{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SRZTORDZWPCJ6N7ZZLAFORFYWL","short_pith_number":"pith:SRZTORDZ","canonical_record":{"source":{"id":"1505.03652","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-14T08:56:16Z","cross_cats_sorted":[],"title_canon_sha256":"2a256950475f846b37bc5bc91fb779e878598d433a542c395b4bbcaa812bac95","abstract_canon_sha256":"05c76bcda549e20ac8498d82430d400d3235487c971a73417bb43513a686c449"},"schema_version":"1.0"},"canonical_sha256":"9473374479b3c49f37f9cac05744b8b2c6f6b6a319aea4974fe5ca8cbaea351a","source":{"kind":"arxiv","id":"1505.03652","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03652","created_at":"2026-05-18T01:36:49Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03652v3","created_at":"2026-05-18T01:36:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03652","created_at":"2026-05-18T01:36:49Z"},{"alias_kind":"pith_short_12","alias_value":"SRZTORDZWPCJ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SRZTORDZWPCJ6N7Z","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SRZTORDZ","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SRZTORDZWPCJ6N7ZZLAFORFYWL","target":"record","payload":{"canonical_record":{"source":{"id":"1505.03652","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-14T08:56:16Z","cross_cats_sorted":[],"title_canon_sha256":"2a256950475f846b37bc5bc91fb779e878598d433a542c395b4bbcaa812bac95","abstract_canon_sha256":"05c76bcda549e20ac8498d82430d400d3235487c971a73417bb43513a686c449"},"schema_version":"1.0"},"canonical_sha256":"9473374479b3c49f37f9cac05744b8b2c6f6b6a319aea4974fe5ca8cbaea351a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:49.652069Z","signature_b64":"Xowow/+8+90kkla4mcdRJ3yjGrFJQu02z8cRRDCFkq7kNJuMwFsJVq4PQJEQRkuqFpMHmesGRX5wZZwL/3rkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9473374479b3c49f37f9cac05744b8b2c6f6b6a319aea4974fe5ca8cbaea351a","last_reissued_at":"2026-05-18T01:36:49.651256Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:49.651256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.03652","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J13vzW20G+3eergZzcp+r6CyOSwX1ARMwsE9okpyjKzUn/Rc8fdlDztII9lIhI/zzEw9y6VhW+4BbDiHc36oAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:09:38.663361Z"},"content_sha256":"09fd212b13fe2525ef9731bb6e1d4f3a43d0ddbc2a6cb87219c4aae036844b46","schema_version":"1.0","event_id":"sha256:09fd212b13fe2525ef9731bb6e1d4f3a43d0ddbc2a6cb87219c4aae036844b46"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SRZTORDZWPCJ6N7ZZLAFORFYWL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solving some Navier-Stokes Equations with the initial conditions being some complex-valued periodic functions on $R^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alatancang Chen, Fan Bai, Tao Zhang","submitted_at":"2015-05-14T08:56:16Z","abstract_excerpt":"In this paper, we utilize some series and an iterative method to solve some Navier-Stokes equations with the initial conditions being some complex-valued periodic functions on $R^3$. Then a new strategy for dealing with the conjecture of the Navier-Stokes equation is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03652","kind":"arxiv","version":3},"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":"2026-05-18T01:36:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y/o2I/iaDGT98zDFVdjC33syLOf0365BeTeT+lLWbWbmjTE3Kl+u94wCydbXCJ2wKxIjwxc3jbZnFE/GvutiBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:09:38.663813Z"},"content_sha256":"5c0ba08ca9007b1c2647dab2a58de362a87c650f81914656125ac658b63c77e0","schema_version":"1.0","event_id":"sha256:5c0ba08ca9007b1c2647dab2a58de362a87c650f81914656125ac658b63c77e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SRZTORDZWPCJ6N7ZZLAFORFYWL/bundle.json","state_url":"https://pith.science/pith/SRZTORDZWPCJ6N7ZZLAFORFYWL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SRZTORDZWPCJ6N7ZZLAFORFYWL/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":"2026-05-27T18:09:38Z","links":{"resolver":"https://pith.science/pith/SRZTORDZWPCJ6N7ZZLAFORFYWL","bundle":"https://pith.science/pith/SRZTORDZWPCJ6N7ZZLAFORFYWL/bundle.json","state":"https://pith.science/pith/SRZTORDZWPCJ6N7ZZLAFORFYWL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SRZTORDZWPCJ6N7ZZLAFORFYWL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SRZTORDZWPCJ6N7ZZLAFORFYWL","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":"05c76bcda549e20ac8498d82430d400d3235487c971a73417bb43513a686c449","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-14T08:56:16Z","title_canon_sha256":"2a256950475f846b37bc5bc91fb779e878598d433a542c395b4bbcaa812bac95"},"schema_version":"1.0","source":{"id":"1505.03652","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03652","created_at":"2026-05-18T01:36:49Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03652v3","created_at":"2026-05-18T01:36:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03652","created_at":"2026-05-18T01:36:49Z"},{"alias_kind":"pith_short_12","alias_value":"SRZTORDZWPCJ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SRZTORDZWPCJ6N7Z","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SRZTORDZ","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:5c0ba08ca9007b1c2647dab2a58de362a87c650f81914656125ac658b63c77e0","target":"graph","created_at":"2026-05-18T01:36:49Z","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":"In this paper, we utilize some series and an iterative method to solve some Navier-Stokes equations with the initial conditions being some complex-valued periodic functions on $R^3$. Then a new strategy for dealing with the conjecture of the Navier-Stokes equation is given.","authors_text":"Alatancang Chen, Fan Bai, Tao Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-14T08:56:16Z","title":"Solving some Navier-Stokes Equations with the initial conditions being some complex-valued periodic functions on $R^3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03652","kind":"arxiv","version":3},"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":"sha256:09fd212b13fe2525ef9731bb6e1d4f3a43d0ddbc2a6cb87219c4aae036844b46","target":"record","created_at":"2026-05-18T01:36:49Z","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":"05c76bcda549e20ac8498d82430d400d3235487c971a73417bb43513a686c449","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-14T08:56:16Z","title_canon_sha256":"2a256950475f846b37bc5bc91fb779e878598d433a542c395b4bbcaa812bac95"},"schema_version":"1.0","source":{"id":"1505.03652","kind":"arxiv","version":3}},"canonical_sha256":"9473374479b3c49f37f9cac05744b8b2c6f6b6a319aea4974fe5ca8cbaea351a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9473374479b3c49f37f9cac05744b8b2c6f6b6a319aea4974fe5ca8cbaea351a","first_computed_at":"2026-05-18T01:36:49.651256Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:49.651256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xowow/+8+90kkla4mcdRJ3yjGrFJQu02z8cRRDCFkq7kNJuMwFsJVq4PQJEQRkuqFpMHmesGRX5wZZwL/3rkBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:49.652069Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.03652","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09fd212b13fe2525ef9731bb6e1d4f3a43d0ddbc2a6cb87219c4aae036844b46","sha256:5c0ba08ca9007b1c2647dab2a58de362a87c650f81914656125ac658b63c77e0"],"state_sha256":"72c1cf0757b7c9985e74c8aefbf118f22682d9967a28e0212b0d12b63d1d9ee6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yxIQfS0QJKuAZDprBiUtS2+LEHVcdyRTYqNxsfDAm3lVjgK0WllQMe47s/2fGs3XGQJd5BtEbvzlIi/c2BZlDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:09:38.666379Z","bundle_sha256":"e2e30f7f1e5cc0b6a63c208286a67751cfcf08ea55c6695a6a7e4f49257a8080"}}