Energetic Confinement on a Selected Branch

Meaning

Energetic confinement on a selected branch means that separating the two nontrivial center sectors by distance requires energy bounded below by a positive linear function of , up to a uniform endpoint constant.

The mechanism is not introduced as a microscopic string. A nontrivial center charge that cannot be ordinarily filled must pass through every certified separator. If each passage has a positive price and a corridor of length contains order disjoint certified passages, the total lower bound is linear.

Example (illustrative)

Think of a long source-free corridor sliced by separated collars. The state is not decomposed into mutually exclusive probabilities at those collars. Rather, each collar is a supported view of the same transported charged datum, and the local forms have disjoint support. The passage costs can therefore add without violating normalization.

Scope and limits

This notion is not identical to a mass gap, a Wilson-loop area law, or a microscopic flux tube. The Wilson-tube consequence requires a separate transfer identity. A string-like worldsheet, if it emerges, is downstream of this theorem.

Source

Phenomenological Implications I, §§8–11, especially Theorem 10.1 and §11.3.

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