{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:FSH6X73PPNQKOZEM6VUDQ725VO","short_pith_number":"pith:FSH6X73P","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"},"canonical_sha256":"2c8febff6f7b60a7648cf568387f5dab96ce67959aee7fa4eb8ac83cf09c6315","source":{"kind":"arxiv","id":"1203.4651","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4651","created_at":"2026-05-18T03:59:37Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4651v1","created_at":"2026-05-18T03:59:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4651","created_at":"2026-05-18T03:59:37Z"},{"alias_kind":"pith_short_12","alias_value":"FSH6X73PPNQK","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FSH6X73PPNQKOZEM","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FSH6X73P","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:FSH6X73PPNQKOZEM6VUDQ725VO","target":"record","payload":{"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"},"canonical_sha256":"2c8febff6f7b60a7648cf568387f5dab96ce67959aee7fa4eb8ac83cf09c6315","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"},"source_kind":"arxiv","source_id":"1203.4651","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":"2026-05-18T03:59:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k8pvvq6E2WO62E/RoQMVFO4miWTlzIMctvkEvHqZxQYILJy171XKs6/CwXg1MU/uZn0OZm97WW4u6RWGK7IRBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T18:10:38.121307Z"},"content_sha256":"ca6e2e9b8b6b6f5e5f3dc30c2bdc58ce68a34b4c5e58c545672346ab5c969b23","schema_version":"1.0","event_id":"sha256:ca6e2e9b8b6b6f5e5f3dc30c2bdc58ce68a34b4c5e58c545672346ab5c969b23"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:FSH6X73PPNQKOZEM6VUDQ725VO","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:59:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IsHpZaGrtX0cEFBqeQzevSHBZtzLR/qsyrZOOvxkQ418hrq9ftuum1s2e7NYoAqfC6wT95gWp8pBNHnL3FvTBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T18:10:38.121951Z"},"content_sha256":"33d102a26d1b3a10845a8e50af58e441a852953bebbd6005f0f7dbae67a7a28a","schema_version":"1.0","event_id":"sha256:33d102a26d1b3a10845a8e50af58e441a852953bebbd6005f0f7dbae67a7a28a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FSH6X73PPNQKOZEM6VUDQ725VO/bundle.json","state_url":"https://pith.science/pith/FSH6X73PPNQKOZEM6VUDQ725VO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FSH6X73PPNQKOZEM6VUDQ725VO/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":"2026-06-09T18:10:38Z","links":{"resolver":"https://pith.science/pith/FSH6X73PPNQKOZEM6VUDQ725VO","bundle":"https://pith.science/pith/FSH6X73PPNQKOZEM6VUDQ725VO/bundle.json","state":"https://pith.science/pith/FSH6X73PPNQKOZEM6VUDQ725VO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FSH6X73PPNQKOZEM6VUDQ725VO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FSH6X73PPNQKOZEM6VUDQ725VO","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":"b5ddbff10c0d6518a218a9639ed605a0909263e805835ee0a1a1b9e0ef34fc7b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-21T04:27:30Z","title_canon_sha256":"9940b8b9896c506ba29984f11cffad35df701610f0118b6a19ca36503fa86890"},"schema_version":"1.0","source":{"id":"1203.4651","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4651","created_at":"2026-05-18T03:59:37Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4651v1","created_at":"2026-05-18T03:59:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4651","created_at":"2026-05-18T03:59:37Z"},{"alias_kind":"pith_short_12","alias_value":"FSH6X73PPNQK","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FSH6X73PPNQKOZEM","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FSH6X73P","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:33d102a26d1b3a10845a8e50af58e441a852953bebbd6005f0f7dbae67a7a28a","target":"graph","created_at":"2026-05-18T03:59:37Z","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 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.","authors_text":"Baoxiang Wang, Michael Ruzhansky, Mitsuru Sugimoto","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-21T04:27:30Z","title":"Modulation Spaces and Nonlinear Evolution Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4651","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:ca6e2e9b8b6b6f5e5f3dc30c2bdc58ce68a34b4c5e58c545672346ab5c969b23","target":"record","created_at":"2026-05-18T03:59:37Z","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":"b5ddbff10c0d6518a218a9639ed605a0909263e805835ee0a1a1b9e0ef34fc7b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-03-21T04:27:30Z","title_canon_sha256":"9940b8b9896c506ba29984f11cffad35df701610f0118b6a19ca36503fa86890"},"schema_version":"1.0","source":{"id":"1203.4651","kind":"arxiv","version":1}},"canonical_sha256":"2c8febff6f7b60a7648cf568387f5dab96ce67959aee7fa4eb8ac83cf09c6315","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c8febff6f7b60a7648cf568387f5dab96ce67959aee7fa4eb8ac83cf09c6315","first_computed_at":"2026-05-18T03:59:37.552269Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:37.552269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rroXuRBJT1IMJKrCjIt07/Dayj7mb4SHj0m/+ygPrhfxxjG8aXt8yGXx51tV/DwqzkzZ1g3amYRIjE895tcwBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:37.552806Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.4651","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca6e2e9b8b6b6f5e5f3dc30c2bdc58ce68a34b4c5e58c545672346ab5c969b23","sha256:33d102a26d1b3a10845a8e50af58e441a852953bebbd6005f0f7dbae67a7a28a"],"state_sha256":"f478480b0bb8c00ea1883bd3001069a1df8cd68e80c738048baf8d32df355c90"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fPXmjNQwqosUtn1ZVTLGDgSD6X0SBoHLyDO+fnes9d1yUPZnHcxLUehOh2PocAltjVve+hadVnNcoHHJrmcnBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T18:10:38.126161Z","bundle_sha256":"845d1694915fe0a0652778b11e8da164e780de069998b19f72d7fb7bead142b0"}}