a cubic balanced-ternary substrate.</p> <p>The register is motivated by the dimensional packet π + π² + 4π³, read as axial circular closure, precessional surface sweep and four coupled body gears. The cubic host is the face-centred six-orbit of the 3×3×3 voxel neighbourhood under the octahedral group O_h.</p> <p>A geared body is treated as a local burdened body carrying a centred balanced-ternary register: one axial channel, one precession channel and four internal body channels. The four body channels are not ordinary spatial axes. They are internal centred gears whose field expression can flatten into a thin slab or distribute through deeper shallow volumes without changing the register identity.</p> <p>The paper defines the body-field-contact mechanism by which register state, field load, signed drive and contact work interact. It also reports browser-prototype validation results using live x:x:x controls, Full 1:1:4 geared drive, fixed four-body layouts, random eleven-body layouts and slab depths n_z = 1, 3, 7 and 11.</p> <p>The reported results support a narrow interpretation: Full 1:1:4 separates from the live x:x:x baseline in the random-register test, and deeper slabs carry larger body-channel loads without replacing the six-channel register. The work is presented as an instantiation and falsifier framework, not as a completed derivation of the local substrate law.</p> |
| title | Voxel Gearing: A 1:1:4 Rotational Register for Geared Bodies on the Cubic Substrate |
| topic | CAELIX voxel gearing balanced ternary cubic lattice discrete substrate rotational register 1:1:4 gearing π + π² + 4π³ integer field dynamics bounded integer Laplacian thin slab dimension uniformity body-field-contact mechanism signed drive contact work projection parity octahedral symmetry O_h 3×3×3 stencil face-centred orbit emergent field physics computational physics Discrete mathematics Mathematical physics Dynamical systems Theoretical physics |
| url | https://doi.org/10.5281/zenodo.19917920 |