APP-02: box and parallelotope approximations

Five authored interval and planar examples exercised the registered public CSL::approximation path at source commit 8fecba49e34c37e5e01c40218a8f014a179818fd. The outer adapters produce H slabs from bounded V vertices. The inner adapters return four supplied corners after checking each against the H input. Exact inclusion checks operate on stored binary64 values. No finite approximation error bound is available.

Checked numerical results

Literal outputs and descriptive 100-call batch durations
CaseRelationChecked outputMedian batch duration
diamond-axis-innerinnerV corners [[1, 1], [1, -1], [-1, -1], [-1, 1]]1,654,900 ns (range 1,569,200–1,692,100)
diamond-axis-outerouterH rows [[1, 0], [-1, 0], [0, 1], [0, -1]], bounds [2, 2, 2, 2]793,200 ns (range 778,400–839,300)
diamond-rotated-outerouterH rows [[1, 1], [-1, -1], [1, -1], [-1, 1]], bounds [2, 2, 2, 2]1,460,200 ns (range 1,386,100–1,469,200)
interval-boxouterH rows [[1], [-1]], bounds [2.25, 1.5]607,100 ns (range 590,000–635,500)
square-rotated-innerinnerV corners [[0, 1], [1, 0], [0, -1], [-1, 0]]1,230,800 ns (range 1,208,900–1,292,500)
Labelled x-y plot of diamond input, outer axis box, rotated outer diamond and inscribed box
The diamond vertices are (0,2), (2,0), (0,-2), (-2,0). The orange axis box encloses it, the blue rotated outer bound coincides with it, and the green box lies inside. These are saved output shapes, drawn as a geometric illustration rather than a trace of algorithm steps.

Inputs and independent check

The 1D interval vertices are −1.5 and 2.25. The complete rows, bounds, orientation and corner declarations for every case, plus SHA-256 request identities, are in records.json. The input_sha256 field hashes the full authored case declaration, including direction, orientation or corners and budget; two requests with the same V set can have different hashes. The driver checks literal H coefficients and bounds or every literal V corner after every public call; it also checks relation, structural proof basis and the explicit absence of an error bound. The independent policy verifies V-to-H containment or H-to-V containment before returning an enclosure.

Measurement scope

One excluded 100-call warmup per case was followed by seven rotated five-case rounds of 100 calls per case: 3,500 measured calls with zero recorded failures. Each per-call steady-clock interval includes registry selection, fresh provider workspace, adapter execution and independent containment verification. Fixture and registry construction, the post-call literal oracle, CSV output, process launch and HTML rendering are excluded. One worker and one native thread were requested and used. Internal counters are unavailable. These single-adapter observations have no comparator, speedup, source-mapped limiter or scalability conclusion.

Host DESKTOP-S9O3F6S: Intel64 Family 6 Model 151 Stepping 5, GenuineIntel; Windows-11-10.0.22631-SP0; MSVC 19.44 x64 Release. HiGHS and Qhull were disabled. Build provenance, configure log, build log, prebuild receipt, postrun receipt, raw CMake cache and compiler receipt are saved.

Reproduce and inspect

At the linked source commit, run python -m cmake -S . -B build/app02 -DBUILD_TESTING=OFF -DCSL_ENABLE_HIGHS=OFF -DCSL_ENABLE_QHULL=OFF -DCSL_BUILD_APP02_REPORT=ON, build target csl_app02_approximation_report in Release, and run it with smoke and measure. The saved driver source and raw measured CSV support independent inspection.

Report ID app02-box-8ff979de60ea9d22. This report is scoped to the declared stored binary64 fixtures; no generic optimality or validated real-arithmetic claim is made.