{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MIOPQL7RNJNDOG5EMEEPSJ6ICW","short_pith_number":"pith:MIOPQL7R","canonical_record":{"source":{"id":"1302.6271","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-25T23:01:40Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"adefbad375dd66f856179782eb5e1d6eac1353b051c0286a936a7454d2173492","abstract_canon_sha256":"305599fcb54f9b9685a1b9d16da3b062aee499c3682bd4cffd3e00b90ce8b3b7"},"schema_version":"1.0"},"canonical_sha256":"621cf82ff16a5a371ba46108f927c815b05ee51fb32df7b7e70089f64665b75e","source":{"kind":"arxiv","id":"1302.6271","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6271","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6271v1","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6271","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"pith_short_12","alias_value":"MIOPQL7RNJND","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MIOPQL7RNJNDOG5E","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MIOPQL7R","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MIOPQL7RNJNDOG5EMEEPSJ6ICW","target":"record","payload":{"canonical_record":{"source":{"id":"1302.6271","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-25T23:01:40Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"adefbad375dd66f856179782eb5e1d6eac1353b051c0286a936a7454d2173492","abstract_canon_sha256":"305599fcb54f9b9685a1b9d16da3b062aee499c3682bd4cffd3e00b90ce8b3b7"},"schema_version":"1.0"},"canonical_sha256":"621cf82ff16a5a371ba46108f927c815b05ee51fb32df7b7e70089f64665b75e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:08.648203Z","signature_b64":"xkeOCrsH/xbNd4v+LJR2Geyn3UPNW78xKXLZeYWJJhRqif6bCdADzBht4k8ykROnKZTFyHacgXuyyeNBCqniAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"621cf82ff16a5a371ba46108f927c815b05ee51fb32df7b7e70089f64665b75e","last_reissued_at":"2026-05-18T01:30:08.647618Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:08.647618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.6271","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":"2026-05-18T01:30:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X+acW2BPPdztejOY3D9APKofsFBnKdtdJDekKHJPAuY/nNK84zP0xKGMPkmnS5KZFKi8YMk0GQVvvlTS4GhXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T17:28:08.314268Z"},"content_sha256":"48abba8fab84da32893e78be77c530adabc10a120c318f4e3ad4696926aa9579","schema_version":"1.0","event_id":"sha256:48abba8fab84da32893e78be77c530adabc10a120c318f4e3ad4696926aa9579"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MIOPQL7RNJNDOG5EMEEPSJ6ICW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Smoothing properties of inhomogeneous equations via canonical transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Michael Ruzhansky, Mitsuru Sugimoto","submitted_at":"2013-02-25T23:01:40Z","abstract_excerpt":"The paper describes a new approach to global smoothing problems for inhomogeneous dispersive evolution equations based on an idea of canonical transformation. In our previous papers, we introduced such a method to show global smoothing estimates for homogeneous dispersive equations. It is remarkable that this method allows us to carry out a global microlocal reduction of equations to some low dimensional model cases. The purpose of this paper is to pursue the same treatment for inhomogeneous equations. Especially, time-global smoothing estimates for the operator $a(D_x)$ with lower order terms"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6271","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":"2026-05-18T01:30:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FoD7U60AMRVfytZ79gIFSkQdXNNyfF9t9H/iCrtlUrEnCeQx2n7s1yMb9H2IonF6/Pv5kWJL06gB941HIIT0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T17:28:08.315121Z"},"content_sha256":"988ea2ba1afe8a6c06ea1a88ce64c29e28628dd4e90e7714949aca7bf8e27912","schema_version":"1.0","event_id":"sha256:988ea2ba1afe8a6c06ea1a88ce64c29e28628dd4e90e7714949aca7bf8e27912"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MIOPQL7RNJNDOG5EMEEPSJ6ICW/bundle.json","state_url":"https://pith.science