{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LMNYGRFQ6NSBK2BLV3W4XMQUBW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"616317591f8536654ccea7beb6a33ffb77a438c83746bbf5ff6771b22af9a45c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-05-14T20:44:04Z","title_canon_sha256":"c55dedb627b229a45ecae8727264f630246c1d25f209dee6ab1617f7930da24e"},"schema_version":"1.0","source":{"id":"1505.03883","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03883","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03883v3","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03883","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"pith_short_12","alias_value":"LMNYGRFQ6NSB","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LMNYGRFQ6NSBK2BL","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LMNYGRFQ","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:5c25771263d4827b6573736daad243e261592cc8a50b16829ea62aee37c83ba0","target":"graph","created_at":"2026-05-18T01:04:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we present a general response-time analysis and schedulability-test framework, called k2Q (k to Q). It provides automatic constructions of closed-form quadratic bounds or utilization bounds for a wide range of applications in real-time systems under fixed-priority scheduling. The key of the framework is a $k$-point schedulability test or a $k$-point response time analysis that is based on the utilizations and the execution times of $k-1$ higher-priority tasks. The natural condition of k2Q is a quadratic form for testing the schedulability or analyzing the response time. The resp","authors_text":"Cong Liu, Jian-Jia Chen, Wen-Hung Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-05-14T20:44:04Z","title":"k2Q: A Quadratic-Form Response Time and Schedulability Analysis Framework for Utilization-Based Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03883","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4f180c14c18299b780d3605d28a9e03bcbdf8a03ccd6261580c3dc4cf0fcf059","target":"record","created_at":"2026-05-18T01:04:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"616317591f8536654ccea7beb6a33ffb77a438c83746bbf5ff6771b22af9a45c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-05-14T20:44:04Z","title_canon_sha256":"c55dedb627b229a45ecae8727264f630246c1d25f209dee6ab1617f7930da24e"},"schema_version":"1.0","source":{"id":"1505.03883","kind":"arxiv","version":3}},"canonical_sha256":"5b1b8344b0f36415682baeedcbb2140d86d6e211e9af335938dafbba32b8adcb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b1b8344b0f36415682baeedcbb2140d86d6e211e9af335938dafbba32b8adcb","first_computed_at":"2026-05-18T01:04:04.289216Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:04.289216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"efu3koua0ZREoujFj7uX2X+tWPgjw3oVYLgWPaHtaoc0xGdQUZrqOhJNrMliWrJ5hRgmQ8Q4XDH5yF1NpGDwDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:04.289707Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.03883","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f180c14c18299b780d3605d28a9e03bcbdf8a03ccd6261580c3dc4cf0fcf059","sha256:5c25771263d4827b6573736daad243e261592cc8a50b16829ea62aee37c83ba0"],"state_sha256":"ea0092e8fc489af726765b334b09959c3e8f3a34b249cc956283f210bc7b166b"}