{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MTI655KAYN7IEZ72Q3XYGFP77B","short_pith_number":"pith:MTI655KA","canonical_record":{"source":{"id":"1412.1540","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-12-04T02:07:36Z","cross_cats_sorted":[],"title_canon_sha256":"fa46c9d4885928b9f05cff097e72b623fbfbfcb99ac29ec93b09b2b3fc1e1a6a","abstract_canon_sha256":"7c7ddb871e04e2ac71c54501af8f16f619affec8b011a31ce6627efef58d7f66"},"schema_version":"1.0"},"canonical_sha256":"64d1eef540c37e8267fa86ef8315fff8770cbf8ac0b5eb864469f36b946a9521","source":{"kind":"arxiv","id":"1412.1540","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1540","created_at":"2026-05-18T01:01:02Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1540v1","created_at":"2026-05-18T01:01:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1540","created_at":"2026-05-18T01:01:02Z"},{"alias_kind":"pith_short_12","alias_value":"MTI655KAYN7I","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MTI655KAYN7IEZ72","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MTI655KA","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MTI655KAYN7IEZ72Q3XYGFP77B","target":"record","payload":{"canonical_record":{"source":{"id":"1412.1540","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-12-04T02:07:36Z","cross_cats_sorted":[],"title_canon_sha256":"fa46c9d4885928b9f05cff097e72b623fbfbfcb99ac29ec93b09b2b3fc1e1a6a","abstract_canon_sha256":"7c7ddb871e04e2ac71c54501af8f16f619affec8b011a31ce6627efef58d7f66"},"schema_version":"1.0"},"canonical_sha256":"64d1eef540c37e8267fa86ef8315fff8770cbf8ac0b5eb864469f36b946a9521","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:02.078934Z","signature_b64":"rMaOOX6UquIDvQslCNUaEfQiyh6zOBhqNESr3NgMUl7pEVzWKCvV8VlEGy5fnNeZSyGA7m2yGoJzteA41nIpBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64d1eef540c37e8267fa86ef8315fff8770cbf8ac0b5eb864469f36b946a9521","last_reissued_at":"2026-05-18T01:01:02.078091Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:02.078091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.1540","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":"2026-05-18T01:01:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ydamFjBiYUjVR5DLp0cRrGo2rGH62GCPOIhOXpZNYPExt1aznbv1V2jTr/rXPqher3xmGn0dOPIbnwy/S4kQDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:55:42.261566Z"},"content_sha256":"21db9fb012cd07e9002c04cd6ba4cb7e1c78892f933b7a94a2348043fd607a91","schema_version":"1.0","event_id":"sha256:21db9fb012cd07e9002c04cd6ba4cb7e1c78892f933b7a94a2348043fd607a91"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MTI655KAYN7IEZ72Q3XYGFP77B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transversality for Cyclic Negative Feedback Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dun Zhou, Yi Wang","submitted_at":"2014-12-04T02:07:36Z","abstract_excerpt":"Transversality of stable and unstable manifolds of hyperbolic periodic trajectories is proved for monotone cyclic systems with negative feedback. Such systems in general are not in the category of monotone dynamical systems in the sense of Hirsch. Our main tool utilized in the proofs is the so-called cone of high rank. We further show that stable and unstable manifolds between a hyperbolic equilibrium and a hyperbolic periodic trajectory, or between two hyperbolic equilibria with different dimensional unstable manifolds also intersect transversely."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1540","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":"2026-05-18T01:01:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DiXdd+4hCTBDC8/XQVKdI9JleObkbYXnZVolYD7v1Edya7R/r/pef/6Kydf8ta6y4a+1U7d6Tf/RS205X7MAAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:55:42.261903Z"},"content_sha256":"95da0f45da49654d989449bab1bff93d92e1a90be74a0d4761d88ca1976a8338","schema_version":"1.0","event_id":"sha256:95da0f45da49654d989449bab1bff93d92e1a90be74a0d4761d88ca1976a8338"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MTI655KAYN7IEZ72Q3XYGFP77B/bundle.json","state_url":"https://pith.science