The Effective Dirac Operator and Fermion Flux on the Observer Slice
An overview of dynamics.
vor 4 Mon.4 mo ago8 Min.8 min
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Ground-state fermion content on $X$
This article describes the ground-sector fermionic content induced on $X$ from the ambient spinor pair $(\nu, \zeta)$.
vor 4 Mon.4 mo ago8 Min.8 min
Axial torsion as a chirality filter: the mechanism
Axial torsion shifts the effective spectrum so one handedness wins the ground state.
vor 4 Mon.4 mo ago6 Min.6 min
Can chirality emerge without imposing a Weyl condition
“Chiral on $X$” is a statement about the pulled-back spectrum in a torsion background, not a constraint pre-imposed on $S_Y$.
vor 4 Mon.4 mo ago4 Min.4 min
Spinors and fermions
How spinors on $Y$ become fermions on $X$. The observer never gets 14D fermions on $X$; they get a pulled-back slice of a 14D spinor, decomposed by the tangent/normal split.
vor 4 Mon.4 mo ago5 Min.5 min
Augmented Torsion
The transport displacement that actually transforms like a field.
vor 8 Mon.8 mo ago3 Min.3 min
The Inhomogeneous Group G: Actions and "Transport"
Once you admit translations in connection space, you're forced into a semidirect product — and it acts on connections in one line.
vor 8 Mon.8 mo ago4 Min.4 min
Welcome to Essayist
Essayist enables community curation and direct support, connecting readers to writers with no intermediary.
vor 4 Mon.4 mo ago1 Min.1 min
Selection rules: why most ambient modes never become 4D bosons
Pullback is only the first gate; $(E,\Theta_E)$, physical-corner projection, and normal spectral suppression do the rest.
vor 5 Mon.5 mo ago7 Min.7 min
Masses for bosons without Higgs: torsion as the mass operator
How a covariant quadratic in augmented torsion becomes a 4D mass matrix.
vor 5 Mon.5 mo ago6 Min.6 min
Diagonalizing the visible adjoint geometry
A basis discipline for spectra and mass terms.
vor 5 Mon.5 mo ago7 Min.7 min
Which components look like gauge bosons after pullback
How to derive spacetime fields $X$ can actually see.
vor 5 Mon.5 mo ago6 Min.6 min
What the bosons are
In this instantiation, "bosons" are not extra fields on $X$; they are the ambient connection, curvature, and torsion data on $Y^{14}$, seen through restriction and pullback.
vor 5 Mon.5 mo ago5 Min.5 min
Projector E: what “gravitational block” means operationally
A block is not a coordinate corner—it is a parallel subbundle selected by transport.
vor 5 Mon.5 mo ago6 Min.6 min
Physics on Y, Experience on X
Geometric Unity separates where physics lives from where it is experienced. This post introduces the native vs invasive distinction and explains how pullback filters physical content.
vor 5 Mon.5 mo ago1 Min.1 min
Why Torsion Can't Be a Perturbation in This Instantiation
Geometric Unity does not introduce torsion as an extension of GR; it introduces it as the only covariant coordinate on the space of connections. This post explains why torsion must be defined as a difference variable relative to a background connection, and why treating it perturbatively is meaningless.
vor 6 Mon.6 mo ago3 Min.3 min
Two Geometries Problem: Riemann vs Ehresmann
Modern physics rests on two incompatible geometric formalisms: Riemannian geometry for gravity and Ehresmann (connection-based) geometry for gauge fields. This post isolates the precise obstruction to unifying them and explains why Geometric Unity (GU) does not attempt to merge them naively, but instead replaces a single crucial operation.
vor 6 Mon.6 mo ago3 Min.3 min
Second-order theory as a square: what you gain, what you lose
The square is where you buy robustness, at the price of admitting extra solutions.
vor 6 Mon.6 mo ago5 Min.5 min
First order torsion-first field equation: structure and interpretation
If torsion-first is going to mean anything operational, the action has to be written in variables you are actually allowed to vary. The only thing you can safely push through an Euler-Lagrange variation is a covariant field on $Y.$ That field is the augmented torsion $T.$
vor 7 Mon.7 mo ago4 Min.4 min
The Shiab Operator: Definition and Geometric Meaning
Shiab is the Einstein projection rebuilt out of transport, wedge, and $\ast_Y$—so gauge symmetry survives.
vor 7 Mon.7 mo ago5 Min.5 min
Einstein Contraction Fails in a Gauge Setting
The Ricci trace is a perfectly good move on tensor curvature—until curvature lives in $\mathrm{ad}(P_H)$.
vor 7 Mon.7 mo ago6 Min.6 min
Gauge-Covariant Bookkeeping: Double Disease Cancellation
Two bad transformation laws, one good variable.
vor 8 Mon.8 mo ago4 Min.4 min
The Distinguished Background
Choosing an affine origin (without adding structure) so transport becomes well-defined.
vor 8 Mon.8 mo ago4 Min.4 min