{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VT6QRMGGJYWVCSBYAWOAT6EMZP","short_pith_number":"pith:VT6QRMGG","canonical_record":{"source":{"id":"1711.11254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-30T06:46:28Z","cross_cats_sorted":[],"title_canon_sha256":"a8afdd6dc11b75a931ee9cb37794611c2a7ba8536bdef5874351622ff14f5640","abstract_canon_sha256":"48aaed60b049baf576356295d044ea4a877709d8afb4319f7efb59369cf30ea8"},"schema_version":"1.0"},"canonical_sha256":"acfd08b0c64e2d514838059c09f88ccbceda53b05c09026fd453f7336696c7ad","source":{"kind":"arxiv","id":"1711.11254","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11254","created_at":"2026-05-18T00:29:12Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11254v1","created_at":"2026-05-18T00:29:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11254","created_at":"2026-05-18T00:29:12Z"},{"alias_kind":"pith_short_12","alias_value":"VT6QRMGGJYWV","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VT6QRMGGJYWVCSBY","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VT6QRMGG","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VT6QRMGGJYWVCSBYAWOAT6EMZP","target":"record","payload":{"canonical_record":{"source":{"id":"1711.11254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-30T06:46:28Z","cross_cats_sorted":[],"title_canon_sha256":"a8afdd6dc11b75a931ee9cb37794611c2a7ba8536bdef5874351622ff14f5640","abstract_canon_sha256":"48aaed60b049baf576356295d044ea4a877709d8afb4319f7efb59369cf30ea8"},"schema_version":"1.0"},"canonical_sha256":"acfd08b0c64e2d514838059c09f88ccbceda53b05c09026fd453f7336696c7ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:12.054381Z","signature_b64":"XFwnk7sn50eZeEE1OnqBzR39m68uuDdLY5mfzAtjgJXaX6oz0Uh1bYQ2Eu6DGWz556C0MXVbTTyopgIA+0EDCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acfd08b0c64e2d514838059c09f88ccbceda53b05c09026fd453f7336696c7ad","last_reissued_at":"2026-05-18T00:29:12.053651Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:12.053651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.11254","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":"2026-05-18T00:29:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1BK2zw69uk+A+cizZ0lbrsjYINd3sDWzuB/7YHv0VNI7Ckr8am2Lx5D5lkCeJRnpQIiDyNHPj06u7NsW4qy0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:17:26.999978Z"},"content_sha256":"86e49cc382d33c3eabeed04c63cebc96d543a8008273cf2ed6624dc1243d6fa5","schema_version":"1.0","event_id":"sha256:86e49cc382d33c3eabeed04c63cebc96d543a8008273cf2ed6624dc1243d6fa5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VT6QRMGGJYWVCSBYAWOAT6EMZP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solutions of quasi-geostrophic turbulence in multi-layered configurations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Sameerah Jamal","submitted_at":"2017-11-30T06:46:28Z","abstract_excerpt":"We consider quasi-geostrophic (Q-G) models in two- and three-layers that are useful in theoretical studies of planetary atmospheres and oceans. In these models, the streamfunctions are given by (1+2) partial differen- tial systems of evolution equations. A two-layer Q-G model, in a simpli- fied version, is dependent exclusively on the Rossby radius of deformation. However, the f-plane Q-G point vortex model contains factors such as the density, thickness of each layer, the Coriolis parameter, and the constant of gravitational acceleration, and this two-layered model admits a lesser number of L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11254","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":"2026-05-18T00:29:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fWaSOZdmSNJb2TeatXJXaV0XtLG5+q6xh4+gzz38f5NLJQNIZTBjm+E6bnmBA7ab0WQKzoCuCLpGN+URzfq4Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:17:27.000357Z"},"content_sha256":"18138cd818a18fa2ee00c212d3f3afa7aaf6a34a0ff2af2718ee91f4c4834994","schema_version":"1.0","event_id":"sha256:18138cd818a18fa2ee00c212d3f3afa7aaf6a34a0ff2af2718ee91f4c4834994"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VT6QRMGGJYWVCSBYAWOAT6EMZP/bundle.json","state_url":"https://pith.science