Observer · Patch · Holography
The three-body
problem,
glued.
Three masses, simple Newtonian forces, three centuries of "no closed-form solution". OPH solves it in one move: the bodies are phase vortices on a 2D holographic screen, and their motion is the unique normal form that glues the screen's overlap data. Same trick handles Aharonov–Bohm, Berry phase, Wilson loops — every loop-holonomy obstruction.
Three equal masses, one figure-eight, one closed loop holonomy. Discovered by Chenciner and Montgomery in 2000 — inevitable in OPH terms.
The claim
Local pairwise consistency
does not imply global orbital consistency.
Each pair of bodies feels a simple, exactly-solvable force. The triangle of three pairs does not glue. That gluing failure is what every "unsolvability" theorem about the three-body problem actually measures — and OPH names it, quantifies it, and zeros it.
On the regular branch (no collisions), the OPH normal form exists, is unique, and is exactly the trajectory you see in the simulator above.
For everyone
It's about gluing.
Imagine three friends each describing a triangle by saying how to walk between two corners. Locally, every instruction makes sense. But if you actually try to walk all three, you sometimes don't end up where you started. The mismatch is real — physics calls it a holonomy. OPH says: what is physically real is exactly the data that survives the gluing.
For physicists
It's a normal form.
On a finite patch net, accepted repairs strictly lower a Lyapunov functional; termination follows on finite state spaces; under local confluence the normal form is schedule-independent. The 3-body trajectory is the continuum limit of that normal form.Full proofs →
The bigger pattern
The same trick, elsewhere.
The three-body problem is the centerpiece, but it is one member of a wider class. Anything where local data is well-defined but loop holonomy is not falls to the same OPH move. These pages are extras.