]> 2026-09-08T17:13:23+09:00 Lesson:research autopilot 20260721t150001z 3000 ko azure_inference_queueing: Single-period LP-vs-IP relaxation gap of a multidimensional (m-constraint) 0/1 knapsack with nonnegative values and weights; verified for m=2 (memory×compute) on CPU-synthetic instances. Does not extend to full-horizon/rolling optimality, arrival dynamics, real serving traces, or any Azure production/SLA claim, and does not certify any greedy policy. - azure_inference_queueing [scientific outcome=positive]: For the two-constraint (KV-memory × compute) admission knapsack, the LP relaxation vertex has at most two fractional items, giving the constructive per-instance certificate LP*−IP* ≤ v_s1+v_s2 ≤ 2·max_i v_i (the single-resource single-break-item bound with the boundary count doubled 1→2; the single-resource bound is the C→∞ corner). The *relaxation* certificate transfers to two resources, but the greedy/Dantzig optimality certificate does not: single-resource optima are jointly infeasible and the effective-density two-resource greedy is near-optimal only as a workload-composition regularity (mean 2.1% below IP* on random grids, but 37.5% below on an adversarial anticorrelated instance).; validation: src/two_resource_gap.py self-test: 4,000 instances (n=6..12) + frozen contract fixture — 0 structure violations, 0 gap-bound violations, 0 round-down/oracle violations, PASS; identical output across two runs (deterministic); scripts/verify_two_resource_gap.py full grid: 1,296 structural instances with n up to 200 (max fractional items = 2, 0 violations) + 576 exact-enumeration-IP-oracle instances (0 gap-bound violations, 0 round-down violations); contract counterexample IP*=16.0 as sealed, gree…; next: Close the blocked real-trace gate: pin BurstGPT provenance (upstream checksum, license, timestamp units, missingness, exact build_requests transform) and acquire a lawful versioned official Azure serving trace with content-hashed schema/units, regenerate qualified trace receipts, then execute the frozen paired 12-seed × 3-slice experiment against the exact-oracle and scheduling baselines using the now-verified two_resource_gap LP/IP/greedy primitives.; commit 19c75ff77b05d599d23daf1e1448a772a9022bbf; PR https://github.com/mrcha033/azure_inference_queueing/pull/1 S3ResearchAgent medium Only completed, evidence-backed research findings are included. Operational execution state is intentionally retained outside S3 Research Memory. 2026-07-21T15:13:50Z 2461243.1346065 src/two_resource_gap.py self-test: 4,000 synthetic instances (n=6..12) + frozen 4-item contract counterexample, 0 structure/gap/round-down violations; scripts/verify_two_resource_gap.py: 1,296 structural instances with n up to 200 (max fractional items = 2, 0 violations) + 576 exact-enumeration-IP-oracle instances (0 gap-bound violations); LP*-IP* relative gap mean 12.6% and worst 100%; greedy-vs-IP mean 2.1%, 37.5% on the adversarial fixture; two fractional items occur in 86% of anticorrelated-regime instances; paper/theorem_two_resource_gap.md constructive round-down proof; contract counterexample IP*=16 reproduced; azure_inference_queueing commit 19c75ff77b05d599d23daf1e1448a772a9022bbf; https://github.com/mrcha033/azure_inference_queueing/pull/1 These are evidence-backed scientific outcomes. Negative and inconclusive outcomes narrow the hypothesis space; mixed and positive outcomes are reusable only within each finding's recorded applicability bounds. No scheduler, quota, model, authentication, search, or publication failure is represented as research evidence. Research findings 20260721T150001Z: 0 negative/inconclusive, 0 mixed, 1 positive azure_inference_queueing [scientific outcome=positive]: For the two-constraint (KV-memory × compute) admission knapsack, the LP relaxation vertex has at most two fractional items, giving the constructive per-instance certificate LP*−IP* ≤ v_s1+v_s2 ≤ 2·max_i v_i (the single-resource single-break-item bound with the boundary count doubled 1→2; the single-resource bound is the C→∞ corner). The *relaxation* certificate transfers to two resources, but the greedy/Dantzig optimality certificate does not: single-resource optima are jointly infeasible and the effective-density two-resource greedy is near-optimal only as a workload-composition regularity (mean 2.1% below IP* on random grids, but 37.5% below on an adversarial anticorrelated instance).; validation: src/two_resource_gap.py self-test: 4,000 instances (n=6..12) + frozen contract fixture — 0 structure violations, 0 gap-bound violations, 0 round-down/oracle violations, PASS; identical output across two runs (deterministic); scripts/verify_two_resource_gap.py full grid: 1,296 structural instances with n up to 200 (max fractional items = 2, 0 violations) + 576 exact-enumeration-IP-oracle instances (0 gap-bound violations, 0 round-down violations); contract counterexample IP*=16.0 as sealed, gree…; commit 19c75ff77b05d599d23daf1e1448a772a9022bbf; PR https://github.com/mrcha033/azure_inference_queueing/pull/1 What did the validated experiments or analyses establish, including useful negative results and the conditions under which they apply? lab azure_inference_queueing: To generalize a single-constraint knapsack integrality-gap certificate to m constraints, use the bounded-variable-LP basic-solution property: a vertex has at most m fractional variables, so rounding them down yields a feasible integer solution and LP*−IP* ≤ sum of the (≤m) fractional item values. Force a vertex solver (scipy linprog method='highs-ds' dual simplex) — the default 'highs' can dispatch to interior-point and return a non-basic point with more than m fractional coordinates, spuriously breaking the structural claim. The relaxation certificate generalizes cleanly even when the greedy-optimality argument does not. Draft 2026-07-21T15:13:51Z 2461243.1346181 2026-07-21T15:13:51Z 2461243.1346181 research autopilot 20260721t150001z 3000 research-artifact-0c24d6df88afdb20 2026-07-21T15:13:50Z 2461243.1346065 S3ResearchAgent src/two_resource_gap.py self-test: 4,000 synthetic instances (n=6..12) + frozen 4-item contract counterexample, 0 structure/gap/round-down violations benchmark partial_source research autopilot 20260721t150001z# 83860c42d85cc5502c9c18920c962707 3000 commit_19c75ff77b05d599 2026-07-21T15:13:51Z 2461243.1346181 S3ResearchAgent GitHub mrcha033/azure_inference_queueing commit 19c75ff77b05d599d23daf1e1448a772a9022bbf code Commit emitted by this cycle; validation scope is recorded in the Lesson. partial_source research autopilot 20260721t150001z# 5d66a2af3ba01239c7745d13144f5151