theorem · THM-PHENI-NO-BOUNDED-SEPARATION

No Bounded-Energy Separation

source-verified gat phenomenology confinement
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Status

Conditional corollary.

Open finite certificate — DP2/P06. The criterion is proved, but a completed numerical pure confinement certificate still requires

and a rigorous positive lower endpoint for the least generalized eigenvalue of every normalized passage block, together with the named imported completion certificates.

Statement

Under the confinement-reduction hypotheses, the minimum energy in either nontrivial center sector diverges as the source separation tends to infinity, and pure adjoint screening does not change that conclusion.

For ,

Example (illustrative)

No sequence of normalized selected states can carry the external charges to arbitrarily large separation while keeping the centered energy uniformly bounded. If such a sequence existed, it would contradict the positive linear lower bound.

Scope and limits

Retain the source designation Corollary. The statement inherits every hypothesis and every open/imported gate of Theorem 10.1. It is not an independent unconditional result.

Source

Phenomenological Implications I, Corollary 10.2.

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