[Kiguli]

Fixes found while documenting the tool for v1.0, so that the tool and the benchmark files match the paper. Nothing here changes the published results: all 82 tests pass, and the benchmarks give the same complexity, risk bounds and degeneracy as before (details below).

Merging deploys to the live site and rebuilds the Docker image (existing workflows).

Risk reporting

• The MOSEK licence-upload path and the normal path now share one solve function (src/solve_form.py). The MOSEK path certified each run at β/(n_τ·n_ρ) but reported 1 − β/(n_τ·n_ρ). It also reported the cost including the τ and ρ terms, and left out n_attempts.
• Degenerate runs: the results table shows the lower bound as N/A and the graphs leave it out, as the paper says.
• Hidden parameters: the selected formulation decides which of τ and ρ apply. Before, a robust program still applied a τ left in the hidden form fields.
• Confidence parameter: a missing or out-of-range β is now an error. It used to be treated as β = 0, which gave an upper bound of 1.

Input handling

• Plain numbers: numbers in matrices (JSON, MAT, paste boxes) no longer give HTTP 500.
• SymPy-style expressions: names such as sin, exp, sqrt, pi and ^ now work; math.sin still works and every other name is still rejected.
• Empty fields: optional program fields may be left empty ([], "", null).
• Readable errors: input errors come back as {"error": ...} and are shown as a message.
• .MAT download: it works when a run in a sweep failed.

Solvers

• The τ‖x − x̄‖ term is only added when τ > 0. It used to add a second-order cone to plain LPs, so LP-only solvers failed and SCS and CLARABEL were less accurate.
• Norms: the regularization is a vector p-norm, so any p ≥ 1 works.
• Silent shape errors fixed: a 1-D b(δ) or h, integer SDP keys, and a column x_ref in SDP no longer change the constraints or solution.
• Q and empty inputs: Q is checked with a tolerance, an empty SDP Q is allowed, and empty deltas raises ValueError.
• Solver table: corrected against CVXPY's metadata, and installed solvers missing from the table get their types from CVXPY.
• quantify_risk: it validates its inputs and enables float64 only inside the function.

Web interface

• Slow solves on the hosted app: after 30 s, a note says problems of this size are better solved locally and links to the install guide.
• Display: tooltips for Risk Bounds, Total Constraints and Optimization Time, full confidence digits, and correct cell help.
• Total Constraints now includes the hard constraints.

Benchmarks

• run.py --solver: every run.py takes --solver (default MOSEK), and prints the actual confidence level.
• Program files reproduce run.py. Inventory and portfolio had a nonzero rho although the penalty is built into c.
• Portfolio ρ: the cost vector now uses ρ = 1/((1−0.95)·1255) = 0.015936 instead of 0.04, left over from N = 500. The published solution is also optimal for 0.015936, so only the objective value changes, from 0.053356 to 0.051337.
• READMEs match metrics.json and the actual files.
• Extra packages: scripts that need packages outside requirements.txt say which ones.
• Leftover folder: SDP_LPV_stability_3d_numeric is removed. It duplicated the main LPV numeric files, which its test now uses.

Docker, README and screenshots

• Docker: the image is built for linux/arm64 as well as amd64, GUNICORN_CMD_ARGS works, and the duplicate docker.yml workflow is removed.
• README: corrections, take_screenshots.py works again, and the screenshots are regenerated.

Verification

• Tests: 82 pass, the original 52 plus 30 new regression tests. They also pass in CI.
• Paper examples: the three paper examples give identical numbers. Pasting their JSON from the paper PDF into the app reproduces them.
• Browser checks: the N/A display, the slow-solve note and the β check were each checked in a real browser.
• Docker: the image built on this branch contains linux/amd64 and linux/arm64.
• Benchmarks: all 12 were run with CLARABEL before and after the changes (MOSEK's licence was unavailable). 10 give identical k, risk bounds and degeneracy. On the ellipsoid, CLARABEL went from a wrong k = 557 to the published k = 5 with [0, 0.0518]. Growth Bound is still running.