{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:K3GXFDKBRGGSDWD2Q7XAZNS6MC","short_pith_number":"pith:K3GXFDKB","schema_version":"1.0","canonical_sha256":"56cd728d41898d21d87a87ee0cb65e6082ff69035ceeb07ed899d0b873426db1","source":{"kind":"arxiv","id":"1406.5927","version":1},"attestation_state":"computed","paper":{"title":"Polytope Lyapunov functions for stable and for stabilizable LSS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Linda Laglia, Nicola Guglielmi, Vladimir Protasov","submitted_at":"2014-06-23T14:39:36Z","abstract_excerpt":"We present a new approach for constructing polytope Lyapunov functions for continuous-time linear switching systems (LSS). This allows us to decide the stability of LSS and to compute the Lyapunov exponent with a good precision in relatively high dimensions. The same technique is also extended for stabilizability of positive systems by evaluating a polytope concave Lyapunov function (\"antinorm\") in the cone. The method is based on a suitable discretization of the underlying continuous system and provides both a lower and an upper bound for the Lyapunov exponent. The absolute error in the Lyapu"},"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":"1406.5927","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-06-23T14:39:36Z","cross_cats_sorted":[],"title_canon_sha256":"029217c8f15d092ce2426893affa5f1cc6069f1608039a005647284adc3d14b4","abstract_canon_sha256":"3e89ee01e5b8d51afb682d6280c5c96199efc09d46ef9fe0108e20d4ef92ebb5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:10.467351Z","signature_b64":"UK6Rsob+CXjKQUurFaV2/VDJTFgqKnC8ry1f2R6OcWHr/3haJ5iYKxD3i3kq2DgSlSCawUYTfpoct/ZeNNhqAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56cd728d41898d21d87a87ee0cb65e6082ff69035ceeb07ed899d0b873426db1","last_reissued_at":"2026-05-18T02:49:10.466736Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:10.466736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polytope Lyapunov functions for stable and for stabilizable LSS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Linda Laglia, Nicola Guglielmi, Vladimir Protasov","submitted_at":"2014-06-23T14:39:36Z","abstract_excerpt":"We present a new approach for constructing polytope Lyapunov functions for continuous-time linear switching systems (LSS). This allows us to decide the stability of LSS and to compute the Lyapunov exponent with a good precision in relatively high dimensions. The same technique is also extended for stabilizability of positive systems by evaluating a polytope concave Lyapunov function (\"antinorm\") in the cone. The method is based on a suitable discretization of the underlying continuous system and provides both a lower and an upper bound for the Lyapunov exponent. The absolute error in the Lyapu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5927","kind":"arxiv","version":1},"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":"1406.5927","created_at":"2026-05-18T02:49:10.466824+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.5927v1","created_at":"2026-05-18T02:49:10.466824+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5927","created_at":"2026-05-18T02:49:10.466824+00:00"},{"alias_kind":"pith_short_12","alias_value":"K3GXFDKBRGGS","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"K3GXFDKBRGGSDWD2","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"K3GXFDKB","created_at":"2026-05-18T12:28:35.611951+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/K3GXFDKBRGGSDWD2Q7XAZNS6MC","json":"https://pith.science/pith/K3GXFDKBRGGSDWD2Q7XAZNS6MC.json","graph_json":"https://pith.science/api/pith-number/K3GXFDKBRGGSDWD2Q7XAZNS6MC/graph.json","events_json":"https://pith.science/api/pith-number/K3GXFDKBRGGSDWD2Q7XAZNS6MC/events.json","paper":"https://pith.science/paper/K3GXFDKB"},"agent_actions":{"view_html":"https://pith.science/pith/K3GXFDKBRGGSDWD2Q7XAZNS6MC","download_json":"https://pith.science/pith/K3GXFDKBRGGSDWD2Q7XAZNS6MC.json","view_paper":"https://pith.science/paper/K3GXFDKB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.5927&json=true","fetch_graph":"https://pith.science/api/pith-number/K3GXFDKBRGGSDWD2Q7XAZNS6MC/graph.json","fetch_events":"https://pith.science/api/pith-number/K3GXFDKBRGGSDWD2Q7XAZNS6MC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K3GXFDKBRGGSDWD2Q7XAZNS6MC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K3GXFDKBRGGSDWD2Q7XAZNS6MC/action/storage_attestation","attest_author":"https://pith.science/pith/K3GXFDKBRGGSDWD2Q7XAZNS6MC/action/author_attestation","sign_citation":"https://pith.science/pith/K3GXFDKBRGGSDWD2Q7XAZNS6MC/action/citation_signature","submit_replication":"https://pith.science/pith/K3GXFDKBRGGSDWD2Q7XAZNS6MC/action/replication_record"}},"created_at":"2026-05-18T02:49:10.466824+00:00","updated_at":"2026-05-18T02:49:10.466824+00:00"}