In this torsion-first, transport-based instantiation, bosons are not planted onto spacetime $X$ as independent ingredients. They live natively on the ambient manifold $Y$ as adjoint-valued geometry.

Definitions / Notation used

• $Y$ is a 14D manifold with split signature $(7,7)$. $X$ is a 4D manifold immersed by $\iota: X \hookrightarrow Y$.
• Along $\iota(X)$: $TY|X \simeq TX \oplus N\iota$, with indices $\mu,\nu$ on $TX$; $a,b$ on $N_\iota$; and $M,N$ on $TY$.
• $g_X := \iota^\ast g_Y$. We use the $\sigma$-split: $g_Y \simeq g_X \oplus \sigma^2(x) \delta_{ab} \hat{n}^a \hat{n}^b$, and distinguish $\ast_X$ from $\ast_Y$.
• $H$ is the gauge group, $N := \Omega^1(Y,\mathrm{ad})$ ($\mathrm{ad} = \mathrm{ad}(P_H)$), and $G := H \ltimes N$. A generic gauge-affine variable is $\omega = (\varepsilon, \eta) \in G$.
• $A_0$ is the chosen background connection on $Y$. From $\omega$ we form $B_{\omega}$ (the transported/rotated connection built from $A_0$ and $\varepsilon$), its curvature $F_B$, and the augmented torsion $T$ (the covariant “difference” built from $\eta$ and $\varepsilon$ relative to $A_0$).
• The Shiab operator: $\bullet_\varepsilon$.

Main technical argument: bosons are not extra fields on $X$

In this instantiation, the bosonic sector is not a list of separate spacetime fields added to $X$. The bosonic sector is the adjoint-valued geometry on $Y$: the connection-like transport data, its curvature, and the torsion variable that makes the first-order theory gauge-covariant.

The basic transport variable is

$$ \omega = (\varepsilon,\vartheta) \in G = H \ltimes N, $$

where

$$ N = \Omega^1(Y,\mathrm{ad}(P_H)). $$

Thus $\vartheta$ is already an adjoint-valued 1-form on $Y$. The rotated connection is

$$ B_\omega := A_0 \cdot \varepsilon, $$

with curvature

$$ F_B \in \Omega^2(Y,\mathrm{ad}(P_H)). $$

A connection is not a tensor. We avoid treating the raw connection as the bosonic tensorial object. Instead, we make use of the augmented torsion

$$ T := \vartheta - \varepsilon^{-1} d_{A_0}\varepsilon, $$

which is an adjoint-valued 1-form with the correct covariance properties.

So the tensorial bosonic data are

$$ T \in \Omega^1(Y,\mathrm{ad}(P_H)), \qquad F_B \in \Omega^2(Y,\mathrm{ad}(P_H)). $$

That is the operational meaning of the phrase “Bosons are adjoint geometry.”

The bosonic degrees of freedom are the components, variations, and representations of $(T,F_B)$ in $\mathrm{ad}(P_H)$, before any low-energy decomposition into familiar particle names.

We are not assuming any symmetry at this point. The ambient structure is $\mathrm{Spin}(7,7)$ on $Y$, and the bosonic variables live in the adjoint geometry associated to $H$ and its transport extension $G=H\ltimes N$. The Standard-Model-like sector, if it appears, must appear later as a consequence of decomposition, projection, spectrum, and pullback.

The fundamental bosonic sector is generated by $(T,F_B)$ on $Y$.

There are no fundamental bosonic fields native to $X$. What $X$ sees are restrictions and pullbacks of $Y$-native objects.

What “adjoint” means operationally

Operationally, “adjoint” means that bosonic quantities transform in the adjoint representation of the gauge/transport structure. The curvature $F_B$ is adjoint-valued. The torsion variable $T$ is adjoint-valued. Linearized bosonic fluctuations are therefore variations of adjoint-valued geometric objects:

$$ \delta T \in \Omega^1(Y,\mathrm{ad}(P_H)), \qquad \delta F_B \in \Omega^2(Y,\mathrm{ad}(P_H)). $$

So a “boson” is not, at this stage, a named particle. It is an excitation direction in the adjoint-valued geometry.

After pullback to $X$, some of these directions may look like gauge bosons. Some may look like spin-connection-like degrees of freedom. Some may become heavy. Some may be projected out of the low-energy observer sector. But none of that should be assumed here.

Assumptions vs Consequences

Definitional

The ambient structure is $\mathrm{Spin}(7,7)$ on $Y$, with split signature $(7,7)$.

The physical spacetime is an immersed four-manifold

$$ \iota:X^4\hookrightarrow Y^{14}. $$

The bosonic variables are native to $Y$, not $X$.

The transport group is

$$ G=H\ltimes N, \qquad N=\Omega^1(Y,\mathrm{ad}(P_H)). $$

Ansatz

The metric split is

$$ g_Y\simeq g_X\oplus \sigma(x)^2\delta_{ab}\hat n^a\otimes \hat n^b. $$

The Shiab operator $\bullet_\varepsilon$ is fixed.

The selectors $E$ and $\Theta_E$ are fixed.

Axial torsion is default and non-perturbative.

Consequence

Bosons are not independent spacetime fields placed on $X$.

They are adjoint-valued geometric degrees of freedom on $Y$:

$$ T,\quad F_B,\quad \delta T,\quad \delta F_B. $$

The effective bosonic fields on $X$ arise by restriction, decomposition, and pullback.

Why this matters

• Once bosons are identified as adjoint geometry, we need a way to choose and describe directions inside $\mathrm{ad}(P_H)$.
• Masses should not be put in by hand. Once bosonic directions are identified, their effective masses can come from overlap, torsion, and normal-direction localization.
• Fermions couple to the pulled-back and induced bosonic geometry. Chirality selection only becomes meaningful once we know which bosonic components survive on $X$.

Key takeaway

Bosons are not extra fields added to spacetime. They are the adjoint-valued geometry of transport on $Y$. Spacetime $X$ sees them only through restriction and pullback.

Technical takeaway

$$ T\in\Omega^1(Y,\mathrm{ad}(P_H)), \quad F_B\in\Omega^2(Y,\mathrm{ad}(P_H)). $$

$$ \Upsilon_\omega=\bullet_\varepsilon(F_B)-\kappa_1T. $$

Bosonic observables on $X$ are derived from $\iota^\ast T,\ \iota^\ast F_B$, and their selected components.