{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MUBRUCEBI3FNCCGQC2WZ6OQGVB","short_pith_number":"pith:MUBRUCEB","canonical_record":{"source":{"id":"1711.09126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-24T20:11:39Z","cross_cats_sorted":[],"title_canon_sha256":"84574944bcfeda99cccbc12e4803a5a1615cae8b7bbc63364cdebb80ac16ad89","abstract_canon_sha256":"891d35f9192cf1f5056ba88bdea7e0fcad595c71737aac6d579feadde1917095"},"schema_version":"1.0"},"canonical_sha256":"65031a088146cad108d016ad9f3a06a8454ff06eaeff39bd5e121eb27cf6d455","source":{"kind":"arxiv","id":"1711.09126","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.09126","created_at":"2026-05-17T23:49:22Z"},{"alias_kind":"arxiv_version","alias_value":"1711.09126v1","created_at":"2026-05-17T23:49:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.09126","created_at":"2026-05-17T23:49:22Z"},{"alias_kind":"pith_short_12","alias_value":"MUBRUCEBI3FN","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MUBRUCEBI3FNCCGQ","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MUBRUCEB","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MUBRUCEBI3FNCCGQC2WZ6OQGVB","target":"record","payload":{"canonical_record":{"source":{"id":"1711.09126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-24T20:11:39Z","cross_cats_sorted":[],"title_canon_sha256":"84574944bcfeda99cccbc12e4803a5a1615cae8b7bbc63364cdebb80ac16ad89","abstract_canon_sha256":"891d35f9192cf1f5056ba88bdea7e0fcad595c71737aac6d579feadde1917095"},"schema_version":"1.0"},"canonical_sha256":"65031a088146cad108d016ad9f3a06a8454ff06eaeff39bd5e121eb27cf6d455","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:22.673015Z","signature_b64":"869EVJ99dr/GiNEH0MBmh5fV6+RoQ7T8ERRzYm9RSyY9BkbyRjwRArqvrkwQAAuyMT2gJeSM2VvmS/PY0bCuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65031a088146cad108d016ad9f3a06a8454ff06eaeff39bd5e121eb27cf6d455","last_reissued_at":"2026-05-17T23:49:22.672568Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:22.672568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.09126","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":"2026-05-17T23:49:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9NF20GDHDQ1SelHEo84lHXKX/nBcdJIcctujrKFU2Eh3J5S+blGYxDvGUNVsipdQcN6NmwANuoVxeVY9G/1RCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:51:19.125508Z"},"content_sha256":"3464336312a490b990564c6733eb6674ebc6606dece5f7ee7f5154cbd3d9eb77","schema_version":"1.0","event_id":"sha256:3464336312a490b990564c6733eb6674ebc6606dece5f7ee7f5154cbd3d9eb77"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MUBRUCEBI3FNCCGQC2WZ6OQGVB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vector potential normal form classification for completely integrable solenoidal nilpotent singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Fahimeh Mokhtari, Jan A. Sanders, Majid Gazor","submitted_at":"2017-11-24T20:11:39Z","abstract_excerpt":"We introduce a sl_2-invariant family of nonlinear vector fields with a non-semisimple triple zero singularity. In this paper we are concerned with characterization and normal form classification of these vector fields. We show that the family constitutes a Lie algebra structure and each vector field from this family is solenoidal, completely integrable and rotational. All such vector fields share a common quadratic invariant. We provide a Poisson structure for the Lie algebra from which the second invariant for each vector field can be readily derived. We show that each vector field from this "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09126","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":"2026-05-17T23:49:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iW04cEHft0fIg5Hz7bVSlVFwDmc5nIYFFWHERZ0zYJgLEx5bhazPBnM+sw761b8DR8nhYhuxoCyFx9wejmLYAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:51:19.125862Z"},"content_sha256":"85e70ccbf5666345f061b467925cadedb9fa96e7fa0b178395d160d1198d0e3b","schema_version":"1.0","event_id":"sha256:85e70ccbf5666345f061b467925cadedb9fa96e7fa0b178395d160d1198d0e3b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MUBRUCEBI3FNCCGQC2WZ6OQGVB/bundle.json","state_url":"https://pith.science/pith