{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:3IQOJEYN7ZEYGHKOZUMBSFMBKH","short_pith_number":"pith:3IQOJEYN","canonical_record":{"source":{"id":"1607.00731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-04T03:27:37Z","cross_cats_sorted":[],"title_canon_sha256":"d01829b70414612461cdb2086617c565a85f6998e565aab8fa2bfc231289c879","abstract_canon_sha256":"c51dc475a4c2e89180d736ccdc098a03de725839eb41594ffe583992863ca0f3"},"schema_version":"1.0"},"canonical_sha256":"da20e4930dfe49831d4ecd1819158151e0e1011643b0cc3786f777e6934fc956","source":{"kind":"arxiv","id":"1607.00731","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00731","created_at":"2026-05-18T01:11:34Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00731v1","created_at":"2026-05-18T01:11:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00731","created_at":"2026-05-18T01:11:34Z"},{"alias_kind":"pith_short_12","alias_value":"3IQOJEYN7ZEY","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3IQOJEYN7ZEYGHKO","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3IQOJEYN","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:3IQOJEYN7ZEYGHKOZUMBSFMBKH","target":"record","payload":{"canonical_record":{"source":{"id":"1607.00731","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-04T03:27:37Z","cross_cats_sorted":[],"title_canon_sha256":"d01829b70414612461cdb2086617c565a85f6998e565aab8fa2bfc231289c879","abstract_canon_sha256":"c51dc475a4c2e89180d736ccdc098a03de725839eb41594ffe583992863ca0f3"},"schema_version":"1.0"},"canonical_sha256":"da20e4930dfe49831d4ecd1819158151e0e1011643b0cc3786f777e6934fc956","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:34.357506Z","signature_b64":"q0Osyo9nCXKcBw4NZVKuzJwEJrlcDJ+evf+DUqz8yM2qFOOpSPLwfXfSYzmvbb0cEuv57YsiBXA+pgzkwLCIAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da20e4930dfe49831d4ecd1819158151e0e1011643b0cc3786f777e6934fc956","last_reissued_at":"2026-05-18T01:11:34.356994Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:34.356994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.00731","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":"2026-05-18T01:11:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E2Q4L+dOq0tKcZblngY2qFniMl2Db57J+FYdhAgeeDU2al3ZYEjQjJpI4We5jIGNUa1wcZfSxc4+pVjR/t34CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:49:16.766847Z"},"content_sha256":"416330dcd1097d3e3cca55c9f8f6923af5c2943e57c6471d35398991d297eead","schema_version":"1.0","event_id":"sha256:416330dcd1097d3e3cca55c9f8f6923af5c2943e57c6471d35398991d297eead"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:3IQOJEYN7ZEYGHKOZUMBSFMBKH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perspectives on Kuperberg flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ana Rechtman, Steven Hurder","submitted_at":"2016-07-04T03:27:37Z","abstract_excerpt":"The \"Seifert Conjecture\" asks, \"Does every non-singular vector field on the 3-sphere ${\\mathbb S}^3$ have a periodic orbit?\" In a celebrated work, Krystyna Kuperberg gave a construction of a smooth aperiodic vector field on a plug, which is then used to construct counter-examples to the Seifert Conjecture for smooth flows on the $3$-sphere, and on compact 3-manifolds in general. The dynamics of the flows in these plugs have been extensively studied, with more precise results known in special \"generic\" cases of the construction. Moreover, the dynamical properties of smooth perturbations of Kupe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00731","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":"2026-05-18T01:11:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W02xDp6l/X6/VH3zfotSUOQbZPu3yqC1jtnnimKPBzSwkMzSP15mljEWpSAnJKOX38D60szXUvOqpJbHgcSlBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:49:16.767183Z"},"content_sha256":"bc929c0d23a621741743c61f08a617eca9b28f823d6f3a6d9613ac28a7a73ac4","schema_version":"1.0","event_id":"sha256:bc929c0d23a621741743c61f08a617eca9b28f823d6f3a6d9613ac28a7a73ac4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3IQOJEYN7ZEYGHKOZUMBSFMBKH/bundle.json","state_url":"https://pith.science/