Refinement depth as the radial axis
Nested luminous shells, four children per parent. Each step inward resolves a cell into the four cells it already contained.
The relation on screen
Refinement depth behaves like a radial scale, in the same role the holographic coordinate plays in RG flow.
Symbols
- refinement depth of a patch
- scale coordinate, small z is fine-grained
why depth deserves to be a direction
Moving inward resolves a cell: each cell is already four cells at the next level, and reading it at low resolution loses detail while staying consistent with the finer reading. That is exactly the property a coordinate needs before you can move along it. In holography this is the radial direction, and in the renormalisation group it is scale. Whether it also behaves like a metre stick is the separate question the next panel probes, and the answer there is no.
what to look for · Depth orders the description by resolution. Reading it as a radial coordinate is an interpretation laid on top of that.
Consensus to physics
- 01a level is a geodesic icosahedral cellulation with 20*4^L cells
- 02adjacent levels are joined by committed transport, up and down
- 03the pair satisfies marg o sect = id, so a coarse record is a fine record read at lower resolution
- 04depth therefore behaves like a direction the observer can move along
In standard physics
The holographic radial direction, and RG flow
Scale as a coordinate. Coarse is far and low-resolution, fine is near and detailed; radial distance is a resolution before it is a length.
boundary · Depth is a resolution coordinate. It is not on the same footing as the three metric directions of V07.