/MUBRUCEBI3FNCCGQC2WZ6OQGVB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MUBRUCEBI3FNCCGQC2WZ6OQGVB/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":"2026-06-05T18:51:19Z","links":{"resolver":"https://pith.science/pith/MUBRUCEBI3FNCCGQC2WZ6OQGVB","bundle":"https://pith.science/pith/MUBRUCEBI3FNCCGQC2WZ6OQGVB/bundle.json","state":"https://pith.science/pith/MUBRUCEBI3FNCCGQC2WZ6OQGVB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MUBRUCEBI3FNCCGQC2WZ6OQGVB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MUBRUCEBI3FNCCGQC2WZ6OQGVB","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":"891d35f9192cf1f5056ba88bdea7e0fcad595c71737aac6d579feadde1917095","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-24T20:11:39Z","title_canon_sha256":"84574944bcfeda99cccbc12e4803a5a1615cae8b7bbc63364cdebb80ac16ad89"},"schema_version":"1.0","source":{"id":"1711.09126","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.09126","created_at":"2026-05-17T23:49:22Z"},{"alias_kind":"arxiv_version","alias_value":"1711.09126v1","created_at":"2026-05-17T23:49:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.09126","created_at":"2026-05-17T23:49:22Z"},{"alias_kind":"pith_short_12","alias_value":"MUBRUCEBI3FN","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MUBRUCEBI3FNCCGQ","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MUBRUCEB","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:85e70ccbf5666345f061b467925cadedb9fa96e7fa0b178395d160d1198d0e3b","target":"graph","created_at":"2026-05-17T23:49:22Z","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 introduce a sl_2-invariant family of nonlinear vector fields with a non-semisimple triple zero singularity. In this paper we are concerned with characterization and normal form classification of these vector fields. We show that the family constitutes a Lie algebra structure and each vector field from this family is solenoidal, completely integrable and rotational. All such vector fields share a common quadratic invariant. We provide a Poisson structure for the Lie algebra from which the second invariant for each vector field can be readily derived. We show that each vector field from this ","authors_text":"Fahimeh Mokhtari, Jan A. Sanders, Majid Gazor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-24T20:11:39Z","title":"Vector potential normal form classification for completely integrable solenoidal nilpotent singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.09126","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":"sha256:3464336312a490b990564c6733eb6674ebc6606dece5f7ee7f5154cbd3d9eb77","target":"record","created_at":"2026-05-17T23:49:22Z","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":"891d35f9192cf1f5056ba88bdea7e0fcad595c71737aac6d579feadde1917095","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-24T20:11:39Z","title_canon_sha256":"84574944bcfeda99cccbc12e4803a5a1615cae8b7bbc63364cdebb80ac16ad89"},"schema_version":"1.0","source":{"id":"1711.09126","kind":"arxiv","version":1}},"canonical_sha256":"65031a088146cad108d016ad9f3a06a8454ff06eaeff39bd5e121eb27cf6d455","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65031a088146cad108d016ad9f3a06a8454ff06eaeff39bd5e121eb27cf6d455","first_computed_at":"2026-05-17T23:49:22.672568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:22.672568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"869EVJ99dr/GiNEH0MBmh5fV6+RoQ7T8ERRzYm9RSyY9BkbyRjwRArqvrkwQAAuyMT2gJeSM2VvmS/PY0bCuDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:22.673015Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.09126","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3464336312a490b990564c6733eb6674ebc6606dece5f7ee7f5154cbd3d9eb77","sha256:85e70ccbf5666345f061b467925cadedb9fa96e7fa0b178395d160d1198d0e3b"],"state_sha256":"a64ff3e09c200e356faa0374be181dac14294ed438b9abb6820b9c19e50c4455"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U9LFN5F+d13xAvtftCy7T9ZHm4YMtpMredKQcXIu6AZEvdfOXpOz1CE3facNzilqPwBkB8UGHRXqyWkoMXKbAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T18:51:19.127869Z","bundle_sha256":"de5c377942382ddb748e992c2ebafdf0df2c12b02f8a5b9636d8de7d7fccacf5"}}