{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:XLOZDMU5XIZHO5UXEDNYNIFQPA","short_pith_number":"pith:XLOZDMU5","canonical_record":{"source":{"id":"1309.5369","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-20T20:10:35Z","cross_cats_sorted":[],"title_canon_sha256":"9f8a0b56f8a3256b4cadd5e94d3bd01a42c9d3c0441cd70c4108491ee5ee2ef3","abstract_canon_sha256":"8665bbf3caf6c9e05aab7f811ae674d00ed48c6d4a1de6e7717be8da3e45aa45"},"schema_version":"1.0"},"canonical_sha256":"badd91b29dba3277769720db86a0b078384cfd49a08c6e2e0e69286125b487f2","source":{"kind":"arxiv","id":"1309.5369","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5369","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5369v4","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5369","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"pith_short_12","alias_value":"XLOZDMU5XIZH","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XLOZDMU5XIZHO5UX","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XLOZDMU5","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:XLOZDMU5XIZHO5UXEDNYNIFQPA","target":"record","payload":{"canonical_record":{"source":{"id":"1309.5369","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-20T20:10:35Z","cross_cats_sorted":[],"title_canon_sha256":"9f8a0b56f8a3256b4cadd5e94d3bd01a42c9d3c0441cd70c4108491ee5ee2ef3","abstract_canon_sha256":"8665bbf3caf6c9e05aab7f811ae674d00ed48c6d4a1de6e7717be8da3e45aa45"},"schema_version":"1.0"},"canonical_sha256":"badd91b29dba3277769720db86a0b078384cfd49a08c6e2e0e69286125b487f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:59:08.576009Z","signature_b64":"ySfDKObut9L9BkHkQUNTaKwbe3wWrf6lNubYiu+QygNfuMLjRhAvLQ8ioVOX3ROtpxBP2A1bVQ+Rvv0ArinfDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"badd91b29dba3277769720db86a0b078384cfd49a08c6e2e0e69286125b487f2","last_reissued_at":"2026-05-18T02:59:08.575380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:59:08.575380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.5369","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:59:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W01E0SBtj7uYUVDKgRUNGDIkZC6yHeMd8Po7l0ZMRugDK9HjF2QfbnRa2PbktLWT1L1LG0SzaiQIx7njUZeUCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:20:24.277680Z"},"content_sha256":"2508c9d062d7ffc1c889c99d9d07938f79755069134035677574640750eb9199","schema_version":"1.0","event_id":"sha256:2508c9d062d7ffc1c889c99d9d07938f79755069134035677574640750eb9199"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:XLOZDMU5XIZHO5UXEDNYNIFQPA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-similar solutions for active scalar equations in Fourier-Besov-Morrey spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lidiane S. M. Lima, Lucas C. F. Ferreira","submitted_at":"2013-09-20T20:10:35Z","abstract_excerpt":"We are concerned with a family of dissipative active scalar equation with velocity fields coupled via multiplier operators that can be of high-order. We consider sub-critical values for the fractional diffusion and prove global well-posedness of solutions with small initial data belonging to a framework based on Fourier transform, namely Fourier-Besov-Morrey spaces. Since the smallness condition is with respect to the weak norm of this space, some initial data with large $L^{2}$-norm can be considered. Self-similar solutions are obtained depending on the homogeneity of the initial data and cou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5369","kind":"arxiv","version":4},"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":"2026-05-18T02:59:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gD1vOJpvSuD+MVFzBBV1Kpy/n1eGpY3t0/LVc0BPe7jPt2FGbMxxZZOV5sk24+gCJEsnsrXVOZslJRDNfySCDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:20:24.278027Z"},"content_sha256":"ec255872ca1042819df5c7316a9662de7c5f97096b6943f813a8a88b976d1e58","schema_version":"1.0","event_id":"sha256:ec255872ca1042819df5c7316a9662de7c5f97096b6943f813a8a88b976d1e58"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XLOZDMU5XIZHO5UXEDNYNIFQPA/bundle.json","state_url":"https://pith.science/pith