/pith/VT6QRMGGJYWVCSBYAWOAT6EMZP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VT6QRMGGJYWVCSBYAWOAT6EMZP/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":"2026-06-22T09:17:27Z","links":{"resolver":"https://pith.science/pith/VT6QRMGGJYWVCSBYAWOAT6EMZP","bundle":"https://pith.science/pith/VT6QRMGGJYWVCSBYAWOAT6EMZP/bundle.json","state":"https://pith.science/pith/VT6QRMGGJYWVCSBYAWOAT6EMZP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VT6QRMGGJYWVCSBYAWOAT6EMZP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VT6QRMGGJYWVCSBYAWOAT6EMZP","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":"48aaed60b049baf576356295d044ea4a877709d8afb4319f7efb59369cf30ea8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-30T06:46:28Z","title_canon_sha256":"a8afdd6dc11b75a931ee9cb37794611c2a7ba8536bdef5874351622ff14f5640"},"schema_version":"1.0","source":{"id":"1711.11254","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11254","created_at":"2026-05-18T00:29:12Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11254v1","created_at":"2026-05-18T00:29:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11254","created_at":"2026-05-18T00:29:12Z"},{"alias_kind":"pith_short_12","alias_value":"VT6QRMGGJYWV","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VT6QRMGGJYWVCSBY","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VT6QRMGG","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:18138cd818a18fa2ee00c212d3f3afa7aaf6a34a0ff2af2718ee91f4c4834994","target":"graph","created_at":"2026-05-18T00:29:12Z","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 quasi-geostrophic (Q-G) models in two- and three-layers that are useful in theoretical studies of planetary atmospheres and oceans. In these models, the streamfunctions are given by (1+2) partial differen- tial systems of evolution equations. A two-layer Q-G model, in a simpli- fied version, is dependent exclusively on the Rossby radius of deformation. However, the f-plane Q-G point vortex model contains factors such as the density, thickness of each layer, the Coriolis parameter, and the constant of gravitational acceleration, and this two-layered model admits a lesser number of L","authors_text":"Sameerah Jamal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-30T06:46:28Z","title":"Solutions of quasi-geostrophic turbulence in multi-layered configurations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11254","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":"sha256:86e49cc382d33c3eabeed04c63cebc96d543a8008273cf2ed6624dc1243d6fa5","target":"record","created_at":"2026-05-18T00:29:12Z","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":"48aaed60b049baf576356295d044ea4a877709d8afb4319f7efb59369cf30ea8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-30T06:46:28Z","title_canon_sha256":"a8afdd6dc11b75a931ee9cb37794611c2a7ba8536bdef5874351622ff14f5640"},"schema_version":"1.0","source":{"id":"1711.11254","kind":"arxiv","version":1}},"canonical_sha256":"acfd08b0c64e2d514838059c09f88ccbceda53b05c09026fd453f7336696c7ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acfd08b0c64e2d514838059c09f88ccbceda53b05c09026fd453f7336696c7ad","first_computed_at":"2026-05-18T00:29:12.053651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:12.053651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XFwnk7sn50eZeEE1OnqBzR39m68uuDdLY5mfzAtjgJXaX6oz0Uh1bYQ2Eu6DGWz556C0MXVbTTyopgIA+0EDCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:12.054381Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.11254","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86e49cc382d33c3eabeed04c63cebc96d543a8008273cf2ed6624dc1243d6fa5","sha256:18138cd818a18fa2ee00c212d3f3afa7aaf6a34a0ff2af2718ee91f4c4834994"],"state_sha256":"6fac5dd03c52e8ae1719b709bf7a9ab71274e16ad7087e9241f240706eea5624"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+0G3GGagfvnRxEPnKPjXsF1bmmS+Ywk7DUKVYubeMhtpJvE1jroOPm8QeOXbA+iztxUCZKez+qlSm6YYJWinDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T09:17:27.002280Z","bundle_sha256":"1b09f4d3506a0efcb4c3b8ab35f7c9ef4e3b10d9461a49a4bbfa68c940f71630"}}