{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QB2DQ6Z3MP7LUQQU7MOHAFSCJ2","short_pith_number":"pith:QB2DQ6Z3","canonical_record":{"source":{"id":"1603.05129","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-16T14:46:40Z","cross_cats_sorted":[],"title_canon_sha256":"2d45cc93182366bb72a86eee185b2ef87e437258184a3ad622035227d8bc8a84","abstract_canon_sha256":"faec2f6609fbad1dea3a40daca57aba32e82201747230a22be37aacadf95386d"},"schema_version":"1.0"},"canonical_sha256":"8074387b3b63feba4214fb1c7016424ea41f98dd1224b107da063e0a38da3127","source":{"kind":"arxiv","id":"1603.05129","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05129","created_at":"2026-05-18T01:18:57Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05129v1","created_at":"2026-05-18T01:18:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05129","created_at":"2026-05-18T01:18:57Z"},{"alias_kind":"pith_short_12","alias_value":"QB2DQ6Z3MP7L","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QB2DQ6Z3MP7LUQQU","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QB2DQ6Z3","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QB2DQ6Z3MP7LUQQU7MOHAFSCJ2","target":"record","payload":{"canonical_record":{"source":{"id":"1603.05129","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-16T14:46:40Z","cross_cats_sorted":[],"title_canon_sha256":"2d45cc93182366bb72a86eee185b2ef87e437258184a3ad622035227d8bc8a84","abstract_canon_sha256":"faec2f6609fbad1dea3a40daca57aba32e82201747230a22be37aacadf95386d"},"schema_version":"1.0"},"canonical_sha256":"8074387b3b63feba4214fb1c7016424ea41f98dd1224b107da063e0a38da3127","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:57.987070Z","signature_b64":"sB9hw+k2h+QEOq/teuchPr8kqSU//rfc5M73Y5Xz6O+7PW//B84XmwnhETuzfHxYT3YY/3qCYTFr6vW4clLYCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8074387b3b63feba4214fb1c7016424ea41f98dd1224b107da063e0a38da3127","last_reissued_at":"2026-05-18T01:18:57.986699Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:57.986699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.05129","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":"2026-05-18T01:18:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uBg1GtO15fCIy+oFmMXVO+TrKNwZld7YgOuIC9Zsx3vUvZ8OCeeaAhdEOzsJH2opGLvhAy0SZGK54drz7vauAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:34:36.284351Z"},"content_sha256":"70b2e14d632adf775b335d9b7531ac3fc116fba5e6bec44ae9e5086d24a0a94e","schema_version":"1.0","event_id":"sha256:70b2e14d632adf775b335d9b7531ac3fc116fba5e6bec44ae9e5086d24a0a94e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QB2DQ6Z3MP7LUQQU7MOHAFSCJ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monotone semiflows with respect to high-rank cones on a Banach space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jianhong Wu, Lirui Feng, Yi Wang","submitted_at":"2016-03-16T14:46:40Z","abstract_excerpt":"We consider semiflows in general Banach spaces motivated by monotone cyclic feedback systems or differential equations with integer-valued Lyapunov functionals. These semiflows enjoy strong monotonicity properties with respect to cones of high ranks, which imply order-related structures on the $\\omega$-limit sets of precompact semi-orbits. We show that for a pseudo-ordered precompact semi-orbit the $\\omega$-limit set $\\Omega$ is either ordered, or is contained in the set of equilibria, or possesses a certain ordered homoclinic property. In particular, we show that if $\\Omega$ contains no equil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05129","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":"2026-05-18T01:18:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jDN9afTp5CRdllP4cJhLuvUUPvnO6PuNgT1g7rfAu28wUTuiArkJT1WC6douuqheFhaif5A9w75EKtLfeH/yCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:34:36.284708Z"},"content_sha256":"54f9ec55353d2da23d086310bac79d8cc1b128f5ad45fb01a9449df05b85b6cf","schema_version":"1.0","event_id":"sha256:54f9ec55353d2da23d086310bac79d8cc1b128f5ad45fb01a9449df05b85b6cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QB2DQ6Z3MP7LUQQU7MOHAFSCJ2/bundle.json","state_url":"https://pith.science