{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:XCRGWNRDF3PNOADNNQOLDQ2B5P","short_pith_number":"pith:XCRGWNRD","schema_version":"1.0","canonical_sha256":"b8a26b36232eded7006d6c1cb1c341ebfe04cc0188f440041b2c4cf854b8ff6e","source":{"kind":"arxiv","id":"0901.3841","version":1},"attestation_state":"computed","paper":{"title":"A Unified Floquet Theory for Discrete, Continuous, and Hybrid Periodic Linear Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jeffrey J. DaCunha, John M. Davis","submitted_at":"2009-01-24T16:20:01Z","abstract_excerpt":"In this paper, we study periodic linear systems on periodic time scales which include not only discrete and continuous dynamical systems but also systems with a mixture of discrete and continuous parts (e.g. hybrid dynamical systems). We develop a comprehensive Floquet theory including Lyapunov transformations and their various stability preserving properties, a unified Floquet theorem which establishes a canonical Floquet decomposition on time scales in terms of the generalized exponential function, and use these results to study homogeneous as well as nonhomogeneous periodic problems. Furthe"},"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":"0901.3841","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-01-24T16:20:01Z","cross_cats_sorted":[],"title_canon_sha256":"f0f35d773ba181e715ac0bef0b0b6d2ab9b0aff7cbda87f7cb5ed3a14cfbd936","abstract_canon_sha256":"f42a7929debb7047243ed11480bf190d4a6064ebfa3f0b0b7fd4a58ee595ee4b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:36:53.218202Z","signature_b64":"eDwe9UcZTxatpMy7Xub7OtCKGO6OXFK1pu0NnblxgK+RZuV9qG0ukJxRABt6J2rxv5DczppkI5MztDJ3wWwoBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8a26b36232eded7006d6c1cb1c341ebfe04cc0188f440041b2c4cf854b8ff6e","last_reissued_at":"2026-07-04T15:36:53.217867Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:36:53.217867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Unified Floquet Theory for Discrete, Continuous, and Hybrid Periodic Linear Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jeffrey J. DaCunha, John M. Davis","submitted_at":"2009-01-24T16:20:01Z","abstract_excerpt":"In this paper, we study periodic linear systems on periodic time scales which include not only discrete and continuous dynamical systems but also systems with a mixture of discrete and continuous parts (e.g. hybrid dynamical systems). We develop a comprehensive Floquet theory including Lyapunov transformations and their various stability preserving properties, a unified Floquet theorem which establishes a canonical Floquet decomposition on time scales in terms of the generalized exponential function, and use these results to study homogeneous as well as nonhomogeneous periodic problems. Furthe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.3841","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0901.3841/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"0901.3841","created_at":"2026-07-04T15:36:53.217924+00:00"},{"alias_kind":"arxiv_version","alias_value":"0901.3841v1","created_at":"2026-07-04T15:36:53.217924+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.3841","created_at":"2026-07-04T15:36:53.217924+00:00"},{"alias_kind":"pith_short_12","alias_value":"XCRGWNRDF3PN","created_at":"2026-07-04T15:36:53.217924+00:00"},{"alias_kind":"pith_short_16","alias_value":"XCRGWNRDF3PNOADN","created_at":"2026-07-04T15:36:53.217924+00:00"},{"alias_kind":"pith_short_8","alias_value":"XCRGWNRD","created_at":"2026-07-04T15:36:53.217924+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/XCRGWNRDF3PNOADNNQOLDQ2B5P","json":"https://pith.science/pith/XCRGWNRDF3PNOADNNQOLDQ2B5P.json","graph_json":"https://pith.science/api/pith-number/XCRGWNRDF3PNOADNNQOLDQ2B5P/graph.json","events_json":"https://pith.science/api/pith-number/XCRGWNRDF3PNOADNNQOLDQ2B5P/events.json","paper":"https://pith.science/paper/XCRGWNRD"},"agent_actions":{"view_html":"https://pith.science/pith/XCRGWNRDF3PNOADNNQOLDQ2B5P","download_json":"https://pith.science/pith/XCRGWNRDF3PNOADNNQOLDQ2B5P.json","view_paper":"https://pith.science/paper/XCRGWNRD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0901.3841&json=true","fetch_graph":"https://pith.science/api/pith-number/XCRGWNRDF3PNOADNNQOLDQ2B5P/graph.json","fetch_events":"https://pith.science/api/pith-number/XCRGWNRDF3PNOADNNQOLDQ2B5P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XCRGWNRDF3PNOADNNQOLDQ2B5P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XCRGWNRDF3PNOADNNQOLDQ2B5P/action/storage_attestation","attest_author":"https://pith.science/pith/XCRGWNRDF3PNOADNNQOLDQ2B5P/action/author_attestation","sign_citation":"https://pith.science/pith/XCRGWNRDF3PNOADNNQOLDQ2B5P/action/citation_signature","submit_replication":"https://pith.science/pith/XCRGWNRDF3PNOADNNQOLDQ2B5P/action/replication_record"}},"created_at":"2026-07-04T15:36:53.217924+00:00","updated_at":"2026-07-04T15:36:53.217924+00:00"}