{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:FSH6X73PPNQKOZEM6VUDQ725VO","short_pith_number":"pith:FSH6X73P","schema_version":"1.0","canonical_sha256":"2c8febff6f7b60a7648cf568387f5dab96ce67959aee7fa4eb8ac83cf09c6315","source":{"kind":"arxiv","id":"1203.4651","version":1},"attestation_state":"computed","paper":{"title":"Modulation Spaces and Nonlinear Evolution Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Baoxiang Wang, Michael Ruzhansky, Mitsuru Sugimoto","submitted_at":"2012-03-21T04:27:30Z","abstract_excerpt":"We survey some recent progress on modulation spaces and the well-posedness results for a class of nonlinear evolution equations by using the frequency-uniform localization techniques."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1203.4651","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-21T04:27:30Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"9940b8b9896c506ba29984f11cffad35df701610f0118b6a19ca36503fa86890","abstract_canon_sha256":"b5ddbff10c0d6518a218a9639ed605a0909263e805835ee0a1a1b9e0ef34fc7b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:37.552806Z","signature_b64":"rroXuRBJT1IMJKrCjIt07/Dayj7mb4SHj0m/+ygPrhfxxjG8aXt8yGXx51tV/DwqzkzZ1g3amYRIjE895tcwBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c8febff6f7b60a7648cf568387f5dab96ce67959aee7fa4eb8ac83cf09c6315","last_reissued_at":"2026-05-18T03:59:37.552269Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:37.552269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modulation Spaces and Nonlinear Evolution Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Baoxiang Wang, Michael Ruzhansky, Mitsuru Sugimoto","submitted_at":"2012-03-21T04:27:30Z","abstract_excerpt":"We survey some recent progress on modulation spaces and the well-posedness results for a class of nonlinear evolution equations by using the frequency-uniform localization techniques."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4651","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1203.4651","created_at":"2026-05-18T03:59:37.552360+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.4651v1","created_at":"2026-05-18T03:59:37.552360+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4651","created_at":"2026-05-18T03:59:37.552360+00:00"},{"alias_kind":"pith_short_12","alias_value":"FSH6X73PPNQK","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"FSH6X73PPNQKOZEM","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"FSH6X73P","created_at":"2026-05-18T12:27:06.952714+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FSH6X73PPNQKOZEM6VUDQ725VO","json":"https://pith.science/pith/FSH6X73PPNQKOZEM6VUDQ725VO.json","graph_json":"https://pith.science/api/pith-number/FSH6X73PPNQKOZEM6VUDQ725VO/graph.json","events_json":"https://pith.science/api/pith-number/FSH6X73PPNQKOZEM6VUDQ725VO/events.json","paper":"https://pith.science/paper/FSH6X73P"},"agent_actions":{"view_html":"https://pith.science/pith/FSH6X73PPNQKOZEM6VUDQ725VO","download_json":"https://pith.science/pith/FSH6X73PPNQKOZEM6VUDQ725VO.json","view_paper":"https://pith.science/paper/FSH6X73P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.4651&json=true","fetch_graph":"https://pith.science/api/pith-number/FSH6X73PPNQKOZEM6VUDQ725VO/graph.json","fetch_events":"https://pith.science/api/pith-number/FSH6X73PPNQKOZEM6VUDQ725VO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FSH6X73PPNQKOZEM6VUDQ725VO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FSH6X73PPNQKOZEM6VUDQ725VO/action/storage_attestation","attest_author":"https://pith.science/pith/FSH6X73PPNQKOZEM6VUDQ725VO/action/author_attestation","sign_citation":"https://pith.science/pith/FSH6X73PPNQKOZEM6VUDQ725VO/action/citation_signature","submit_replication":"https://pith.science/pith/FSH6X73PPNQKOZEM6VUDQ725VO/action/replication_record"}},"created_at":"2026-05-18T03:59:37.552360+00:00","updated_at":"2026-05-18T03:59:37.552360+00:00"}