Manuscript XXII-C@1 · XXII-C.tex · remark · b9a05a24

Remark: A closed-cone limit can introduce a new comparison

Continuum, refinement, and evidence discipline › Event and cone extensions · lines 1239–1253

XXII-C@1#rem:closure

Even with a fixed closed Lorentz cone, vectors outside it may converge to its boundary:

v_{n} = (1, 1 + 1/ n, 0, \dots, 0) \in / L_{m}, v_{n} ⟶ (1, 1, 0, \dots, 0) \in L_{m} .

Thus convergence of coordinates alone does not prove the absence of spurious order comparisons at the limit.

This is a mathematical diagnostic, not a Lorentz cone installed as the output of the frozen extraction.

Displayed formulas in this passage

unlabeled · line 1243
$v_{n} = (1, 1 + 1/ n, 0, \dots, 0) \in / L_{m}, v_{n} ⟶ (1, 1, 0, \dots, 0) \in L_{m} .$