OBSERVATION CONTRACT
From phase difference to winding
This is a 64×64 XY phase field with periodic boundaries. Vortices and anti-vortices are detected from the looped phase difference around each plaquette. The global charge Q remains neutral.
OBSERVATION CHAMBER / ACTIVE
Topological Defect Winding Observatory
Observe vortices, anti-vortices, winding, current, and energy in a 64×64 periodic XY phase field.
defect / winding
Observation Model
ROUTE 81 / STRUCTURE / DEFECT · WINDING
PHASE DEFECT / PERIODIC LATTICE
Read winding around vortices
Move a 64×64 periodic XY field and observe local winding from wrapped phase differences around each plaquette.
+1 vortex
-1 anti-vortex
plaquette winding
Canvas 2D is unavailable. Numeric DOM readings remain available.
- Grid
- 64×64
- Boundary
- periodic
- Defects
- 0
- Total charge Q
- 0
Drag a vortex or anti-vortex marker to select and move it. Focus the Canvas for 1–4, Space/P, S, R, L, and Arrow keys.
READY
- Preset
- PAIR
- Lens
- PHASE
- Defects
- 0
- Total winding Q
- 0
- Energy E
- 0
- Current mean / max
- 0 / 0
READOUTS
Periodic field readings
- Q
- 0
- Vortices / anti-vortices
- 0
- E
- 0
- Mean current
- 0
- Max current
- 0
- Selected
- none
- Boundary
- periodic / 64 x 64
- Chunk time
- 0.00 ms
Observation report
SELF-TEST
Mathematical acceptance values
Initialization and reruns check periodicity, symmetry, finiteness, and annihilation conditions.
| TEST | RESULT | DETAIL |
|---|
The single ±1 case is a local plaquette fixture only. No global periodic single-vortex claim is made.
WHAT TO WATCH
Pairs disappear when close
- Compare ±1 defect layouts in PAIR and QUAD.
- Switch the WINDING, CURRENT, and ENERGY lenses.
- Drag a pair together to trigger annihilation and return to Q=0.
MODEL SCOPE
Reading the periodic XY field
Current uses the sine of a wrapped phase difference, and energy uses 1−cos. This chamber does not model causal structure, relativity, or a unique continuum solution.
Open the formula
wrap(δ) = atan2(sin δ, cos δ)
qₚ = (1/2π) Σ∂p wrap(θnext − θcurrent)
E = (J/2) Σ<ij> [1 − cos(wrap(θj − θi))]
jij = J sin(wrap(θj − θi))
Every index wraps on the 64×64 periodic lattice. Q=Σp qp is zero for a periodic neutral configuration.
Route for this chamber
Route for this chamber
The Structure route observes local defects and phase circulation.
STRUCTUREBack to Structure routeOBSERVATION POLICY
This chamber is an observation model, not a claim about a continuum single vortex on a periodic torus. A local ±1 plaquette fixture is tested locally; global periodic configurations remain charge-neutral.
Route
This chamber belongs to Structures & Symmetries.
STRUCTURE Back to Structures & Symmetries Route.