{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:LMNYGRFQ6NSBK2BLV3W4XMQUBW","short_pith_number":"pith:LMNYGRFQ","schema_version":"1.0","canonical_sha256":"5b1b8344b0f36415682baeedcbb2140d86d6e211e9af335938dafbba32b8adcb","source":{"kind":"arxiv","id":"1505.03883","version":3},"attestation_state":"computed","paper":{"title":"k2Q: A Quadratic-Form Response Time and Schedulability Analysis Framework for Utilization-Based Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Cong Liu, Jian-Jia Chen, Wen-Hung Huang","submitted_at":"2015-05-14T20:44:04Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1505.03883","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-05-14T20:44:04Z","cross_cats_sorted":[],"title_canon_sha256":"c55dedb627b229a45ecae8727264f630246c1d25f209dee6ab1617f7930da24e","abstract_canon_sha256":"616317591f8536654ccea7beb6a33ffb77a438c83746bbf5ff6771b22af9a45c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:04.289707Z","signature_b64":"efu3koua0ZREoujFj7uX2X+tWPgjw3oVYLgWPaHtaoc0xGdQUZrqOhJNrMliWrJ5hRgmQ8Q4XDH5yF1NpGDwDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b1b8344b0f36415682baeedcbb2140d86d6e211e9af335938dafbba32b8adcb","last_reissued_at":"2026-05-18T01:04:04.289216Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:04.289216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"k2Q: A Quadratic-Form Response Time and Schedulability Analysis Framework for Utilization-Based Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Cong Liu, Jian-Jia Chen, Wen-Hung Huang","submitted_at":"2015-05-14T20:44:04Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03883","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1505.03883","created_at":"2026-05-18T01:04:04.289287+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.03883v3","created_at":"2026-05-18T01:04:04.289287+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03883","created_at":"2026-05-18T01:04:04.289287+00:00"},{"alias_kind":"pith_short_12","alias_value":"LMNYGRFQ6NSB","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"LMNYGRFQ6NSBK2BL","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"LMNYGRFQ","created_at":"2026-05-18T12:29:29.992203+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LMNYGRFQ6NSBK2BLV3W4XMQUBW","json":"https://pith.science/pith/LMNYGRFQ6NSBK2BLV3W4XMQUBW.json","graph_json":"https://pith.science/api/pith-number/LMNYGRFQ6NSBK2BLV3W4XMQUBW/graph.json","events_json":"https://pith.science/api/pith-number/LMNYGRFQ6NSBK2BLV3W4XMQUBW/events.json","paper":"https://pith.science/paper/LMNYGRFQ"},"agent_actions":{"view_html":"https://pith.science/pith/LMNYGRFQ6NSBK2BLV3W4XMQUBW","download_json":"https://pith.science/pith/LMNYGRFQ6NSBK2BLV3W4XMQUBW.json","view_paper":"https://pith.science/paper/LMNYGRFQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.03883&json=true","fetch_graph":"https://pith.science/api/pith-number/LMNYGRFQ6NSBK2BLV3W4XMQUBW/graph.json","fetch_events":"https://pith.science/api/pith-number/LMNYGRFQ6NSBK2BLV3W4XMQUBW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LMNYGRFQ6NSBK2BLV3W4XMQUBW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LMNYGRFQ6NSBK2BLV3W4XMQUBW/action/storage_attestation","attest_author":"https://pith.science/pith/LMNYGRFQ6NSBK2BLV3W4XMQUBW/action/author_attestation","sign_citation":"https://pith.science/pith/LMNYGRFQ6NSBK2BLV3W4XMQUBW/action/citation_signature","submit_replication":"https://pith.science/pith/LMNYGRFQ6NSBK2BLV3W4XMQUBW/action/replication_record"}},"created_at":"2026-05-18T01:04:04.289287+00:00","updated_at":"2026-05-18T01:04:04.289287+00:00"}