We experience a four-dimensional world. GU claims that world is a projection. The machinery that generates it lives elsewhere.

The single technical move: pullback kills normal legs

Fields on $Y$ decompose relative to $TY|X \simeq TX \oplus N\iota$.

Under pullback:

• Components with any normal index vanish.
• Only fully tangential components survive.

This simple fact enforces the native/invasive distinction.

Native vs invasive

• Native on $X$: the immersion $\iota$ (equivalently $g_X$).
• Invasive from $Y$ : $\omega$, $T$, $F_B$, spinors, gauge fields.

Observers never access invasive fields directly—only their tangential projections or invariant effects.

Why this matters

This explains why internal symmetries and particle content can originate geometrically without being visible as extra dimensions. The observerse filters information by pullback, not by truncation.

Key takeaway

We live on $X$, but physics lives on $Y$. Pullback determines what survives.

Technical takeaway

$\iota^*$ annihilates normal components. Physical fields on $X$ are tangential projections or invariants of $Y$-fields.