{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:B7TEGWUJ2J62LQ7XIMBUWEMNKA","short_pith_number":"pith:B7TEGWUJ","canonical_record":{"source":{"id":"1905.06787","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-16T14:39:32Z","cross_cats_sorted":[],"title_canon_sha256":"756f791997c71d47d591120f7f0dc3b2dd90c6811be53d9b40ab56a6adedffa9","abstract_canon_sha256":"2b7b98abdb4c229159f4fa8a3961da3a827bd4915b0886e1f9966ff0d1f215e3"},"schema_version":"1.0"},"canonical_sha256":"0fe6435a89d27da5c3f743034b118d502b8e04234213561b59201bacaafb7bc9","source":{"kind":"arxiv","id":"1905.06787","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.06787","created_at":"2026-05-17T23:46:01Z"},{"alias_kind":"arxiv_version","alias_value":"1905.06787v1","created_at":"2026-05-17T23:46:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.06787","created_at":"2026-05-17T23:46:01Z"},{"alias_kind":"pith_short_12","alias_value":"B7TEGWUJ2J62","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"B7TEGWUJ2J62LQ7X","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"B7TEGWUJ","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:B7TEGWUJ2J62LQ7XIMBUWEMNKA","target":"record","payload":{"canonical_record":{"source":{"id":"1905.06787","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-16T14:39:32Z","cross_cats_sorted":[],"title_canon_sha256":"756f791997c71d47d591120f7f0dc3b2dd90c6811be53d9b40ab56a6adedffa9","abstract_canon_sha256":"2b7b98abdb4c229159f4fa8a3961da3a827bd4915b0886e1f9966ff0d1f215e3"},"schema_version":"1.0"},"canonical_sha256":"0fe6435a89d27da5c3f743034b118d502b8e04234213561b59201bacaafb7bc9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:01.038959Z","signature_b64":"sAGEch7BBuQbld1COfhnfkeg5cLAN8Dl9zweDLcbKb+fDbdj2K4GCP/EXvaxg7VeI7yiw5D6y8Gbz63Ns5zyAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fe6435a89d27da5c3f743034b118d502b8e04234213561b59201bacaafb7bc9","last_reissued_at":"2026-05-17T23:46:01.038379Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:01.038379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.06787","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":"2026-05-17T23:46:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"us4vqNaiNJlLO7pl8K4dUs1l8374sRKHb1bc1LjPGQ1WmHQXtoQV0XD2wOUDQpmSc33T9scOx65ofQUhbJPsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:55:05.535738Z"},"content_sha256":"eab53a68f9e73a3ff34b9240ba13585b49893e24cbc7c6db95dbadc6fd733206","schema_version":"1.0","event_id":"sha256:eab53a68f9e73a3ff34b9240ba13585b49893e24cbc7c6db95dbadc6fd733206"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:B7TEGWUJ2J62LQ7XIMBUWEMNKA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generical behavior of flows strongly monotone with respect to high-rank cones","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":"2019-05-16T14:39:32Z","abstract_excerpt":"We consider a $C^{1,\\alpha}$ smooth flow in $\\mathbb{R}^n$ which is \"strongly monotone\" with respect to a cone $C$ of rank $k$, a closed set that contains a linear subspace of dimension $k$ and no linear subspaces of higher dimension. We prove that orbits with initial data from an open and dense subset of the phase space are either pseudo-ordered or convergent to equilibria. This covers the celebrated Hirsch's Generic Convergence Theorem in the case $k=1$, yields a generic Poincar\\'{e}-Bendixson Theorem for the case $k=2$, and holds true with arbitrary dimension $k$. Our approach involves the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.06787","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":"2026-05-17T23:46:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FDVzyr0/t2UtrEvAuF/hncpr42yNeWjWSQ/s68mDsQwThOgKMS3VLZfZ5lsv/uhDlMv4vtAU4h/TZFhpUiErBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:55:05.536095Z"},"content_sha256":"110a9ecb7c6673edc0536026d0c03eab9476a43e73be81cac379501a2ebd9b32","schema_version":"1.0","event_id":"sha256:110a9ecb7c6673edc0536026d0c03eab9476a43e73be81cac379501a2ebd9b32"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B7TEGWUJ2J62LQ7XIMBUWEMNKA/bundle.json","state_url":"https://