{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:KRHZVKSHCBIYUEKDWPNSEXACF5","short_pith_number":"pith:KRHZVKSH","canonical_record":{"source":{"id":"0901.3583","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-01-23T00:12:52Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"40dea13fc13c215cb6e706f7b180048cf5831a21879ad4ea0b2de07e221a9f8a","abstract_canon_sha256":"dfe1980d9160399481b2d57cfdba5c9cc7d3f2bb0b7efbcee56f50d4b7f86170"},"schema_version":"1.0"},"canonical_sha256":"544f9aaa4710518a1143b3db225c022f6e5048ea19c2ea0056ee4488cdc6978e","source":{"kind":"arxiv","id":"0901.3583","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.3583","created_at":"2026-05-18T00:58:48Z"},{"alias_kind":"arxiv_version","alias_value":"0901.3583v1","created_at":"2026-05-18T00:58:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.3583","created_at":"2026-05-18T00:58:48Z"},{"alias_kind":"pith_short_12","alias_value":"KRHZVKSHCBIY","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KRHZVKSHCBIYUEKD","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KRHZVKSH","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:KRHZVKSHCBIYUEKDWPNSEXACF5","target":"record","payload":{"canonical_record":{"source":{"id":"0901.3583","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-01-23T00:12:52Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"40dea13fc13c215cb6e706f7b180048cf5831a21879ad4ea0b2de07e221a9f8a","abstract_canon_sha256":"dfe1980d9160399481b2d57cfdba5c9cc7d3f2bb0b7efbcee56f50d4b7f86170"},"schema_version":"1.0"},"canonical_sha256":"544f9aaa4710518a1143b3db225c022f6e5048ea19c2ea0056ee4488cdc6978e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:48.262347Z","signature_b64":"Mxk1M4mhwuMfVdYk+K/vfwQn5gMUVkv6kOow5SQLgJ759dh762tPJ6vPUr47rah/KXAE/C3x5HfncN4qRlwHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"544f9aaa4710518a1143b3db225c022f6e5048ea19c2ea0056ee4488cdc6978e","last_reissued_at":"2026-05-18T00:58:48.261811Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:48.261811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0901.3583","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+eyFkiyUCmefiNF+YdxSWGFVsE0PbqDGINKYCn687xSqS1RpTb/+djrIBsAn+JqhmO80C0EBF7ssbhQxsUB9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T14:57:10.972459Z"},"content_sha256":"065e268e27c20c69845bc2aaefefc09d5659c36d10d216d2abcaba047550d855","schema_version":"1.0","event_id":"sha256:065e268e27c20c69845bc2aaefefc09d5659c36d10d216d2abcaba047550d855"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:KRHZVKSHCBIYUEKDWPNSEXACF5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discontinuous Dynamical Systems: A tutorial on solutions, nonsmooth analysis, and stability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.DS","authors_text":"Jorge Cortes","submitted_at":"2009-01-23T00:12:52Z","abstract_excerpt":"This paper considers discontinuous dynamical systems, i.e., systems whose associated vector field is a discontinuous function of the state. Discontinuous dynamical systems arise in a large number of applications, including optimal control, nonsmooth mechanics, and robotic manipulation. Independently of the particular application, one always faces similar questions when dealing with discontinuous dynamical systems. The most basic one is the notion of solution. We begin by introducing the notions of Caratheodory, Filippov and sample-and-hold solutions, discuss existence and uniqueness results fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.3583","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4u8HV03tFORv92P9Am6K3HVoBw8zPy3a5CG5YakdkY+PZJMP4BK4jtTSo9Qa7xwemB6Kep3vJsBTEjIxEfnfBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T14:57:10.973200Z"},"content_sha256":"6ca0040a64c62ec7e67317605c6c73231b502b35018682b848cdda4e7e3e082a","schema_version":"1.0","event_id":"sha256:6ca0040a64c62ec7e67317605c6c73231b502b35018682b848cdda4e7e3e082a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KRHZVKSHCBIYUEKDWPNSEXACF5/bundle.json","state_url":"https://pith.science/pith/KRHZVKSHCBIYUEKDWPNSEXACF5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