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geometric unity

(27 articles)

Ground-state fermion content on $X$

This article describes the ground-sector fermionic content induced on $X$ from the ambient spinor pair $(\nu, \zeta)$.

geometric unityguphysicssciencefermions

Axial torsion as a chirality filter: the mechanism

Axial torsion shifts the effective spectrum so one handedness wins the ground state.

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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 $S_Y$.

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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.

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Augmented Torsion

The transport displacement that actually transforms like a field.

geometric unityguphysicsscienceaugmented torsion

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.

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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.

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Masses for bosons without Higgs: torsion as the mass operator

How a covariant quadratic in augmented torsion becomes a 4D mass matrix.

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Diagonalizing the visible adjoint geometry

A basis discipline for spectra and mass terms.

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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.

geometric unityguphysicssciencebosons

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.

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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.

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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.

geometric unityguphysicssciencegeometry

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.

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About

Or how I tried to make GU grow a universe.

introaboutgugeometric unity

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 $T.$

geometric unityguphysicsscienceactioneuler-lagrangetorsion

The Shiab Operator: Definition and Geometric Meaning

Shiab is the Einstein projection rebuilt out of transport, wedge, and $\ast_Y$—so gauge symmetry survives.

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The Distinguished Background

Choosing an affine origin (without adding structure) so transport becomes well-defined.

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Native vs Invasive Fields: Pullback Rules that Prevent Cheating

Fields don't live on spacetime by default—they must survive pullback from the observerse.

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Axial Torsion as the Default: Where It Lives and What It Does

Axial torsion is the engine that distinguishes chirality, drives overlap physics, and deforms geometry from the inside.

geometric unityguphysicssciencetorsion

Axial Torsion as the Default: Where It Lives and What It Does

Axial torsion is the engine that distinguishes chirality, drives overlap physics, and deforms geometry from the inside.

geometric unityguphysicssciencetorsion

Metric Split Ansatz

We introduce a single scalar that controls how the ambient geometry breathes along unobserved directions.

geometric unityguphysicssciencemetric

Metric Split Ansatz

We introduce a single scalar that controls how the ambient geometry breathes along unobserved directions.

geometric unityguphysicssciencemetric

Immersion and the Tangent/Normal Split

The immersion is an observation map that carves spacetime into the ambient geometry and defines what survives pullback.

geometric unityguphysicsscienceimmersion

The Ambient Stage: Y with Split Signature and Why It’s Not Optional

In this post, we zoom out to the 14D ambient space Y, where Geometric Unity actually lives. We’re not compactifying, slicing, or bolting on extra fields. Instead, everything we observe—fields, particles, interactions—is a consequence of how 4D spacetime immerses into a larger, structurally rigid arena.

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What Counts as an Observable: Invariants After Pullback

This post defines observables in Geometric Unity: quantities that are invariant under transport symmetry and stable under pullback.

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Chirality from Torsion and Immersion in Geometric Unity

In Geometric Unity (GU), chirality is not fundamental on the ambient space $Y$. It emerges on the observed $4$-manifold $X$ from three intertwined ingredients: (i) an immersion (observation map) $\iota: X \hookrightarrow Y$ and pullback of fields, (ii) a gauge-equivariant torsion that generates a $\gamma_5$ coupling, and (iii) the signature/orientation data that fixes which chirality survives upon pullback.

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