Single-adapter, fixed-source evidence for an affine image, a correlated cancellation, and a constrained dependent sum. Representation algebra preserves shared factor identity. Coefficient evaluation is binary64 with no validated rounding enclosure.
| Fixture | Expected physical relation | Observed output | Evidence |
|---|---|---|---|
| Affine image of a two-factor box | Physical H: 2 ≤ x ≤ 12 | center 7; generator columns [2, 3]; factor IDs horizontal, vertical | 8/8 verified batches, including one excluded warmup |
| Correlated cancellation | Physical H: x = 0 | center 0; shared history.0 column cancels to 0 | 8/8 verified batches, including one excluded warmup |
| Dependent sum with two distinct equalities | Physical H: x = 0, y = 0 | center [0, 0]; factor IDs u, v, w; two joined equalities | 8/8 verified batches, including one excluded warmup |
Every fresh call checks feasible factor witnesses against the literal physical H relation, separate outside points, factor IDs and coefficients. The constrained case retains two distinct equality systems. An infeasible factor tuple may map inside a noninjective physical image; no false feasibility equivalence is asserted. Residual vectors are unavailable from this public API. These are three bounded examples, not a general correctness or complete-family proof.
One excluded warmup and seven measured batches per fixture, in alternating order; 5,000 freshly constructed, fully checked calls per batch. All 24 warmup and measured batches passed; there were zero observed failures. Values are verified-batch milliseconds, not isolated operation or per-call latency. The measured interval includes public construction and operations, the independent-sum rejection control, factor lift, literal H/identity/coefficient checks, and per-call nlohmann JSON result construction and assignment. It excludes process startup, JSONL serialization, saved-row verification, persistence and rendering.
| Fixture | Calls/batch | Successful batches | Median ms | Range ms |
|---|---|---|---|---|
| box image | 5,000 | 7/7 | 37.555 | 36.684–37.870 |
| shared cancellation | 5,000 | 7/7 | 30.668 | 30.388–32.356 |
| constrained sum | 5,000 | 7/7 | 42.760 | 41.641–45.262 |
Performance interpretation is exploratory and inconclusive. There is no comparator, source-mapped limiter profile, application-scale workload, or throughput/scalability claim. Internal phase timings and measured native thread count are unavailable.
Algorithm source db7906cb33ca40da55e31b9bf6b21cf7ffcc1ee4; reviewed harness 580da5368aac21b14d9e817da5937b4494a905aa; saved artifact geo07-9ef0d347291774da; raw JSONL SHA-256 768dae54cb5aabcec1445a2703df4ae45ed26145de7f52a012307b8d267dfd36; records SHA-256 4dc756380e87bd4e9342f55777bb2adb9a9aaeba62e9e142fb656d60d393d7c6; native manifest SHA-256 be4c075afa202348e35d800fcca3413f4501f58ce4faefde7cff2d394344366d. The artifact Git commit is the repository revision carrying these files and is separate from source and harness commits.
MSVC 19.44.35215.0, C++20 x64 Release /O2 /Ob2 /DNDEBUG. Host: Windows-11-10.0.22631-SP0; 12 logical processors. One sequential driver was requested; observed native thread count is unavailable. The saved concurrent-work note says: UTC 2026-10-16T13:16:02.6364135Z; i5-12400F 12 logical processors; CPU load=2%; processor idle=94%; recent stable WMI load samples=0,1,0,1%; active cmake/cl/link=none; resident MSBuild count=3; no other known local build active; ordinary background agents/processes uncontrolled.
Source fixture payloads and per-fixture hashes, the exact raw driver description, Release compiler/link settings, process status and raw trial bytes are downloadable below. The earlier collection-001 failed the provenance parser and is excluded from this report. The accepted collection-002 used the reviewed CRLF parser fix. Its collection-status file records acceptance for report review and a then-pending publication gate.