KRHZVKSHCBIYUEKDWPNSEXACF5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T14:57:10Z","links":{"resolver":"https://pith.science/pith/KRHZVKSHCBIYUEKDWPNSEXACF5","bundle":"https://pith.science/pith/KRHZVKSHCBIYUEKDWPNSEXACF5/bundle.json","state":"https://pith.science/pith/KRHZVKSHCBIYUEKDWPNSEXACF5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KRHZVKSHCBIYUEKDWPNSEXACF5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:KRHZVKSHCBIYUEKDWPNSEXACF5","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":"dfe1980d9160399481b2d57cfdba5c9cc7d3f2bb0b7efbcee56f50d4b7f86170","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-01-23T00:12:52Z","title_canon_sha256":"40dea13fc13c215cb6e706f7b180048cf5831a21879ad4ea0b2de07e221a9f8a"},"schema_version":"1.0","source":{"id":"0901.3583","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.3583","created_at":"2026-05-18T00:58:48Z"},{"alias_kind":"arxiv_version","alias_value":"0901.3583v1","created_at":"2026-05-18T00:58:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.3583","created_at":"2026-05-18T00:58:48Z"},{"alias_kind":"pith_short_12","alias_value":"KRHZVKSHCBIY","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KRHZVKSHCBIYUEKD","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KRHZVKSH","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:6ca0040a64c62ec7e67317605c6c73231b502b35018682b848cdda4e7e3e082a","target":"graph","created_at":"2026-05-18T00:58:48Z","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":"This paper considers discontinuous dynamical systems, i.e., systems whose associated vector field is a discontinuous function of the state. Discontinuous dynamical systems arise in a large number of applications, including optimal control, nonsmooth mechanics, and robotic manipulation. Independently of the particular application, one always faces similar questions when dealing with discontinuous dynamical systems. The most basic one is the notion of solution. We begin by introducing the notions of Caratheodory, Filippov and sample-and-hold solutions, discuss existence and uniqueness results fo","authors_text":"Jorge Cortes","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-01-23T00:12:52Z","title":"Discontinuous Dynamical Systems: A tutorial on solutions, nonsmooth analysis, and stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.3583","kind":"arxiv","version":1},"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":"sha256:065e268e27c20c69845bc2aaefefc09d5659c36d10d216d2abcaba047550d855","target":"record","created_at":"2026-05-18T00:58:48Z","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":"dfe1980d9160399481b2d57cfdba5c9cc7d3f2bb0b7efbcee56f50d4b7f86170","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-01-23T00:12:52Z","title_canon_sha256":"40dea13fc13c215cb6e706f7b180048cf5831a21879ad4ea0b2de07e221a9f8a"},"schema_version":"1.0","source":{"id":"0901.3583","kind":"arxiv","version":1}},"canonical_sha256":"544f9aaa4710518a1143b3db225c022f6e5048ea19c2ea0056ee4488cdc6978e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"544f9aaa4710518a1143b3db225c022f6e5048ea19c2ea0056ee4488cdc6978e","first_computed_at":"2026-05-18T00:58:48.261811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:48.261811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mxk1M4mhwuMfVdYk+K/vfwQn5gMUVkv6kOow5SQLgJ759dh762tPJ6vPUr47rah/KXAE/C3x5HfncN4qRlwHCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:48.262347Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.3583","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:065e268e27c20c69845bc2aaefefc09d5659c36d10d216d2abcaba047550d855","sha256:6ca0040a64c62ec7e67317605c6c73231b502b35018682b848cdda4e7e3e082a"],"state_sha256":"d3e5a97c4912a4cc49e2a66ed5966aa21f0e66fc24ec7e731a19dbf3a854d3a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uoEm1+gk3pwSKevP2pKfEgNWSfScSbTvcz1wK58bbuLfiifr8zWOC2orEBHarDFtb+D1RpI2Aa61/1MtO22zDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T14:57:10.977188Z","bundle_sha256":"2d100907612b69f3821f0fc93158e0aca1106fbe0587c5c2a35221e75248e939"}}