Touch the geometry. The diagrams below are communication instruments, not screenshots from a notebook; each has a text/table equivalent immediately alongside it.
01 / GEOMETRY
Unit-hypersphere state
Drag horizontally to rotate the projection. The radius stays fixed while direction carries the changing state.
Drag sideways to rotate · swipe vertically to scroll · keyboard: ← →
02 / LOCAL GEOMETRY
Radial vs tangent change
Move the control to decompose an update into radial and tangent components.
03 / READOUT
Accessible does not mean used.
The frozen representation can expose a distinction strongly to a small probe while the native consumer extracts almost none of it.
Loading frozen evidence…
04 / DYNAMICS
What survives depth?
Adjust the horizon to inspect a conceptual decomposition of task and nuisance directions across recurrent depth.
Task-relevant directionNuisance direction
05 / EVIDENCE GRAPH
Claims have boundaries.
Follow the chain from mathematical constraint to representation evidence to consumer behavior.
→→
Geometry
Normalization constrains state to the unit hypersphere; mathematical structure narrows what kinds of change are available.
06 / ARCHITECTURE
Representation and consumer are separate machines.
Tap a stage to inspect what changes—and what stays frozen—when testing where information is lost.
→→→
Hypersphere state
The recurrent representation is frozen. Probes ask what information is present here without retraining the state.
07 / DEPENDENCY LEDGER
Evidence accumulates; it does not blur.
Select a result class to see what it can support downstream.
Theorem
Constrains admissible interpretations and architectures. It does not establish empirical performance by itself.