What EH Says

Every result you have read in this body of work hangs on one thread.

The Embedding Hypothesis (EH) states: the algebraic pre-state structure defined by {S, B, R, C} embeds into physical reality.

Every Artist’s Proof — AP05 through AP19, and AP24 — is conditional on EH.

The derivations are valid: if EH holds, then spacetime, quantum mechanics, general relativity, the Standard Model gauge structure, and all other results follow from the axioms.

But if EH does not hold, the derivations remain mathematical theorems about an algebraic structure that may or may not describe our world.

This paper proves that EH holds.

The conditional is removed. The results become unconditional.

A common misreading separates EH into two claims: an algebraic claim (the axioms hold in reality) and a geometric claim (the algebra embeds into a smooth manifold).

This separation imports assumptions from outside the argument.

Within the axioms, these are the same claim read from two sides. The argument is given in 5.