{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:Z57JEPKG6GQ4LL5LESVNVQFSB5","short_pith_number":"pith:Z57JEPKG","canonical_record":{"source":{"id":"math/0607020","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2006-07-01T12:36:44Z","cross_cats_sorted":[],"title_canon_sha256":"c9a7bcd34cebb35568b03ef49bf4ab05bb04cdd061f6ac7d9bdf43debd725095","abstract_canon_sha256":"6a981bd75769e62490486d3eba78645b73e392f1e5b7f615078c92ab07721b1b"},"schema_version":"1.0"},"canonical_sha256":"cf7e923d46f1a1c5afab24aadac0b20f5523b6a1679b4fb7fe4c4aae4cb67db0","source":{"kind":"arxiv","id":"math/0607020","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0607020","created_at":"2026-07-04T15:14:58Z"},{"alias_kind":"arxiv_version","alias_value":"math/0607020v3","created_at":"2026-07-04T15:14:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0607020","created_at":"2026-07-04T15:14:58Z"},{"alias_kind":"pith_short_12","alias_value":"Z57JEPKG6GQ4","created_at":"2026-07-04T15:14:58Z"},{"alias_kind":"pith_short_16","alias_value":"Z57JEPKG6GQ4LL5L","created_at":"2026-07-04T15:14:58Z"},{"alias_kind":"pith_short_8","alias_value":"Z57JEPKG","created_at":"2026-07-04T15:14:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:Z57JEPKG6GQ4LL5LESVNVQFSB5","target":"record","payload":{"canonical_record":{"source":{"id":"math/0607020","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2006-07-01T12:36:44Z","cross_cats_sorted":[],"title_canon_sha256":"c9a7bcd34cebb35568b03ef49bf4ab05bb04cdd061f6ac7d9bdf43debd725095","abstract_canon_sha256":"6a981bd75769e62490486d3eba78645b73e392f1e5b7f615078c92ab07721b1b"},"schema_version":"1.0"},"canonical_sha256":"cf7e923d46f1a1c5afab24aadac0b20f5523b6a1679b4fb7fe4c4aae4cb67db0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:14:58.963939Z","signature_b64":"fPrrWtOjdaGT5jaAaUzq+N1AGluA7B0SAHYJV1X3wAY5AVzkVwiTfISrduF0R6/g/IcufqkBEZ0DiODWquVMBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf7e923d46f1a1c5afab24aadac0b20f5523b6a1679b4fb7fe4c4aae4cb67db0","last_reissued_at":"2026-07-04T15:14:58.963499Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:14:58.963499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0607020","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":"2026-07-04T15:14:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8gFYdfr+1wUB7WFjm99iKa+/b+q0J9HeMOHv6aolXl5nhyXKhbTLKujT8vjymOpQjg/ciaMiU1qSgz6VPkf2Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:28:21.093048Z"},"content_sha256":"251df1622516e1b19c8c0c1c8208f251158ff99d117ac2a3b60865cd6c342afc","schema_version":"1.0","event_id":"sha256:251df1622516e1b19c8c0c1c8208f251158ff99d117ac2a3b60865cd6c342afc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:Z57JEPKG6GQ4LL5LESVNVQFSB5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changxing Miao, Qionglei Chen, Zhifei Zhang","submitted_at":"2006-07-01T12:36:44Z","abstract_excerpt":"We show a new Bernstein's inequality which generalizes the results of Cannone-Planchon, Danchin and Lemari\\'{e}-Rieusset. As an application of this inequality, we prove the global well-posedness of the 2D quasi-geostrophic equation with the critical and super-critical dissipation for the small initial data in the critical Besov space, and local well-posedness for the large initial data."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607020","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0607020/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:14:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3cT7uc1KCDizEMd5XslUjU2NIgsxFfa3ulUsAegrZa+Tgyn4Vt9mbZ7P0IM62UV8H9bWy3j4bBx43MD4r2pSCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:28:21.093437Z"},"content_sha256":"2a9fa52179264efdcc807783e926e4ebdb88d13d427b7b3778effa35b1fb2c27","schema_version":"1.0","event_id":"sha256:2a9fa52179264efdcc807783e926e4ebdb88d13d427b7b3778effa35b1fb2c27"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z57JEPKG6GQ4LL5LESVNVQFSB5/bundle.json","state_url":"https://pith.science/pith/Z57JEPKG6GQ4LL5LESVNVQFSB5