Through the Bank Gate: Thomas Holonomy and the R^8 Lorentz Atlas A Bank-Anchored Synthesis of Contact Gates, Two Gears, Disk Boosts, and Sector Holonomy
Fuente:
Zenodo
Saved in:
| Main Author: | |
|---|---|
| Format: | Recurso digital |
| Published: |
Zenodo
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866901153832239104 |
|---|---|
| author | Diogenes |
| author_facet | Diogenes |
| contents | <p>This synthesis note assembles the current \(R^8\) projection route into one claim-bounded architecture. The internal Bank is modeled as an \(E_8\)-torus carrier \(T^8_{E_8}=\mathbb R^8/\Lambda_{E_8}\), equipped with affine \(Z_{48}\) governance and a non-split hidden parity fiber \(0\to Z_{24}\to Z_{48}\to Z_2\to0\). A rank-4 selector \(P(x)\) supplies the formal Bank-to-Leaf visible channel, while a distinct parity-blind projection \(\Pi_p\) coarse-grains the hidden \(Z_2\) sheet. In the effective projected equation, residual projection leakage \(\epsilon>0\), together with positive coefficients \(Z_t,Z_x\), activates a hyperbolic principal form and a finite causal speed \(c^2=Z_x/(2\epsilon Z_t)\). This establishes a Lorentzian causal seed, not a completed Lorentz-covariant dynamics theorem.</p> <p>The same leakage parameter supports a specific bounded-regime parity-dephasing channel, producing a projection-ratchet entropy arrow for states with hidden parity coherence. Once a finite causal cone is present, the aligned real disk slice recovers SR-like boost kinematics, while exact disk-boost algebra produces Thomas/Wigner holonomy for non-collinear boosts. A Bank-centered \(Z_6\) contact atlas organizes sector-orientation grammar, and a Hopf/shear TT branch is retained only as a candidate diagnostic bridge toward tensor sourcing. The note does not claim a completed Lorentz/Poincare theorem, a full GR derivation, or a measured value of \(c\). Full \(SO(3,1)\) closure, event-address covariance, the exact microscopic form of \(P(x)\), and physical calibration of \(Z_x/Z_t\) remain open courts.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19659933 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Through the Bank Gate: Thomas Holonomy and the R^8 Lorentz Atlas A Bank-Anchored Synthesis of Contact Gates, Two Gears, Disk Boosts, and Sector Holonomy Diogenes Crystalline Axiverse <p>This synthesis note assembles the current \(R^8\) projection route into one claim-bounded architecture. The internal Bank is modeled as an \(E_8\)-torus carrier \(T^8_{E_8}=\mathbb R^8/\Lambda_{E_8}\), equipped with affine \(Z_{48}\) governance and a non-split hidden parity fiber \(0\to Z_{24}\to Z_{48}\to Z_2\to0\). A rank-4 selector \(P(x)\) supplies the formal Bank-to-Leaf visible channel, while a distinct parity-blind projection \(\Pi_p\) coarse-grains the hidden \(Z_2\) sheet. In the effective projected equation, residual projection leakage \(\epsilon>0\), together with positive coefficients \(Z_t,Z_x\), activates a hyperbolic principal form and a finite causal speed \(c^2=Z_x/(2\epsilon Z_t)\). This establishes a Lorentzian causal seed, not a completed Lorentz-covariant dynamics theorem.</p> <p>The same leakage parameter supports a specific bounded-regime parity-dephasing channel, producing a projection-ratchet entropy arrow for states with hidden parity coherence. Once a finite causal cone is present, the aligned real disk slice recovers SR-like boost kinematics, while exact disk-boost algebra produces Thomas/Wigner holonomy for non-collinear boosts. A Bank-centered \(Z_6\) contact atlas organizes sector-orientation grammar, and a Hopf/shear TT branch is retained only as a candidate diagnostic bridge toward tensor sourcing. The note does not claim a completed Lorentz/Poincare theorem, a full GR derivation, or a measured value of \(c\). Full \(SO(3,1)\) closure, event-address covariance, the exact microscopic form of \(P(x)\), and physical calibration of \(Z_x/Z_t\) remain open courts.</p> |
| title | Through the Bank Gate: Thomas Holonomy and the R^8 Lorentz Atlas A Bank-Anchored Synthesis of Contact Gates, Two Gears, Disk Boosts, and Sector Holonomy |
| topic | Crystalline Axiverse |
| url | https://doi.org/10.5281/zenodo.19659933 |