2+1 generations
Three generations of fermions and how they are related.
Gu
Ground-state fermion content on $X$
This article describes the ground-sector fermionic content induced on $X$ from the ambient spinor pair $(\nu, \zeta)$.
Axial torsion as a chirality filter: the mechanism
Axial torsion shifts the effective spectrum so one handedness wins the ground state.
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 $S_Y$.
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.
Augmented Torsion
The transport displacement that actually transforms like a field.
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.
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.
Masses for bosons without Higgs: torsion as the mass operator
How a covariant quadratic in augmented torsion becomes a 4D mass matrix.
Diagonalizing the visible adjoint geometry
A basis discipline for spectra and mass terms.
Which components look like gauge bosons after pullback
How to derive spacetime fields $X$ can actually see.
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.
Projector E: what “gravitational block” means operationally
A block is not a coordinate corner—it is a parallel subbundle selected by transport.
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.
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.
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.
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.
About
Or how I tried to make GU grow a universe.
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 $T.$
The calibrator form and what it selects
Normal saturation is the “trace” you are allowed to take in a gauge-covariant ambient theory.