{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:EXDWSBZTBWNJRMWZGXM3KVLIVF","short_pith_number":"pith:EXDWSBZT","canonical_record":{"source":{"id":"math/0401019","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2004-01-04T06:44:24Z","cross_cats_sorted":[],"title_canon_sha256":"66f4075f6d3e61de315fb1e5b3aaeff83aa200567a742ce2ca1d504b08266ce1","abstract_canon_sha256":"26822f309d19aa117ebd015366921479cd553caf38f8ed94772c11a107ac9e66"},"schema_version":"1.0"},"canonical_sha256":"25c76907330d9a98b2d935d9b55568a94e96af3d86fb6d7a94e893ef92a0eee4","source":{"kind":"arxiv","id":"math/0401019","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0401019","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"arxiv_version","alias_value":"math/0401019v2","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0401019","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"pith_short_12","alias_value":"EXDWSBZTBWNJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"EXDWSBZTBWNJRMWZ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"EXDWSBZT","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:EXDWSBZTBWNJRMWZGXM3KVLIVF","target":"record","payload":{"canonical_record":{"source":{"id":"math/0401019","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2004-01-04T06:44:24Z","cross_cats_sorted":[],"title_canon_sha256":"66f4075f6d3e61de315fb1e5b3aaeff83aa200567a742ce2ca1d504b08266ce1","abstract_canon_sha256":"26822f309d19aa117ebd015366921479cd553caf38f8ed94772c11a107ac9e66"},"schema_version":"1.0"},"canonical_sha256":"25c76907330d9a98b2d935d9b55568a94e96af3d86fb6d7a94e893ef92a0eee4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:05.464548Z","signature_b64":"B/lLu+EUul0GVV6bj6YRe2qLhaVaIMNUKtrR8As5QaYaUhkcRj/mVT0bg3l6DoG6/1SykkI0Q8mSg5792eUOAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25c76907330d9a98b2d935d9b55568a94e96af3d86fb6d7a94e893ef92a0eee4","last_reissued_at":"2026-05-18T04:41:05.464072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:05.464072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0401019","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":"2026-05-18T04:41:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QMdD6yAxBXMnutuMr4kGogHabn30SsPqA19XOff/aiUPAIx3oXoRh8OflRmq6zDVIuJD5LLdIoPHYcBltAuSCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:37:33.010580Z"},"content_sha256":"d1498374ddc0d980c3a6b4cf3b94d9c6b31a0640df0ed56e88ce579ead3b9bdb","schema_version":"1.0","event_id":"sha256:d1498374ddc0d980c3a6b4cf3b94d9c6b31a0640df0ed56e88ce579ead3b9bdb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:EXDWSBZTBWNJRMWZGXM3KVLIVF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strichartz estimates for the Wave and Schrodinger Equations with Potentials of Critical Decay","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A. Shadi Tahvildar-Zadeh, Fabrice Planchon, John G. Stalker, Nicolas Burq","submitted_at":"2004-01-04T06:44:24Z","abstract_excerpt":"We prove weighted L^2 (Morawetz) estimates for the solutions of linear Schrodinger and wave equation with potentials that decay like |x|^{-2} for large x, by deducing them from estimates on the resolvent of the associated elliptic operator. We then deduce Strichartz estimates for these equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401019","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":"2026-05-18T04:41:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LA3jfhSxbZnQBIjCMK5BoykZxg1h0c0ALQe7tmDUfvejeeAyEHTtof+vy5h0GgoLtgpiLZruDIkd9xCU1+HFDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:37:33.011183Z"},"content_sha256":"e6cf11dde4934c99d76f42f93de0a2a7ffbcac5c639cc4d6d35ff98e9cd08938","schema_version":"1.0","event_id":"sha256:e6cf11dde4934c99d76f42f93de0a2a7ffbcac5c639cc4d6d35ff98e9cd08938"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EXDWSBZTBWNJRMWZGXM3KVLIVF/bundle.json","state_url":"https://pith.science