org.appliedtopology.tda4j.matlab

A finished circular-coordinates computation (homology.CircularCoordinates, .claude/WORKLOG-mainstream- feature-gap-analysis.md item 2), in the same MATLAB-marshalable shape PersistenceResult uses -- see TDA4j.circularCoordinates's own doc for how this gets constructed.

A landmark selection, in a shape callable directly from MATLAB (or any other plain-Java caller): every public method here takes/returns only int[] or double -- see TDA4j.selectLandmarksFromPoints/ selectLandmarksFromDistanceMatrix (step 1 of the two-step witness-complex recipe) for how this gets constructed, and TDA4j.computeFromPointsAndLandmarks/computeFromDistanceMatrixAndLandmarks (step 2) for where landmarks() goes next.

A finished persistence computation, in a shape callable directly from MATLAB (or any other plain-Java caller) via MATLAB's built-in Java interface: every public method here takes/returns only int, double, double[][], int[][], or another PersistenceResult handle (MATLAB's Java bridge holds and passes those around like any other Java object -- already established by TDA4j.computeFrom* itself returning one) -- no other Scala types, no generics, no java.util.Map -- since none of those marshal reliably across MATLAB's Java bridge. See TDA4j for how this gets constructed and WORKLOG-matlab-api.md for the design rationale, including what was deliberately left out of this first pass.

Bars are indexed 0 until size() - 1, in no particular guaranteed order (the underlying engines don't sort their output beyond grouping by dimension). An essential (never-dying) class reports death(i) == Double.POSITIVE_INFINITY.

Representative-chain access (cycleVertices/cycleCoefficients) is engine-dependent in what kind of chain it returns, not in whether one is available -- every engine records one for every bar; see the per-method doc. For engine="ripser" the chain is a representative cocycle; for engine="naive" it is a representative cycle. Both are reported the same way here (a list of simplices, each given as its sorted vertex array, with a parallel coefficient array) because MATLAB-side code that only wants "the simplices spanning this bar" doesn't need to care which.