{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:4FLG2KRDBFTHZVSZ7235DOZKJT","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":"57a6a27be8bf8fc9ef3ec8b7b6c42bfcd599264bd3e2d039265ed7d648ee47d3","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"2006-07-03T16:25:44Z","title_canon_sha256":"5cb872b47cd1bbef40ea3f0316cbf65e21eb8221ec994d280ac41cb59dbc5c05"},"schema_version":"1.0","source":{"id":"math/0607059","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0607059","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"arxiv_version","alias_value":"math/0607059v2","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0607059","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"pith_short_12","alias_value":"4FLG2KRDBFTH","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"pith_short_16","alias_value":"4FLG2KRDBFTHZVSZ","created_at":"2026-07-04T17:23:15Z"},{"alias_kind":"pith_short_8","alias_value":"4FLG2KRD","created_at":"2026-07-04T17:23:15Z"}],"graph_snapshots":[{"event_id":"sha256:a3a793e898090c4c11443c7c049e9778a9c4b46755206fdbd3750010a257e984","target":"graph","created_at":"2026-07-04T17:23:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0607059/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider Fourier transforms of densities supported on curves in R^d. We obtain sharp lower and close to sharp upper bounds for the L^q decay rates.","authors_text":"Alexander Iosevich, Allan Greenleaf, Andreas Seeger, Giacomo Gigante, Giancarlo Travaglini, Luca Brandolini","cross_cats":[],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2006-07-03T16:25:44Z","title":"Average decay estimates for Fourier transforms of measures supported on curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607059","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":"sha256:9c941d75368fa8475d617603ce7523662d5614cffb6347b4c29b5d911642cff0","target":"record","created_at":"2026-07-04T17:23:15Z","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":"57a6a27be8bf8fc9ef3ec8b7b6c42bfcd599264bd3e2d039265ed7d648ee47d3","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"2006-07-03T16:25:44Z","title_canon_sha256":"5cb872b47cd1bbef40ea3f0316cbf65e21eb8221ec994d280ac41cb59dbc5c05"},"schema_version":"1.0","source":{"id":"math/0607059","kind":"arxiv","version":2}},"canonical_sha256":"e1566d2a2309667cd659feb7d1bb2a4cd4910f9152c4e72f7088758e17967d17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1566d2a2309667cd659feb7d1bb2a4cd4910f9152c4e72f7088758e17967d17","first_computed_at":"2026-07-04T17:23:15.444281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:23:15.444281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d6BdR9VlgVEOwHmE1fHWIV4xwQn6UNDZ1pmCkaC/x/Sl1Z62Q7vzwxS5vH+xt/XqgJWG2jF3zJodBwc0I/L5AA==","signature_status":"signed_v1","signed_at":"2026-07-04T17:23:15.444721Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0607059","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c941d75368fa8475d617603ce7523662d5614cffb6347b4c29b5d911642cff0","sha256:a3a793e898090c4c11443c7c049e9778a9c4b46755206fdbd3750010a257e984"],"state_sha256":"ceaede36b27abd4bb9f9c8a81031d8a8e302afd88d6fb3f752a868a8b7c90ab0"}