/pith/MTI655KAYN7IEZ72Q3XYGFP77B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MTI655KAYN7IEZ72Q3XYGFP77B/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":"2026-06-27T10:55:42Z","links":{"resolver":"https://pith.science/pith/MTI655KAYN7IEZ72Q3XYGFP77B","bundle":"https://pith.science/pith/MTI655KAYN7IEZ72Q3XYGFP77B/bundle.json","state":"https://pith.science/pith/MTI655KAYN7IEZ72Q3XYGFP77B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MTI655KAYN7IEZ72Q3XYGFP77B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MTI655KAYN7IEZ72Q3XYGFP77B","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":"7c7ddb871e04e2ac71c54501af8f16f619affec8b011a31ce6627efef58d7f66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-12-04T02:07:36Z","title_canon_sha256":"fa46c9d4885928b9f05cff097e72b623fbfbfcb99ac29ec93b09b2b3fc1e1a6a"},"schema_version":"1.0","source":{"id":"1412.1540","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1540","created_at":"2026-05-18T01:01:02Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1540v1","created_at":"2026-05-18T01:01:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1540","created_at":"2026-05-18T01:01:02Z"},{"alias_kind":"pith_short_12","alias_value":"MTI655KAYN7I","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MTI655KAYN7IEZ72","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MTI655KA","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:95da0f45da49654d989449bab1bff93d92e1a90be74a0d4761d88ca1976a8338","target":"graph","created_at":"2026-05-18T01:01:02Z","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":"Transversality of stable and unstable manifolds of hyperbolic periodic trajectories is proved for monotone cyclic systems with negative feedback. Such systems in general are not in the category of monotone dynamical systems in the sense of Hirsch. Our main tool utilized in the proofs is the so-called cone of high rank. We further show that stable and unstable manifolds between a hyperbolic equilibrium and a hyperbolic periodic trajectory, or between two hyperbolic equilibria with different dimensional unstable manifolds also intersect transversely.","authors_text":"Dun Zhou, Yi Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-12-04T02:07:36Z","title":"Transversality for Cyclic Negative Feedback Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1540","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":"sha256:21db9fb012cd07e9002c04cd6ba4cb7e1c78892f933b7a94a2348043fd607a91","target":"record","created_at":"2026-05-18T01:01:02Z","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":"7c7ddb871e04e2ac71c54501af8f16f619affec8b011a31ce6627efef58d7f66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-12-04T02:07:36Z","title_canon_sha256":"fa46c9d4885928b9f05cff097e72b623fbfbfcb99ac29ec93b09b2b3fc1e1a6a"},"schema_version":"1.0","source":{"id":"1412.1540","kind":"arxiv","version":1}},"canonical_sha256":"64d1eef540c37e8267fa86ef8315fff8770cbf8ac0b5eb864469f36b946a9521","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64d1eef540c37e8267fa86ef8315fff8770cbf8ac0b5eb864469f36b946a9521","first_computed_at":"2026-05-18T01:01:02.078091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:02.078091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rMaOOX6UquIDvQslCNUaEfQiyh6zOBhqNESr3NgMUl7pEVzWKCvV8VlEGy5fnNeZSyGA7m2yGoJzteA41nIpBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:02.078934Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.1540","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21db9fb012cd07e9002c04cd6ba4cb7e1c78892f933b7a94a2348043fd607a91","sha256:95da0f45da49654d989449bab1bff93d92e1a90be74a0d4761d88ca1976a8338"],"state_sha256":"75e5fa67f87755372fb6af3f70c9fbfefa86286c6943d1abd3b1f9a7e9660d49"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aE3WLGVT/1SMpXZWAaX5kFPR6emC3QASNwSO7jGHDo1UhQIp2tcXWXtgKBLyp0uKrYK7fFE5+P/nSbg/jH4/Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T10:55:42.263950Z","bundle_sha256":"dcd03ad78cd2fb9eea9b6ba4bee60be6c3da1cf9e59bdc4fbf5717d6b4733856"}}