{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XVVCREIBTXFIESWWRGN77W77KR","short_pith_number":"pith:XVVCREIB","canonical_record":{"source":{"id":"1707.00094","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-01T04:19:38Z","cross_cats_sorted":[],"title_canon_sha256":"d88ba38349c5aa29c69ac0f15cc719f941a3e39180dd0602c31ff6644aea2627","abstract_canon_sha256":"41c126c22dce312cef1d33c6da5ed8e944c4c0a3584df91227349a121bbeafe4"},"schema_version":"1.0"},"canonical_sha256":"bd6a2891019dca824ad6899bffdbff5471ccc0ce4332f2e6692f19d74a959945","source":{"kind":"arxiv","id":"1707.00094","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.00094","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"arxiv_version","alias_value":"1707.00094v1","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00094","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"pith_short_12","alias_value":"XVVCREIBTXFI","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XVVCREIBTXFIESWW","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XVVCREIB","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XVVCREIBTXFIESWWRGN77W77KR","target":"record","payload":{"canonical_record":{"source":{"id":"1707.00094","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-01T04:19:38Z","cross_cats_sorted":[],"title_canon_sha256":"d88ba38349c5aa29c69ac0f15cc719f941a3e39180dd0602c31ff6644aea2627","abstract_canon_sha256":"41c126c22dce312cef1d33c6da5ed8e944c4c0a3584df91227349a121bbeafe4"},"schema_version":"1.0"},"canonical_sha256":"bd6a2891019dca824ad6899bffdbff5471ccc0ce4332f2e6692f19d74a959945","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:06.506509Z","signature_b64":"gHrSA7Hz06DjSXb0vljb13J9HKNZcY9accr+SCmi9yTJ1rNMUok3jFx2cfTAydHOdvntanCA/JsMMl2pp48bCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd6a2891019dca824ad6899bffdbff5471ccc0ce4332f2e6692f19d74a959945","last_reissued_at":"2026-05-18T00:41:06.505803Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:06.505803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.00094","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":"2026-05-18T00:41:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yxa9CT1MUIVHp0pQkjDN6EugO1fFeeJnFV1PfFgJ3aLORZLMkoYLdX4itsPyMivHxbxOnWlG2xbTLzXFdZ80AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:18:37.125456Z"},"content_sha256":"03955695773daff274ffbc7c8f418ae5f6c8c67c44db65fb56fd82a7bc2d8a3b","schema_version":"1.0","event_id":"sha256:03955695773daff274ffbc7c8f418ae5f6c8c67c44db65fb56fd82a7bc2d8a3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XVVCREIBTXFIESWWRGN77W77KR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An inequality for solutions of the Navier-Stokes equations in Rn","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jana\\'ina P. Zingano, Jens Lorenz, Paulo R. Zingano, Thomas Hagstrom","submitted_at":"2017-07-01T04:19:38Z","abstract_excerpt":"We obtain a new inequality that holds for general Leray solutions of the incompressible Navier-Stokes equations in Rn (n <= 4). This recovers important results previously obtained by other authors regarding the time decay of solution derivatives (of arbitrary order)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00094","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":"2026-05-18T00:41:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uAtlI8+syS5HOhJlK4dVYJ/f2yPmu1GI/3QZ4/CpdzVLccLoBKAVPobArDq3NTiF2JmwGJJOLUtliph08FdBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:18:37.125800Z"},"content_sha256":"9e2cb53e109710dc37fbf6821ab38a8b3efd7178a88a3c559e7d42533ef64d6c","schema_version":"1.0","event_id":"sha256:9e2cb53e109710dc37fbf6821ab38a8b3efd7178a88a3c559e7d42533ef64d6c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XVVCREIBTXFIESWWRGN77W77KR/bundle.json","state_url":"https://pith.science/pith/XVVCREIBTXFIESWWRGN77W77KR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XVVCREIBTXFIESWWRGN77W77KR/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":"2026-06-04T06:18:37Z","links":{"resolver":"https://pith.science/pith/XVVCREIBTXFIESWWRGN77W77KR","bundle":"https://pith.science/pith/XVVCREIBTXFIESWWRGN77W77KR/bundle.json","state":"https://pith.science/pith/XVVCREIBTXFIESWWRGN77W77KR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XVVCREIBTXFIESWWRGN77W77KR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XVVCREIBTXFIESWWRGN77W77KR","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":"41c126c22dce312cef1d33c6da5ed8e944c4c0a3584df91227349a121bbeafe4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-01T04:19:38Z","title_canon_sha256":"d88ba38349c5aa29c69ac0f15cc719f941a3e39180dd0602c31ff6644aea2627"},"schema_version":"1.0","source":{"id":"1707.00094","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.00094","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"arxiv_version","alias_value":"1707.00094v1","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00094","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"pith_short_12","alias_value":"XVVCREIBTXFI","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XVVCREIBTXFIESWW","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XVVCREIB","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:9e2cb53e109710dc37fbf6821ab38a8b3efd7178a88a3c559e7d42533ef64d6c","target":"graph","created_at":"2026-05-18T00:41:06Z","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 obtain a new inequality that holds for general Leray solutions of the incompressible Navier-Stokes equations in Rn (n <= 4). This recovers important results previously obtained by other authors regarding the time decay of solution derivatives (of arbitrary order).","authors_text":"Jana\\'ina P. Zingano, Jens Lorenz, Paulo R. Zingano, Thomas Hagstrom","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-01T04:19:38Z","title":"An inequality for solutions of the Navier-Stokes equations in Rn"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00094","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":"sha256:03955695773daff274ffbc7c8f418ae5f6c8c67c44db65fb56fd82a7bc2d8a3b","target":"record","created_at":"2026-05-18T00:41:06Z","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":"41c126c22dce312cef1d33c6da5ed8e944c4c0a3584df91227349a121bbeafe4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-01T04:19:38Z","title_canon_sha256":"d88ba38349c5aa29c69ac0f15cc719f941a3e39180dd0602c31ff6644aea2627"},"schema_version":"1.0","source":{"id":"1707.00094","kind":"arxiv","version":1}},"canonical_sha256":"bd6a2891019dca824ad6899bffdbff5471ccc0ce4332f2e6692f19d74a959945","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd6a2891019dca824ad6899bffdbff5471ccc0ce4332f2e6692f19d74a959945","first_computed_at":"2026-05-18T00:41:06.505803Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:06.505803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gHrSA7Hz06DjSXb0vljb13J9HKNZcY9accr+SCmi9yTJ1rNMUok3jFx2cfTAydHOdvntanCA/JsMMl2pp48bCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:06.506509Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.00094","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03955695773daff274ffbc7c8f418ae5f6c8c67c44db65fb56fd82a7bc2d8a3b","sha256:9e2cb53e109710dc37fbf6821ab38a8b3efd7178a88a3c559e7d42533ef64d6c"],"state_sha256":"205cb150e1f3358294e2aa1080699a8941ebd7da24c160495edc3f0f19023ecc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fltCNRY2kCLcAuhsmS7MRxdP0Jpb+NTR4ewoGrn5sl+mRayxXUotkWIJhAtibLRh1y3fl3ETMpiDjggWMnnSDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:18:37.127671Z","bundle_sha256":"4a23a49fd28f36aa419a7c65bd99bfb929bab3bdb748d396aff384dfb7441e5d"}}