/pith/QB2DQ6Z3MP7LUQQU7MOHAFSCJ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QB2DQ6Z3MP7LUQQU7MOHAFSCJ2/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":"2026-06-23T15:34:36Z","links":{"resolver":"https://pith.science/pith/QB2DQ6Z3MP7LUQQU7MOHAFSCJ2","bundle":"https://pith.science/pith/QB2DQ6Z3MP7LUQQU7MOHAFSCJ2/bundle.json","state":"https://pith.science/pith/QB2DQ6Z3MP7LUQQU7MOHAFSCJ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QB2DQ6Z3MP7LUQQU7MOHAFSCJ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QB2DQ6Z3MP7LUQQU7MOHAFSCJ2","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":"faec2f6609fbad1dea3a40daca57aba32e82201747230a22be37aacadf95386d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-16T14:46:40Z","title_canon_sha256":"2d45cc93182366bb72a86eee185b2ef87e437258184a3ad622035227d8bc8a84"},"schema_version":"1.0","source":{"id":"1603.05129","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05129","created_at":"2026-05-18T01:18:57Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05129v1","created_at":"2026-05-18T01:18:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05129","created_at":"2026-05-18T01:18:57Z"},{"alias_kind":"pith_short_12","alias_value":"QB2DQ6Z3MP7L","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QB2DQ6Z3MP7LUQQU","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QB2DQ6Z3","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:54f9ec55353d2da23d086310bac79d8cc1b128f5ad45fb01a9449df05b85b6cf","target":"graph","created_at":"2026-05-18T01:18:57Z","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":"We consider semiflows in general Banach spaces motivated by monotone cyclic feedback systems or differential equations with integer-valued Lyapunov functionals. These semiflows enjoy strong monotonicity properties with respect to cones of high ranks, which imply order-related structures on the $\\omega$-limit sets of precompact semi-orbits. We show that for a pseudo-ordered precompact semi-orbit the $\\omega$-limit set $\\Omega$ is either ordered, or is contained in the set of equilibria, or possesses a certain ordered homoclinic property. In particular, we show that if $\\Omega$ contains no equil","authors_text":"Jianhong Wu, Lirui Feng, Yi Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-16T14:46:40Z","title":"Monotone semiflows with respect to high-rank cones on a Banach space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05129","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":"sha256:70b2e14d632adf775b335d9b7531ac3fc116fba5e6bec44ae9e5086d24a0a94e","target":"record","created_at":"2026-05-18T01:18:57Z","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":"faec2f6609fbad1dea3a40daca57aba32e82201747230a22be37aacadf95386d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-16T14:46:40Z","title_canon_sha256":"2d45cc93182366bb72a86eee185b2ef87e437258184a3ad622035227d8bc8a84"},"schema_version":"1.0","source":{"id":"1603.05129","kind":"arxiv","version":1}},"canonical_sha256":"8074387b3b63feba4214fb1c7016424ea41f98dd1224b107da063e0a38da3127","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8074387b3b63feba4214fb1c7016424ea41f98dd1224b107da063e0a38da3127","first_computed_at":"2026-05-18T01:18:57.986699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:57.986699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sB9hw+k2h+QEOq/teuchPr8kqSU//rfc5M73Y5Xz6O+7PW//B84XmwnhETuzfHxYT3YY/3qCYTFr6vW4clLYCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:57.987070Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05129","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70b2e14d632adf775b335d9b7531ac3fc116fba5e6bec44ae9e5086d24a0a94e","sha256:54f9ec55353d2da23d086310bac79d8cc1b128f5ad45fb01a9449df05b85b6cf"],"state_sha256":"0eac6e9d4e55d83725e4d40c5cde9e424bd7ccfe72735944f253bc346c160edf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1BGKx8IBQk4dK2kfJSXr6dqeqE4tyo1m238v3dHQoJZwly3aS6ZIl+mc3mAmN/I117BDqapNG3CoTIexvIXaDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:34:36.286603Z","bundle_sha256":"d61d1103b21fb06fd5015e9890766efd6571775934515ab96e4e3a65d93c87d7"}}