pith/3IQOJEYN7ZEYGHKOZUMBSFMBKH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3IQOJEYN7ZEYGHKOZUMBSFMBKH/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":"2026-06-24T08:49:16Z","links":{"resolver":"https://pith.science/pith/3IQOJEYN7ZEYGHKOZUMBSFMBKH","bundle":"https://pith.science/pith/3IQOJEYN7ZEYGHKOZUMBSFMBKH/bundle.json","state":"https://pith.science/pith/3IQOJEYN7ZEYGHKOZUMBSFMBKH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3IQOJEYN7ZEYGHKOZUMBSFMBKH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3IQOJEYN7ZEYGHKOZUMBSFMBKH","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":"c51dc475a4c2e89180d736ccdc098a03de725839eb41594ffe583992863ca0f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-04T03:27:37Z","title_canon_sha256":"d01829b70414612461cdb2086617c565a85f6998e565aab8fa2bfc231289c879"},"schema_version":"1.0","source":{"id":"1607.00731","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00731","created_at":"2026-05-18T01:11:34Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00731v1","created_at":"2026-05-18T01:11:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00731","created_at":"2026-05-18T01:11:34Z"},{"alias_kind":"pith_short_12","alias_value":"3IQOJEYN7ZEY","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3IQOJEYN7ZEYGHKO","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3IQOJEYN","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:bc929c0d23a621741743c61f08a617eca9b28f823d6f3a6d9613ac28a7a73ac4","target":"graph","created_at":"2026-05-18T01:11:34Z","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":"The \"Seifert Conjecture\" asks, \"Does every non-singular vector field on the 3-sphere ${\\mathbb S}^3$ have a periodic orbit?\" In a celebrated work, Krystyna Kuperberg gave a construction of a smooth aperiodic vector field on a plug, which is then used to construct counter-examples to the Seifert Conjecture for smooth flows on the $3$-sphere, and on compact 3-manifolds in general. The dynamics of the flows in these plugs have been extensively studied, with more precise results known in special \"generic\" cases of the construction. Moreover, the dynamical properties of smooth perturbations of Kupe","authors_text":"Ana Rechtman, Steven Hurder","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-04T03:27:37Z","title":"Perspectives on Kuperberg flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00731","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":"sha256:416330dcd1097d3e3cca55c9f8f6923af5c2943e57c6471d35398991d297eead","target":"record","created_at":"2026-05-18T01:11:34Z","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":"c51dc475a4c2e89180d736ccdc098a03de725839eb41594ffe583992863ca0f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-04T03:27:37Z","title_canon_sha256":"d01829b70414612461cdb2086617c565a85f6998e565aab8fa2bfc231289c879"},"schema_version":"1.0","source":{"id":"1607.00731","kind":"arxiv","version":1}},"canonical_sha256":"da20e4930dfe49831d4ecd1819158151e0e1011643b0cc3786f777e6934fc956","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da20e4930dfe49831d4ecd1819158151e0e1011643b0cc3786f777e6934fc956","first_computed_at":"2026-05-18T01:11:34.356994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:34.356994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q0Osyo9nCXKcBw4NZVKuzJwEJrlcDJ+evf+DUqz8yM2qFOOpSPLwfXfSYzmvbb0cEuv57YsiBXA+pgzkwLCIAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:34.357506Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.00731","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:416330dcd1097d3e3cca55c9f8f6923af5c2943e57c6471d35398991d297eead","sha256:bc929c0d23a621741743c61f08a617eca9b28f823d6f3a6d9613ac28a7a73ac4"],"state_sha256":"952a69ca6aaf6eb9aac14d89842780291526b214c7d9c8e500d5675905ec3190"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eboSJKqNvlmeAkwfi+RFcW4DOuSKX8Bg44NuF4Esib8ZyMMYmai9GgC0kYb+XLWBoZrxYZp06oAEzlJQlINXBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T08:49:16.769114Z","bundle_sha256":"c259f893b3ee457088c14ac4b37ed5673eab9b6bf62309e47ad4c9d1494cec7c"}}