OPT-06: within-solve basis-reuse hull classification

Descriptive Release measurements for one implementation and three small 2D fixtures. No speedup or general scaling claim is made.

Measured source commit: ef70e8c580a9556b0f5d96e49070d33221bf5b64
Evidence: 42 measured rows, 0 failed rows; no separate limiter profile was collected.
Timing scope: steady_clock around reduce_hull or reduce_hull_basis_reuse only; point cloud setup, HiGHS LP workspace creation, and post-timing validation excluded.

Median durations

Standalone SVG chart

Per-method summary

case_id	method	attempts	successes	median_ns	min_ns	max_ns	Membership LP calls (excludes Phase-I solve)	Phase-I basis solves	median_pivots	median_degenerate_pivots	median_bulk_candidates	median_bulk_removals
degenerate	baseline	7	7	644600	623100	660100	7	0	0	0	0	3
degenerate	basis-reuse	7	7	50600	48400	54000	0	1	4	0	4	2
interior-basis	baseline	7	7	474700	459600	492100	5	0	0	0	0	1
interior-basis	basis-reuse	7	7	44200	43100	50300	0	1	4	2	2	0
permuted	baseline	7	7	917400	872000	993900	10	0	0	0	0	6
permuted	basis-reuse	7	7	54300	52000	59300	0	1	4	0	7	2

Complexity and representation

For n points in R^d, the Phase-I formulation has n structural variables and d+1 equalities. The assembled matrix stores (d+1)n coefficients, O(nd), plus O(n+d) indexing/RHS data; solver workspace/factorization storage is backend dependent.

One Phase-I LP solve is performed. At most n basis-coordinate queries and exact convex-combination certification attempts are made (one per nonbasis candidate; actual count depends on basis and validation outcomes). Each certificate uses at most d+1 structural basis points. The Phase-I LP solve cost is backend dependent; no general runtime bound or scaling claim is stated.

Evaluation plan

This report tests small permuted, duplicate/degenerate, and interior-basis 2D clouds against the generic LP-membership reducer. Follow-up evaluation should vary n and d, rank/degeneracy, duplicates and interior/face points, compare paired outputs to the same baseline, retain exact counter and failure records, and use a separate limiter profile before any performance conclusion. Include fuel-consumption workloads when the matching scenario fixture is available.

Evidence and limits

Every warmup and measured result is complete, has unique retained IDs in range, and contains every original input point by independent HiGHS LP membership checks. For each timed pair, this is checked for both exact outputs produced inside the timed calls, after timing ends; mutual output containment is also checked. The deterministic interior fixture has a completed baseline and basis-reuse structural basis IDs [0, 3, 4], including center ID 0. The harness self-test exercises valid, duplicate and out-of-range ID sets and positive/negative input-containment cases.

Hardware/compiler/build details and all raw rows are retained in records.json, trials.csv, summary.csv, raw stdout JSONL, raw stderr, and the sanitized build log. LP/pivot/bulk counters describe operations, not elapsed-time components.

The fixtures are small and do not model the fuel-consumption workload or establish production workload scaling. The timings are descriptive and inconclusive.