Phase 35 · dynamic geometry

Move the geometry, not the traveller

AT-0273 → AT-0282. Benchmark seed 273. One small theorem closes the easy escape, two deliberate fakes show what a false result looks like, and the only surviving version of the idea — a relationship map that is itself dynamical — is put on the books and charged for.

The no-go that shapes the rest

For a fixed smooth projection pi: Y -> X and a continuous path gamma in Y, the image pi . gamma is continuous in X.

Plain language

A fixed map cannot make a continuous path teleport. If our idea is to work, the relationship map itself may have to become dynamical — and then changing it must be paid for and tested like any other physical degree of freedom.

Controls

SeedSeed 273 reproduces the recorded normalised-map benchmark.Links — 8Links in the emergent chain. Regions are links plus one.Max compression — 2.40Largest compression exponent allowed on any single link.Rate cap — 0.32Largest geometry edit permitted on one link in one step. Geometry cannot change instantly.Geometry price — 1.00Action charged per unit of geometry edit, relative to traveller motion. No free edits.Identity coupling from motion — 1.00How much the traveller's own displacement disturbs its operational identity.Identity coupling from local geometry — 0.55How much a geometry edit at the traveller's own site disturbs it.Identity tolerance — 0.25Fixed before the run. Peak deviation is scored against it, never the endpoint value.

Running the dynamic-geometry package…