The Shiab Operator: Definition and Geometric Meaning
Shiab is the Einstein projection rebuilt out of transport, wedge, and $\ast_Y$—so gauge symmetry survives.
Gu
Einstein Contraction Fails in a Gauge Setting
The Ricci trace is a perfectly good move on tensor curvature—until curvature lives in $\mathrm{ad}(P_H)$.
Gauge-Covariant Bookkeeping: Double Disease Cancellation
Two bad transformation laws, one good variable.
The Distinguished Background
Choosing an affine origin (without adding structure) so transport becomes well-defined.
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.
Native vs Invasive Fields: Pullback Rules that Prevent Cheating
Fields don't live on spacetime by default—they must survive pullback from the observerse.
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.
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.
Metric Split Ansatz
We introduce a single scalar that controls how the ambient geometry breathes along unobserved directions.
Metric Split Ansatz
We introduce a single scalar that controls how the ambient geometry breathes along unobserved directions.
Immersion and the Tangent/Normal Split
The immersion is an observation map that carves spacetime into the ambient geometry and defines what survives 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.
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.
Transport-Based Viewpoint: Connections as Primary, Metric as Induced
Once torsion is recognized as a coordinate on connection space, geometry becomes a transport problem.