We Are So Skewed

A torsion-first instantiation of Geometric Unity

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About

Or how I tried to make GU grow a universe.

Introduction — Why torsion-first / transport / observables

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.

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.

Transport-Based Viewpoint: Connections as Primary, Metric as Induced

Once torsion is recognized as a coordinate on connection space, geometry becomes a transport problem.

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.

Setup — Spin(7,7) stage, immersion, σ-split, axial torsion, no-cheating pullback

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.

Immersion and the Tangent/Normal Split

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

Metric Split Ansatz

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

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.

Gauge — H⋉N, A₀, augmented torsion T

Affine Space of Connections and Why the Gauge Group Must Be Inhomogeneous

Connections don't form a vector space, and that single fact quietly forces a bigger symmetry.

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.

The Distinguished Background

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

Augmented Torsion

The transport displacement that actually transforms like a field.

GR — Shiab, projectors, action, the GR corner

Einstein Contraction Fails in a Gauge Setting

The Ricci trace is a perfectly good move on tensor curvature—until curvature lives in $\mathrm{ad}(P_H)$.

The Shiab Operator: Definition and Geometric Meaning

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

Projector E: what “gravitational block” means operationally

A block is not a coordinate corner—it is a parallel subbundle selected by transport.

The calibrator form and what it selects

Normal saturation is the “trace” you are allowed to take in a gauge-covariant ambient theory.