{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:NXJ6MUGBARCKFLZLC2PYG4HVCE","short_pith_number":"pith:NXJ6MUGB","schema_version":"1.0","canonical_sha256":"6dd3e650c10444a2af2b169f8370f51104453d81d9ec11d0a1367f95e59eb54f","source":{"kind":"arxiv","id":"1808.00290","version":2},"attestation_state":"computed","paper":{"title":"Description of Stability for Two and Three-Dimensional Linear Time-Invariant Systems Based on Curvature and Torsion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Huafei Sun, Shiqiang Zhang, Yang Song, Yueqi Cao, Yuxin Wang","submitted_at":"2018-08-01T12:13:58Z","abstract_excerpt":"This paper focuses on using curvature and torsion to describe the stability of linear time-invariant system. We prove that for a two-dimensional system $\\dot{r}(t)= Ar(t)$, (i) if there exists an initial value, such that zero is not the limit of curvature of trajectory as $t\\to+\\infty$, then the zero solution of the system is stable; (ii) if there exists an initial value, such that the limit of curvature of trajectory is infinity as $t\\to+\\infty$, then the zero solution of the system is asymptotically stable. For a three-dimensional system, (i) if there exists a measurable set whose Lebesgue m"},"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":"1808.00290","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-01T12:13:58Z","cross_cats_sorted":[],"title_canon_sha256":"789270eab96dce1329e705fe0f15f0a888c69322290e9e7e542586b85ca54df3","abstract_canon_sha256":"3e19e21d61eccf2eb7a1a756031ac15110d3b4acb2e1efa97e47b766349508be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:45.168977Z","signature_b64":"EL0kVn3b+wso3D7Ef0ob01iPMb7HDxDIQABX2Zh6wqSD3ssck9z1hcX6RZpOaMNzTP1pRbzoNDG45/2VbJxVDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dd3e650c10444a2af2b169f8370f51104453d81d9ec11d0a1367f95e59eb54f","last_reissued_at":"2026-05-18T00:05:45.168235Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:45.168235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Description of Stability for Two and Three-Dimensional Linear Time-Invariant Systems Based on Curvature and Torsion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Huafei Sun, Shiqiang Zhang, Yang Song, Yueqi Cao, Yuxin Wang","submitted_at":"2018-08-01T12:13:58Z","abstract_excerpt":"This paper focuses on using curvature and torsion to describe the stability of linear time-invariant system. We prove that for a two-dimensional system $\\dot{r}(t)= Ar(t)$, (i) if there exists an initial value, such that zero is not the limit of curvature of trajectory as $t\\to+\\infty$, then the zero solution of the system is stable; (ii) if there exists an initial value, such that the limit of curvature of trajectory is infinity as $t\\to+\\infty$, then the zero solution of the system is asymptotically stable. For a three-dimensional system, (i) if there exists a measurable set whose Lebesgue m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00290","kind":"arxiv","version":2},"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":"1808.00290","created_at":"2026-05-18T00:05:45.168360+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.00290v2","created_at":"2026-05-18T00:05:45.168360+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.00290","created_at":"2026-05-18T00:05:45.168360+00:00"},{"alias_kind":"pith_short_12","alias_value":"NXJ6MUGBARCK","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_16","alias_value":"NXJ6MUGBARCKFLZL","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_8","alias_value":"NXJ6MUGB","created_at":"2026-05-18T12:32:40.477152+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/NXJ6MUGBARCKFLZLC2PYG4HVCE","json":"https://pith.science/pith/NXJ6MUGBARCKFLZLC2PYG4HVCE.json","graph_json":"https://pith.science/api/pith-number/NXJ6MUGBARCKFLZLC2PYG4HVCE/graph.json","events_json":"https://pith.science/api/pith-number/NXJ6MUGBARCKFLZLC2PYG4HVCE/events.json","paper":"https://pith.science/paper/NXJ6MUGB"},"agent_actions":{"view_html":"https://pith.science/pith/NXJ6MUGBARCKFLZLC2PYG4HVCE","download_json":"https://pith.science/pith/NXJ6MUGBARCKFLZLC2PYG4HVCE.json","view_paper":"https://pith.science/paper/NXJ6MUGB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.00290&json=true","fetch_graph":"https://pith.science/api/pith-number/NXJ6MUGBARCKFLZLC2PYG4HVCE/graph.json","fetch_events":"https://pith.science/api/pith-number/NXJ6MUGBARCKFLZLC2PYG4HVCE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NXJ6MUGBARCKFLZLC2PYG4HVCE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NXJ6MUGBARCKFLZLC2PYG4HVCE/action/storage_attestation","attest_author":"https://pith.science/pith/NXJ6MUGBARCKFLZLC2PYG4HVCE/action/author_attestation","sign_citation":"https://pith.science/pith/NXJ6MUGBARCKFLZLC2PYG4HVCE/action/citation_signature","submit_replication":"https://pith.science/pith/NXJ6MUGBARCKFLZLC2PYG4HVCE/action/replication_record"}},"created_at":"2026-05-18T00:05:45.168360+00:00","updated_at":"2026-05-18T00:05:45.168360+00:00"}