{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:P6JYBDF4H43T2BXLOTWHNQL3LW","short_pith_number":"pith:P6JYBDF4","canonical_record":{"source":{"id":"1008.5397","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-08-31T19:35:59Z","cross_cats_sorted":[],"title_canon_sha256":"d396efc73650ce39df6d9de03ec8f7c12736380fcd2d5fc94aa419712c241fff","abstract_canon_sha256":"0376ba57b4ad766dc9782ac2ff4d49c04feec3e43849cc1727f28f788420a006"},"schema_version":"1.0"},"canonical_sha256":"7f93808cbc3f373d06eb74ec76c17b5d80991582442ab35bd997de815c24e3de","source":{"kind":"arxiv","id":"1008.5397","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.5397","created_at":"2026-05-18T03:50:26Z"},{"alias_kind":"arxiv_version","alias_value":"1008.5397v2","created_at":"2026-05-18T03:50:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.5397","created_at":"2026-05-18T03:50:26Z"},{"alias_kind":"pith_short_12","alias_value":"P6JYBDF4H43T","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"P6JYBDF4H43T2BXL","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"P6JYBDF4","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:P6JYBDF4H43T2BXLOTWHNQL3LW","target":"record","payload":{"canonical_record":{"source":{"id":"1008.5397","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-08-31T19:35:59Z","cross_cats_sorted":[],"title_canon_sha256":"d396efc73650ce39df6d9de03ec8f7c12736380fcd2d5fc94aa419712c241fff","abstract_canon_sha256":"0376ba57b4ad766dc9782ac2ff4d49c04feec3e43849cc1727f28f788420a006"},"schema_version":"1.0"},"canonical_sha256":"7f93808cbc3f373d06eb74ec76c17b5d80991582442ab35bd997de815c24e3de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:26.034836Z","signature_b64":"vbD5mwPGOko5Vu0+AscPxikvUDIi2LE7EmyprjM7x7HdJlG5lE1PU/UKRw6W8tZDsfv35IjAlHoj2ESHR08VAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f93808cbc3f373d06eb74ec76c17b5d80991582442ab35bd997de815c24e3de","last_reissued_at":"2026-05-18T03:50:26.034028Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:26.034028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.5397","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:50:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZmLg1bxKoUhwHpFCmrjn7nDEjolCFl4yhSINdKHzqsRH29p5aKbYlO3uwMC0ZViIF6615bDXWGLKeQVIJBOrAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T02:00:31.073647Z"},"content_sha256":"22cab6a9ba858b421b9903ee5ca849514c081913a116b7c46fe5f4399b308d21","schema_version":"1.0","event_id":"sha256:22cab6a9ba858b421b9903ee5ca849514c081913a116b7c46fe5f4399b308d21"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:P6JYBDF4H43T2BXLOTWHNQL3LW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized and weighted Strichartz estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chengbo Wang, Jin-Cheng Jiang, Xin Yu","submitted_at":"2010-08-31T19:35:59Z","abstract_excerpt":"In this paper, we explore the relations between different kinds of Strichartz estimates and give new estimates in Euclidean space $\\mathbb{R}^n$. In particular, we prove the generalized and weighted Strichartz estimates for a large class of dispersive operators including the Schr\\\"odinger and wave equation. As a sample application of these new estimates, we are able to prove the Strauss conjecture with low regularity for dimension 2 and 3."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.5397","kind":"arxiv","version":2},"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":"2026-05-18T03:50:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QHF9v7eXTTTZPC7w1yjiYGLIJS9sX4uNZUEfbJdhSTJJgY3fVi/vXwcpBFhRmXosAmYzw1PHhvxWccA4naXlDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T02:00:31.073985Z"},"content_sha256":"3dd9770fef18912d1db0536146451219f927798ab5c48af809d6975c3b09b8ef","schema_version":"1.0","event_id":"sha256:3dd9770fef18912d1db0536146451219f927798ab5c48af809d6975c3b09b8ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P6JYBDF4H43T2BXLOTWHNQL3LW/bundle.json","state_url":"https://pith.science/pith/P6JYBDF4H43T2BXLOTWHNQL3LW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P6JYBDF4H43T2BXLOTWHNQL3LW/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":"2026-06-22T02:00:31Z","links":{"resolver":"https://pith.science/pith/P6JYBDF4H43T2BXLOTWHNQL3LW","bundle":"https://pith.science/pith/P6JYBDF4H43T2BXLOTWHNQL3LW/bundle.json","state":"https://pith.science/pith/P6JYBDF4H43T2BXLOTWHNQL3LW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P6JYBDF4H43T2BXLOTWHNQL3LW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:P6JYBDF4H43T2BXLOTWHNQL3LW","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":"0376ba57b4ad766dc9782ac2ff4d49c04feec3e43849cc1727f28f788420a006","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-08-31T19:35:59Z","title_canon_sha256":"d396efc73650ce39df6d9de03ec8f7c12736380fcd2d5fc94aa419712c241fff"},"schema_version":"1.0","source":{"id":"1008.5397","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.5397","created_at":"2026-05-18T03:50:26Z"},{"alias_kind":"arxiv_version","alias_value":"1008.5397v2","created_at":"2026-05-18T03:50:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.5397","created_at":"2026-05-18T03:50:26Z"},{"alias_kind":"pith_short_12","alias_value":"P6JYBDF4H43T","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"P6JYBDF4H43T2BXL","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"P6JYBDF4","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:3dd9770fef18912d1db0536146451219f927798ab5c48af809d6975c3b09b8ef","target":"graph","created_at":"2026-05-18T03:50:26Z","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":"In this paper, we explore the relations between different kinds of Strichartz estimates and give new estimates in Euclidean space $\\mathbb{R}^n$. In particular, we prove the generalized and weighted Strichartz estimates for a large class of dispersive operators including the Schr\\\"odinger and wave equation. As a sample application of these new estimates, we are able to prove the Strauss conjecture with low regularity for dimension 2 and 3.","authors_text":"Chengbo Wang, Jin-Cheng Jiang, Xin Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-08-31T19:35:59Z","title":"Generalized and weighted Strichartz estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.5397","kind":"arxiv","version":2},"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":"sha256:22cab6a9ba858b421b9903ee5ca849514c081913a116b7c46fe5f4399b308d21","target":"record","created_at":"2026-05-18T03:50:26Z","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":"0376ba57b4ad766dc9782ac2ff4d49c04feec3e43849cc1727f28f788420a006","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-08-31T19:35:59Z","title_canon_sha256":"d396efc73650ce39df6d9de03ec8f7c12736380fcd2d5fc94aa419712c241fff"},"schema_version":"1.0","source":{"id":"1008.5397","kind":"arxiv","version":2}},"canonical_sha256":"7f93808cbc3f373d06eb74ec76c17b5d80991582442ab35bd997de815c24e3de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f93808cbc3f373d06eb74ec76c17b5d80991582442ab35bd997de815c24e3de","first_computed_at":"2026-05-18T03:50:26.034028Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:26.034028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vbD5mwPGOko5Vu0+AscPxikvUDIi2LE7EmyprjM7x7HdJlG5lE1PU/UKRw6W8tZDsfv35IjAlHoj2ESHR08VAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:26.034836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.5397","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22cab6a9ba858b421b9903ee5ca849514c081913a116b7c46fe5f4399b308d21","sha256:3dd9770fef18912d1db0536146451219f927798ab5c48af809d6975c3b09b8ef"],"state_sha256":"3174079850e38d79cd20e7ffafb532635e01327a9c75e8d9f919465892935e90"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hj2XFV1T0ZxZXjvoCUvegjj5d1avvQiof507jHtyL7bnVRJD095BEytcQltcpe3lIyBgkAq9dz4XgzN2Ur2qCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T02:00:31.075875Z","bundle_sha256":"66961bf6baefecc42b131b771b1ef2e88ec9c87a647411328db644c86af81e64"}}