/pith/MIOPQL7RNJNDOG5EMEEPSJ6ICW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MIOPQL7RNJNDOG5EMEEPSJ6ICW/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":"2026-06-10T17:28:08Z","links":{"resolver":"https://pith.science/pith/MIOPQL7RNJNDOG5EMEEPSJ6ICW","bundle":"https://pith.science/pith/MIOPQL7RNJNDOG5EMEEPSJ6ICW/bundle.json","state":"https://pith.science/pith/MIOPQL7RNJNDOG5EMEEPSJ6ICW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MIOPQL7RNJNDOG5EMEEPSJ6ICW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MIOPQL7RNJNDOG5EMEEPSJ6ICW","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":"305599fcb54f9b9685a1b9d16da3b062aee499c3682bd4cffd3e00b90ce8b3b7","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-25T23:01:40Z","title_canon_sha256":"adefbad375dd66f856179782eb5e1d6eac1353b051c0286a936a7454d2173492"},"schema_version":"1.0","source":{"id":"1302.6271","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6271","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6271v1","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6271","created_at":"2026-05-18T01:30:08Z"},{"alias_kind":"pith_short_12","alias_value":"MIOPQL7RNJND","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MIOPQL7RNJNDOG5E","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MIOPQL7R","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:988ea2ba1afe8a6c06ea1a88ce64c29e28628dd4e90e7714949aca7bf8e27912","target":"graph","created_at":"2026-05-18T01:30:08Z","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":"The paper describes a new approach to global smoothing problems for inhomogeneous dispersive evolution equations based on an idea of canonical transformation. In our previous papers, we introduced such a method to show global smoothing estimates for homogeneous dispersive equations. It is remarkable that this method allows us to carry out a global microlocal reduction of equations to some low dimensional model cases. The purpose of this paper is to pursue the same treatment for inhomogeneous equations. Especially, time-global smoothing estimates for the operator $a(D_x)$ with lower order terms","authors_text":"Michael Ruzhansky, Mitsuru Sugimoto","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-25T23:01:40Z","title":"Smoothing properties of inhomogeneous equations via canonical transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6271","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":"sha256:48abba8fab84da32893e78be77c530adabc10a120c318f4e3ad4696926aa9579","target":"record","created_at":"2026-05-18T01:30:08Z","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":"305599fcb54f9b9685a1b9d16da3b062aee499c3682bd4cffd3e00b90ce8b3b7","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-25T23:01:40Z","title_canon_sha256":"adefbad375dd66f856179782eb5e1d6eac1353b051c0286a936a7454d2173492"},"schema_version":"1.0","source":{"id":"1302.6271","kind":"arxiv","version":1}},"canonical_sha256":"621cf82ff16a5a371ba46108f927c815b05ee51fb32df7b7e70089f64665b75e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"621cf82ff16a5a371ba46108f927c815b05ee51fb32df7b7e70089f64665b75e","first_computed_at":"2026-05-18T01:30:08.647618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:08.647618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xkeOCrsH/xbNd4v+LJR2Geyn3UPNW78xKXLZeYWJJhRqif6bCdADzBht4k8ykROnKZTFyHacgXuyyeNBCqniAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:08.648203Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.6271","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48abba8fab84da32893e78be77c530adabc10a120c318f4e3ad4696926aa9579","sha256:988ea2ba1afe8a6c06ea1a88ce64c29e28628dd4e90e7714949aca7bf8e27912"],"state_sha256":"4ecc25c0ad2dd70ccf475864c92b1acfb487b9f341eefd224c0537ae61fff4a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OkWkcZ19t4aMod4TtgF9ojfISwId8Iu1NLwo+5dTZsbenxbSDmHcoO6Ke+p63SlDKyG3c2Zrn6xzpuKdkVlZCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T17:28:08.319692Z","bundle_sha256":"a27c0dda97732a497fea80c86455a9301ad8fc277af6df2ea7492afe4db4b01d"}}