/pith/EXDWSBZTBWNJRMWZGXM3KVLIVF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EXDWSBZTBWNJRMWZGXM3KVLIVF/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":"2026-06-07T16:37:33Z","links":{"resolver":"https://pith.science/pith/EXDWSBZTBWNJRMWZGXM3KVLIVF","bundle":"https://pith.science/pith/EXDWSBZTBWNJRMWZGXM3KVLIVF/bundle.json","state":"https://pith.science/pith/EXDWSBZTBWNJRMWZGXM3KVLIVF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EXDWSBZTBWNJRMWZGXM3KVLIVF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:EXDWSBZTBWNJRMWZGXM3KVLIVF","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":"26822f309d19aa117ebd015366921479cd553caf38f8ed94772c11a107ac9e66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2004-01-04T06:44:24Z","title_canon_sha256":"66f4075f6d3e61de315fb1e5b3aaeff83aa200567a742ce2ca1d504b08266ce1"},"schema_version":"1.0","source":{"id":"math/0401019","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0401019","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"arxiv_version","alias_value":"math/0401019v2","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0401019","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"pith_short_12","alias_value":"EXDWSBZTBWNJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"EXDWSBZTBWNJRMWZ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"EXDWSBZT","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:e6cf11dde4934c99d76f42f93de0a2a7ffbcac5c639cc4d6d35ff98e9cd08938","target":"graph","created_at":"2026-05-18T04:41:05Z","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 prove weighted L^2 (Morawetz) estimates for the solutions of linear Schrodinger and wave equation with potentials that decay like |x|^{-2} for large x, by deducing them from estimates on the resolvent of the associated elliptic operator. We then deduce Strichartz estimates for these equations.","authors_text":"A. Shadi Tahvildar-Zadeh, Fabrice Planchon, John G. Stalker, Nicolas Burq","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2004-01-04T06:44:24Z","title":"Strichartz estimates for the Wave and Schrodinger Equations with Potentials of Critical Decay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0401019","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:d1498374ddc0d980c3a6b4cf3b94d9c6b31a0640df0ed56e88ce579ead3b9bdb","target":"record","created_at":"2026-05-18T04:41:05Z","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":"26822f309d19aa117ebd015366921479cd553caf38f8ed94772c11a107ac9e66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2004-01-04T06:44:24Z","title_canon_sha256":"66f4075f6d3e61de315fb1e5b3aaeff83aa200567a742ce2ca1d504b08266ce1"},"schema_version":"1.0","source":{"id":"math/0401019","kind":"arxiv","version":2}},"canonical_sha256":"25c76907330d9a98b2d935d9b55568a94e96af3d86fb6d7a94e893ef92a0eee4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25c76907330d9a98b2d935d9b55568a94e96af3d86fb6d7a94e893ef92a0eee4","first_computed_at":"2026-05-18T04:41:05.464072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:05.464072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B/lLu+EUul0GVV6bj6YRe2qLhaVaIMNUKtrR8As5QaYaUhkcRj/mVT0bg3l6DoG6/1SykkI0Q8mSg5792eUOAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:05.464548Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0401019","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1498374ddc0d980c3a6b4cf3b94d9c6b31a0640df0ed56e88ce579ead3b9bdb","sha256:e6cf11dde4934c99d76f42f93de0a2a7ffbcac5c639cc4d6d35ff98e9cd08938"],"state_sha256":"bc73cf0b33f314db70306aa9a536eb1c46f818e5f3aee576e8436abd7068a071"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A/ou4UdH0aWXbtVh8b3MzovYETZ9W0uA0kMhG0QqsAw6u/GTyNdy9FPMEKACbP8DoT1jJ/R8jbb00soNfyh5Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:37:33.014254Z","bundle_sha256":"64153aeca9a4806ee5a2d75099d3f5a8d8aea1daddeb1f38fd98488b56756a83"}}