pith.science/pith/B7TEGWUJ2J62LQ7XIMBUWEMNKA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B7TEGWUJ2J62LQ7XIMBUWEMNKA/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":"2026-06-23T14:55:05Z","links":{"resolver":"https://pith.science/pith/B7TEGWUJ2J62LQ7XIMBUWEMNKA","bundle":"https://pith.science/pith/B7TEGWUJ2J62LQ7XIMBUWEMNKA/bundle.json","state":"https://pith.science/pith/B7TEGWUJ2J62LQ7XIMBUWEMNKA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B7TEGWUJ2J62LQ7XIMBUWEMNKA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:B7TEGWUJ2J62LQ7XIMBUWEMNKA","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":"2b7b98abdb4c229159f4fa8a3961da3a827bd4915b0886e1f9966ff0d1f215e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-16T14:39:32Z","title_canon_sha256":"756f791997c71d47d591120f7f0dc3b2dd90c6811be53d9b40ab56a6adedffa9"},"schema_version":"1.0","source":{"id":"1905.06787","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.06787","created_at":"2026-05-17T23:46:01Z"},{"alias_kind":"arxiv_version","alias_value":"1905.06787v1","created_at":"2026-05-17T23:46:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.06787","created_at":"2026-05-17T23:46:01Z"},{"alias_kind":"pith_short_12","alias_value":"B7TEGWUJ2J62","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"B7TEGWUJ2J62LQ7X","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"B7TEGWUJ","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:110a9ecb7c6673edc0536026d0c03eab9476a43e73be81cac379501a2ebd9b32","target":"graph","created_at":"2026-05-17T23:46:01Z","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 a $C^{1,\\alpha}$ smooth flow in $\\mathbb{R}^n$ which is \"strongly monotone\" with respect to a cone $C$ of rank $k$, a closed set that contains a linear subspace of dimension $k$ and no linear subspaces of higher dimension. We prove that orbits with initial data from an open and dense subset of the phase space are either pseudo-ordered or convergent to equilibria. This covers the celebrated Hirsch's Generic Convergence Theorem in the case $k=1$, yields a generic Poincar\\'{e}-Bendixson Theorem for the case $k=2$, and holds true with arbitrary dimension $k$. Our approach involves the ","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":"2019-05-16T14:39:32Z","title":"Generical behavior of flows strongly monotone with respect to high-rank cones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.06787","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:eab53a68f9e73a3ff34b9240ba13585b49893e24cbc7c6db95dbadc6fd733206","target":"record","created_at":"2026-05-17T23:46:01Z","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":"2b7b98abdb4c229159f4fa8a3961da3a827bd4915b0886e1f9966ff0d1f215e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-16T14:39:32Z","title_canon_sha256":"756f791997c71d47d591120f7f0dc3b2dd90c6811be53d9b40ab56a6adedffa9"},"schema_version":"1.0","source":{"id":"1905.06787","kind":"arxiv","version":1}},"canonical_sha256":"0fe6435a89d27da5c3f743034b118d502b8e04234213561b59201bacaafb7bc9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fe6435a89d27da5c3f743034b118d502b8e04234213561b59201bacaafb7bc9","first_computed_at":"2026-05-17T23:46:01.038379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:01.038379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sAGEch7BBuQbld1COfhnfkeg5cLAN8Dl9zweDLcbKb+fDbdj2K4GCP/EXvaxg7VeI7yiw5D6y8Gbz63Ns5zyAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:01.038959Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.06787","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eab53a68f9e73a3ff34b9240ba13585b49893e24cbc7c6db95dbadc6fd733206","sha256:110a9ecb7c6673edc0536026d0c03eab9476a43e73be81cac379501a2ebd9b32"],"state_sha256":"78f34ee4cda00c465a74bff73a41886bf91fb10d15407f2c23a59c2f00f14a08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"moxgIhQtZE/hpCZJwGyLAqLUz1uqaPEQjP1rB8ebLxpdFANtUE4Bsc87soBQ2TvhKOcEhrUTkDPic2IHM3//Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:55:05.538127Z","bundle_sha256":"b6a549c9a8a96fbd1e1e677f4d758869bbe2f3e9cd79eb48f2dc20bfbaa42182"}}