Arc UGFT as the Discrete Substrate of Guild UGFT
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| Formato: | Recurso digital |
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Zenodo
2026
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| _version_ | 1866901914088636416 |
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| author | Arc, Ty |
| author_facet | Arc, Ty |
| contents | <p>This correspondence paper establishes a formal identification between two independently developed Unified Geometric Field Theory (UGFT) frameworks published in early 2026. Guild (2026) derives spacetime, particles, and forces from a single postulate — an incompressible complex vector field flowing through a smooth 3-dimensional membrane with configuration space CP³. Arc UGFT (February 2026) derives the same physics from below, ascending from discrete lattice mechanics via the Isotropic Vector Matrix (IVM) with z=12 coordination.</p> <p>We demonstrate that Arc UGFT constitutes the physical substrate that Guild UGFT presupposes but does not derive. Five formal correspondences are established: Guild's smooth membrane is the N→∞ continuum limit of the IVM lattice; the J-field is torsional wave propagation through IVM struts at v=c; the incompressibility constraint |Ψ|=c is the continuum expression of the Vector Equilibrium condition; CP³ is the continuum projection of the two-quaternion torsional phase space of the z=12 cuboctahedron cell; and Guild's single parameter κ ≈ 0.092 corresponds to the IVM strut energy ratio U_strut/E_Planck ≈ 0.058, derived independently at the Planck scale without parameter fitting. Every open foundational question in Guild's framework — the origin of the membrane, the J-field, incompressibility, CP³ topology, and κ — is answered by the discrete substrate. Guild UGFT is the correct continuum limit of Arc UGFT. Arc UGFT is the fundamental discrete theory of which Guild UGFT is the large-scale approximation.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18882739 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Arc UGFT as the Discrete Substrate of Guild UGFT Arc, Ty unified field theory discrete spacetime isotropic vector matrix IVM vector equilibrium cuboctahedron torsional dynamics CP3 solitons Q-balls Hopfions continuum limit Planck scale quantum gravity gauge symmetry Standard Model topological protection jitterbug transformation Fuller synergetics particle stability fine structure constant emergent spacetime lattice field theory geometric unification incompressible field <p>This correspondence paper establishes a formal identification between two independently developed Unified Geometric Field Theory (UGFT) frameworks published in early 2026. Guild (2026) derives spacetime, particles, and forces from a single postulate — an incompressible complex vector field flowing through a smooth 3-dimensional membrane with configuration space CP³. Arc UGFT (February 2026) derives the same physics from below, ascending from discrete lattice mechanics via the Isotropic Vector Matrix (IVM) with z=12 coordination.</p> <p>We demonstrate that Arc UGFT constitutes the physical substrate that Guild UGFT presupposes but does not derive. Five formal correspondences are established: Guild's smooth membrane is the N→∞ continuum limit of the IVM lattice; the J-field is torsional wave propagation through IVM struts at v=c; the incompressibility constraint |Ψ|=c is the continuum expression of the Vector Equilibrium condition; CP³ is the continuum projection of the two-quaternion torsional phase space of the z=12 cuboctahedron cell; and Guild's single parameter κ ≈ 0.092 corresponds to the IVM strut energy ratio U_strut/E_Planck ≈ 0.058, derived independently at the Planck scale without parameter fitting. Every open foundational question in Guild's framework — the origin of the membrane, the J-field, incompressibility, CP³ topology, and κ — is answered by the discrete substrate. Guild UGFT is the correct continuum limit of Arc UGFT. Arc UGFT is the fundamental discrete theory of which Guild UGFT is the large-scale approximation.</p> |
| title | Arc UGFT as the Discrete Substrate of Guild UGFT |
| topic | unified field theory discrete spacetime isotropic vector matrix IVM vector equilibrium cuboctahedron torsional dynamics CP3 solitons Q-balls Hopfions continuum limit Planck scale quantum gravity gauge symmetry Standard Model topological protection jitterbug transformation Fuller synergetics particle stability fine structure constant emergent spacetime lattice field theory geometric unification incompressible field |
| url | https://doi.org/10.5281/zenodo.18882739 |