OBSERVATION CHAMBER / ACTIVE
Hyperbolic Isometry Studio
Apply two disk isometries in opposite orders, then compare geodesic paths, endpoints, trace classes, and preserved hyperbolic distance.
01 · SHARED SNAPSHOT
Run the same maps in both orders
Ready — run both orders from the same snapshot.
02 · COMPOSITION CHECK
Same final configuration
Classifications appear after both compositions are checked.
03 · SYNCHRONIZED DISKS
One snapshot, two orders
time 0.00 / 1.20 s
Drag P, Q, A, or B directly. P/Q stay within radius 0.96; A/B stay within radius 0.92. The selected handle never switches automatically.
Advanced matrices, classification, and limits
Source snapshot
SU(1,1) matrices
Run both orders to inspect A, B, B·A, and A·B.
Trace and fixed points
Classification tolerance: 1e-9.
Independent cross-checks
- matrix/direct
- —
- disk/hyperboloid
- —
- SU(1,1)
- —
- revision / job
- 0 / 0
RESULT OUTPUT
Report and image
Both outputs use the immutable committed result shown above.
Orientation-preserving unit-disk isometries, double-precision arithmetic, finite geodesic samples, and an explicit trace tolerance. This is not a formal proof system or a cryptographic design tool.
OBSERVATION GUIDE
Touchpoints for Observation
Apply the same orientation-preserving disk isometries to P and Q in opposite orders, then compare computed geodesics, endpoints, trace classes, and preserved hyperbolic distance.
- Start with Order matters and run both orders. Drag P, Q, A, or B directly, then compare B(A(z)) with A(B(z)) from the same source snapshot.
- The model uses double-precision arithmetic and finite geodesic samples.
- Identity is detected before the trace-boundary parabolic test; the reported tolerance remains part of the result.
- Only orientation-preserving unit-disk isometries are in scope, and near-boundary inputs are capped for numerical safety.
This is a finite browser model, not a formal proof system or a cryptographic design tool. Residuals and tolerances are numerical diagnostics rather than proof certificates.
Runs inside the browser with no upload and no registration.
SYSTEM NOTE
For |v|<1, F(v,θ)(z)=exp(iθ)(z+v)/(1+conj(v)z). Here A THEN B means B(A(z)) with M_(A THEN B)=M_B M_A, while B THEN A means A(B(z)) with M_(B THEN A)=M_A M_B. The disk distance is d(z,w)=2 atanh |(z−w)/(1−conj(z)w)|. Normalized SU(1,1) matrices preserve the disk Hermitian form and have determinant one. After projective identity is tested first, T=|trace(M)| classifies elliptic, parabolic, or hyperbolic behavior using the reported tolerance. A geodesic is sampled by moving one endpoint to zero, interpolating on the diameter, and applying the inverse disk automorphism.
OBSERVATION POLICY
This lab runs in your browser. Point positions, generator inputs, calculations, reports, and images are not uploaded by this lab.
Route
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