Manuscript VII-E@1 · VII-E.tex · proposition · b713cf3c
Proposition: Frozen exterior and particle data
One certified four-face slicing exchange › Attachment to one frozen conical exterior · lines 2331–2360 · proof included or linked
VII-E@1#prop:exterior, VII-E@1#eq:frozen-observables
Both event germs use the same boundary labels, eight fixed spatial boundary segments, constant boundary lengths, resting boundary time law , and fixed outgoing transitions. The exterior cellulation, cone metric, and resting particle neighbourhood are not rewritten.
On both sides of the event,
Proof. The construction matches the same resting plane near the same fixed boundary. The exterior grid is independent of in spatial coordinates, and its affine time law is prescribed once.
A particle loop can be chosen in the unchanged neighbourhood of the axis and has exactly the word eq:particle-word. A path that enters the patch acquires a telescoping affine word determined by its endpoint charts. Changing internal incidence cannot change that word. The particle's slice normal remains , proving the remaining claims.
Displayed formulas in this passage
VII-E@1#eq:frozen-observables · line 2340