Persistent Center Obstruction

Status

Proved under stated hypotheses.

Statement

The two nontrivial center sectors define conjugate nonzero relative cohomology classes that persist through the selected cofinal refinement family and retain meridional evaluations and .

For , the compatible finite-scale classes assemble into

Hence , and charge conjugation gives .

The point is persistence. A refinement may change the representative, but it cannot erase the marked meridional value while respecting the declared collar comparison.

Why it works

The collar-incision representative evaluates nontrivially on the canonical relative meridional cycle. Homotopy naturality identifies those evaluations under refinement; the extra refinement-representative term is exact in the homotopy fiber.

Example (illustrative)

At one regulator, the marked meridian evaluates to . After an allowed refinement, the meridian may be subdivided and its cochain representative altered, but the transported evaluation remains . The theorem identifies this as one persistent relative sector rather than unrelated finite-scale labels.

Scope and limits

The theorem labels and preserves the charged sector. It does not produce a positive Hamiltonian form, a passage eigenvalue, or a confinement slope.

Source

Phenomenological Implications I, §§3.1–3.2, Proposition 3.2 and Theorem 3.3.

Read the source manuscript.