OPH · 64k
V27·Act VI · Spacetime

Charts and the overlap cocycle

Overlapping coordinate patches, each with its own axes, sliding into registration where they overlap.

The relation on screen

Observer charts overlap and their transition maps agree on triple overlaps, which is what makes a manifold.

Symbols

chart of observer i
shared region, seen by both
loading charts

what to look for · Space is assembled from views. No global coordinate exists anywhere in the substrate.

Consensus to physics

  1. 01each observer builds a chart from its own records
  2. 02two observers with overlapping support compare records on the overlap
  3. 03the comparison is a transition map
  4. 04if transition maps agree on triple overlaps, one atlas covers them all

In standard physics

The manifold atlas, run backwards

Charts and cocycle conditions first, the space they describe second. This is the step where 'my world' becomes 'the world'.

boundary · Overlap and agreement statistics on chart pairs. Assembling them into an event manifold is the next step, and it is not done here.