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z57JEPKG6GQ4LL5LESVNVQFSB5/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":"2026-07-07T13:28:21Z","links":{"resolver":"https://pith.science/pith/Z57JEPKG6GQ4LL5LESVNVQFSB5","bundle":"https://pith.science/pith/Z57JEPKG6GQ4LL5LESVNVQFSB5/bundle.json","state":"https://pith.science/pith/Z57JEPKG6GQ4LL5LESVNVQFSB5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z57JEPKG6GQ4LL5LESVNVQFSB5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:Z57JEPKG6GQ4LL5LESVNVQFSB5","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":"6a981bd75769e62490486d3eba78645b73e392f1e5b7f615078c92ab07721b1b","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2006-07-01T12:36:44Z","title_canon_sha256":"c9a7bcd34cebb35568b03ef49bf4ab05bb04cdd061f6ac7d9bdf43debd725095"},"schema_version":"1.0","source":{"id":"math/0607020","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0607020","created_at":"2026-07-04T15:14:58Z"},{"alias_kind":"arxiv_version","alias_value":"math/0607020v3","created_at":"2026-07-04T15:14:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0607020","created_at":"2026-07-04T15:14:58Z"},{"alias_kind":"pith_short_12","alias_value":"Z57JEPKG6GQ4","created_at":"2026-07-04T15:14:58Z"},{"alias_kind":"pith_short_16","alias_value":"Z57JEPKG6GQ4LL5L","created_at":"2026-07-04T15:14:58Z"},{"alias_kind":"pith_short_8","alias_value":"Z57JEPKG","created_at":"2026-07-04T15:14:58Z"}],"graph_snapshots":[{"event_id":"sha256:2a9fa52179264efdcc807783e926e4ebdb88d13d427b7b3778effa35b1fb2c27","target":"graph","created_at":"2026-07-04T15:14:58Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0607020/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show a new Bernstein's inequality which generalizes the results of Cannone-Planchon, Danchin and Lemari\\'{e}-Rieusset. As an application of this inequality, we prove the global well-posedness of the 2D quasi-geostrophic equation with the critical and super-critical dissipation for the small initial data in the critical Besov space, and local well-posedness for the large initial data.","authors_text":"Changxing Miao, Qionglei Chen, Zhifei Zhang","cross_cats":[],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2006-07-01T12:36:44Z","title":"A new Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607020","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":"sha256:251df1622516e1b19c8c0c1c8208f251158ff99d117ac2a3b60865cd6c342afc","target":"record","created_at":"2026-07-04T15:14:58Z","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":"6a981bd75769e62490486d3eba78645b73e392f1e5b7f615078c92ab07721b1b","cross_cats_sorted":[],"license":"","primary_cat":"math.AP","submitted_at":"2006-07-01T12:36:44Z","title_canon_sha256":"c9a7bcd34cebb35568b03ef49bf4ab05bb04cdd061f6ac7d9bdf43debd725095"},"schema_version":"1.0","source":{"id":"math/0607020","kind":"arxiv","version":3}},"canonical_sha256":"cf7e923d46f1a1c5afab24aadac0b20f5523b6a1679b4fb7fe4c4aae4cb67db0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf7e923d46f1a1c5afab24aadac0b20f5523b6a1679b4fb7fe4c4aae4cb67db0","first_computed_at":"2026-07-04T15:14:58.963499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:14:58.963499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fPrrWtOjdaGT5jaAaUzq+N1AGluA7B0SAHYJV1X3wAY5AVzkVwiTfISrduF0R6/g/IcufqkBEZ0DiODWquVMBg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:14:58.963939Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0607020","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:251df1622516e1b19c8c0c1c8208f251158ff99d117ac2a3b60865cd6c342afc","sha256:2a9fa52179264efdcc807783e926e4ebdb88d13d427b7b3778effa35b1fb2c27"],"state_sha256":"955f98c2e05a4f73a2d90224ecd87f216f3740f8d3cf1a720a6d75acfdcdc669"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FkkASUr0HieVuKnWAE8LfJN68kmicUnYtPW3hcnhn8PrWPmxNGXj6AzQDysPlRJS808MOrWNHgHRKTP+7241BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T13:28:21.095374Z","bundle_sha256":"ad80f839caee8fb9b4c4f88d11cc5de160e44919d0d6c6ad0ae6e43386a62ab2"}}