/XLOZDMU5XIZHO5UXEDNYNIFQPA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XLOZDMU5XIZHO5UXEDNYNIFQPA/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":"2026-06-25T06:20:24Z","links":{"resolver":"https://pith.science/pith/XLOZDMU5XIZHO5UXEDNYNIFQPA","bundle":"https://pith.science/pith/XLOZDMU5XIZHO5UXEDNYNIFQPA/bundle.json","state":"https://pith.science/pith/XLOZDMU5XIZHO5UXEDNYNIFQPA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XLOZDMU5XIZHO5UXEDNYNIFQPA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XLOZDMU5XIZHO5UXEDNYNIFQPA","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":"8665bbf3caf6c9e05aab7f811ae674d00ed48c6d4a1de6e7717be8da3e45aa45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-20T20:10:35Z","title_canon_sha256":"9f8a0b56f8a3256b4cadd5e94d3bd01a42c9d3c0441cd70c4108491ee5ee2ef3"},"schema_version":"1.0","source":{"id":"1309.5369","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5369","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5369v4","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5369","created_at":"2026-05-18T02:59:08Z"},{"alias_kind":"pith_short_12","alias_value":"XLOZDMU5XIZH","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XLOZDMU5XIZHO5UX","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XLOZDMU5","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:ec255872ca1042819df5c7316a9662de7c5f97096b6943f813a8a88b976d1e58","target":"graph","created_at":"2026-05-18T02:59:08Z","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 are concerned with a family of dissipative active scalar equation with velocity fields coupled via multiplier operators that can be of high-order. We consider sub-critical values for the fractional diffusion and prove global well-posedness of solutions with small initial data belonging to a framework based on Fourier transform, namely Fourier-Besov-Morrey spaces. Since the smallness condition is with respect to the weak norm of this space, some initial data with large $L^{2}$-norm can be considered. Self-similar solutions are obtained depending on the homogeneity of the initial data and cou","authors_text":"Lidiane S. M. Lima, Lucas C. F. Ferreira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-20T20:10:35Z","title":"Self-similar solutions for active scalar equations in Fourier-Besov-Morrey spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5369","kind":"arxiv","version":4},"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":"sha256:2508c9d062d7ffc1c889c99d9d07938f79755069134035677574640750eb9199","target":"record","created_at":"2026-05-18T02:59:08Z","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":"8665bbf3caf6c9e05aab7f811ae674d00ed48c6d4a1de6e7717be8da3e45aa45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-09-20T20:10:35Z","title_canon_sha256":"9f8a0b56f8a3256b4cadd5e94d3bd01a42c9d3c0441cd70c4108491ee5ee2ef3"},"schema_version":"1.0","source":{"id":"1309.5369","kind":"arxiv","version":4}},"canonical_sha256":"badd91b29dba3277769720db86a0b078384cfd49a08c6e2e0e69286125b487f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"badd91b29dba3277769720db86a0b078384cfd49a08c6e2e0e69286125b487f2","first_computed_at":"2026-05-18T02:59:08.575380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:08.575380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ySfDKObut9L9BkHkQUNTaKwbe3wWrf6lNubYiu+QygNfuMLjRhAvLQ8ioVOX3ROtpxBP2A1bVQ+Rvv0ArinfDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:08.576009Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5369","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2508c9d062d7ffc1c889c99d9d07938f79755069134035677574640750eb9199","sha256:ec255872ca1042819df5c7316a9662de7c5f97096b6943f813a8a88b976d1e58"],"state_sha256":"1cf3c0b1f19d95fe47c8e42d940a461fe99b0d56ffcbdc278618ed7971afed74"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CFXYwRURCrkdWY3Jt6VkLmRFGYF9Jet9ZzULrzIdo5XO82tAjZiQAEeEvVDutQetlKRJaZylItrlT06br6qxCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T06:20:24.279975Z","bundle_sha256":"002b6ea48cabf9531724f05f6380a547a776bfa4a6b4b57977b6a8de40839748"}}