{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MT3SAZDD42GETNXWKFBI5ASKPH","short_pith_number":"pith:MT3SAZDD","canonical_record":{"source":{"id":"1805.09668","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-21T19:42:41Z","cross_cats_sorted":[],"title_canon_sha256":"e92a147e111b2fa2b762587336197b273f9c5e38b54e5b4d83828515258741e5","abstract_canon_sha256":"869cbfbecf0784ab4a070f42ffc89cfe2689fc065f5ddda0d10bdba9c3b1d87a"},"schema_version":"1.0"},"canonical_sha256":"64f7206463e68c49b6f651428e824a79c39f07ade5916ad2ded07c907067ca42","source":{"kind":"arxiv","id":"1805.09668","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.09668","created_at":"2026-05-18T00:12:24Z"},{"alias_kind":"arxiv_version","alias_value":"1805.09668v2","created_at":"2026-05-18T00:12:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09668","created_at":"2026-05-18T00:12:24Z"},{"alias_kind":"pith_short_12","alias_value":"MT3SAZDD42GE","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MT3SAZDD42GETNXW","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MT3SAZDD","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MT3SAZDD42GETNXWKFBI5ASKPH","target":"record","payload":{"canonical_record":{"source":{"id":"1805.09668","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-21T19:42:41Z","cross_cats_sorted":[],"title_canon_sha256":"e92a147e111b2fa2b762587336197b273f9c5e38b54e5b4d83828515258741e5","abstract_canon_sha256":"869cbfbecf0784ab4a070f42ffc89cfe2689fc065f5ddda0d10bdba9c3b1d87a"},"schema_version":"1.0"},"canonical_sha256":"64f7206463e68c49b6f651428e824a79c39f07ade5916ad2ded07c907067ca42","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:24.218198Z","signature_b64":"F+vkjWnYNJyLdpb2z9+vFIdkjuGkf42DZXM/TCtgiHxjeOzUe3u6yiuZgoMFSakT5SrSFWD3I/WN6Zaunm67BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64f7206463e68c49b6f651428e824a79c39f07ade5916ad2ded07c907067ca42","last_reissued_at":"2026-05-18T00:12:24.217447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:24.217447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.09668","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:12:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zf+QXnKZOTuXrqNzscKAdc14PIH2nOUTT2jhBgUWlwA3GqDR9yoVlj29KiKDXNuV6zZtsq5ZLFrj8aJuV2LcDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T08:44:02.471828Z"},"content_sha256":"276fa5d6afcf338a2003cfc484082979cf8f0a1f67b09d466a7874d79858f94a","schema_version":"1.0","event_id":"sha256:276fa5d6afcf338a2003cfc484082979cf8f0a1f67b09d466a7874d79858f94a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MT3SAZDD42GETNXWKFBI5ASKPH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monotone local flows with dense periodic orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Morris W. Hirsch","submitted_at":"2018-05-21T19:42:41Z","abstract_excerpt":"Let X be a connected open set in n-dimensional Euclidean space, partially ordered by a closed convex cone K with nonempty interior: y > x if and only if y-x is nonzero and in K.\n  Theorem: If F is a monotone local flow in X whose periodic points are dense in X, then F is globally periodic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09668","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:12:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3fuufJXegSqRUrPTeO9c0iTKSBF4T+nepe5t/OJLnr5jA4ktVAhPbGBFIbq8p0xBSP2fbzHVHvlADyfdxOA1AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T08:44:02.472163Z"},"content_sha256":"c49e666e5bface253367c852517442084e1fbdcd337085b7a91e088a7ef0b4d2","schema_version":"1.0","event_id":"sha256:c49e666e5bface253367c852517442084e1fbdcd337085b7a91e088a7ef0b4d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MT3SAZDD42GETNXWKFBI5ASKPH/bundle.json","state_url":"https://pith.science/pith/MT3SAZDD42GETNXWKFBI5ASKPH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MT3SAZDD42GETNXWKFBI5ASKPH/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":"2026-06-23T08:44:02Z","links":{"resolver":"https://pith.science/pith/MT3SAZDD42GETNXWKFBI5ASKPH","bundle":"https://pith.science/pith/MT3SAZDD42GETNXWKFBI5ASKPH/bundle.json","state":"https://pith.science/pith/MT3SAZDD42GETNXWKFBI5ASKPH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MT3SAZDD42GETNXWKFBI5ASKPH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MT3SAZDD42GETNXWKFBI5ASKPH","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":"869cbfbecf0784ab4a070f42ffc89cfe2689fc065f5ddda0d10bdba9c3b1d87a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-21T19:42:41Z","title_canon_sha256":"e92a147e111b2fa2b762587336197b273f9c5e38b54e5b4d83828515258741e5"},"schema_version":"1.0","source":{"id":"1805.09668","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.09668","created_at":"2026-05-18T00:12:24Z"},{"alias_kind":"arxiv_version","alias_value":"1805.09668v2","created_at":"2026-05-18T00:12:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09668","created_at":"2026-05-18T00:12:24Z"},{"alias_kind":"pith_short_12","alias_value":"MT3SAZDD42GE","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MT3SAZDD42GETNXW","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MT3SAZDD","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:c49e666e5bface253367c852517442084e1fbdcd337085b7a91e088a7ef0b4d2","target":"graph","created_at":"2026-05-18T00:12:24Z","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":"Let X be a connected open set in n-dimensional Euclidean space, partially ordered by a closed convex cone K with nonempty interior: y > x if and only if y-x is nonzero and in K.\n  Theorem: If F is a monotone local flow in X whose periodic points are dense in X, then F is globally periodic.","authors_text":"Morris W. Hirsch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-21T19:42:41Z","title":"Monotone local flows with dense periodic orbits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09668","kind":"arxiv","version":2},"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":"sha256:276fa5d6afcf338a2003cfc484082979cf8f0a1f67b09d466a7874d79858f94a","target":"record","created_at":"2026-05-18T00:12:24Z","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":"869cbfbecf0784ab4a070f42ffc89cfe2689fc065f5ddda0d10bdba9c3b1d87a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-21T19:42:41Z","title_canon_sha256":"e92a147e111b2fa2b762587336197b273f9c5e38b54e5b4d83828515258741e5"},"schema_version":"1.0","source":{"id":"1805.09668","kind":"arxiv","version":2}},"canonical_sha256":"64f7206463e68c49b6f651428e824a79c39f07ade5916ad2ded07c907067ca42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64f7206463e68c49b6f651428e824a79c39f07ade5916ad2ded07c907067ca42","first_computed_at":"2026-05-18T00:12:24.217447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:24.217447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F+vkjWnYNJyLdpb2z9+vFIdkjuGkf42DZXM/TCtgiHxjeOzUe3u6yiuZgoMFSakT5SrSFWD3I/WN6Zaunm67BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:24.218198Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.09668","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:276fa5d6afcf338a2003cfc484082979cf8f0a1f67b09d466a7874d79858f94a","sha256:c49e666e5bface253367c852517442084e1fbdcd337085b7a91e088a7ef0b4d2"],"state_sha256":"ce23763d6babb8a72c4525591a898a01ae414da1c34ae913b3a2828cff91c6a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"63WULmvVUpo0vjkX1UrGOAP+JY8AIxZXdSUE/AA42+XIHbra11zAy67k+Z9FFg5uTBDHv8JWR66/wPPrfYduCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T08:44:02.474103Z","bundle_sha256":"2f1bf0b3e6b0bbee1421e9a3d0f64f4f9452707b4f34b893312fbfa570753f3f"}}