{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:J6DJTOIOBNHDYGZN5CT74Q5SQQ","short_pith_number":"pith:J6DJTOIO","canonical_record":{"source":{"id":"1011.3919","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-17T10:02:09Z","cross_cats_sorted":[],"title_canon_sha256":"9faa29d26e2f09143f8f066f4eb97867e821c99322e7f7ef469528e62794fa71","abstract_canon_sha256":"ffa4538bad881ca357c2d4f0d9d1de279252219362172072689a5d3b4c4cc1dc"},"schema_version":"1.0"},"canonical_sha256":"4f8699b90e0b4e3c1b2de8a7fe43b2842af0eb849fdc18d4bbfe8e079ef2222c","source":{"kind":"arxiv","id":"1011.3919","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3919","created_at":"2026-05-18T04:34:08Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3919v2","created_at":"2026-05-18T04:34:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3919","created_at":"2026-05-18T04:34:08Z"},{"alias_kind":"pith_short_12","alias_value":"J6DJTOIOBNHD","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"J6DJTOIOBNHDYGZN","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"J6DJTOIO","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:J6DJTOIOBNHDYGZN5CT74Q5SQQ","target":"record","payload":{"canonical_record":{"source":{"id":"1011.3919","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-17T10:02:09Z","cross_cats_sorted":[],"title_canon_sha256":"9faa29d26e2f09143f8f066f4eb97867e821c99322e7f7ef469528e62794fa71","abstract_canon_sha256":"ffa4538bad881ca357c2d4f0d9d1de279252219362172072689a5d3b4c4cc1dc"},"schema_version":"1.0"},"canonical_sha256":"4f8699b90e0b4e3c1b2de8a7fe43b2842af0eb849fdc18d4bbfe8e079ef2222c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:08.614761Z","signature_b64":"vwWmxlkwk20pSLVOGe1l2U7j+T6mC08i74Q4gLb6SZdxSr4CQvZvosqPC/22hzWZDxDkVLOJ+U26THduHOg+CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f8699b90e0b4e3c1b2de8a7fe43b2842af0eb849fdc18d4bbfe8e079ef2222c","last_reissued_at":"2026-05-18T04:34:08.614147Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:08.614147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.3919","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":"2026-05-18T04:34:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iqN9kCta0mbcHkuWUwvZCKOXQgKgG8ZP1jIXOR2hH5etFbHG3ju8zGqTc+bVqVvVKGdwisHrbOIvwndecCt3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T03:10:40.111353Z"},"content_sha256":"80e5855bf8bad7cb9729717579e67cd403bd005b1d52a3139133d4e2e3902aa9","schema_version":"1.0","event_id":"sha256:80e5855bf8bad7cb9729717579e67cd403bd005b1d52a3139133d4e2e3902aa9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:J6DJTOIOBNHDYGZN5CT74Q5SQQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal dispersive estimates for the wave equation with $C^{(n-3)/2}$ potentials in dimensions $4\\le n\\le 7$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fernando Cardoso, Georgi Vodev","submitted_at":"2010-11-17T10:02:09Z","abstract_excerpt":"We prove optimal dispersive estimates for the wave group $e^{it\\sqrt{-\\Delta+V}}$ for a class of real-valued potentials $V\\in C^{(n-3)/2}({\\bf R}^n)$, $4\\le n\\le 7$, such that $\\partial_x^\\alpha V(x)=O(|x|^{-\\delta})$ for $|x|>1$, where $\\delta>(n+1)/2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3919","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":"2026-05-18T04:34:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YmdwlYekCM1yAHmE6WQkvxQBkzk5UkJ9H8Ohv/Dkj+KuC6D88yoCF2zpAkIpk3QRTQoJj9v2ltH6ryv4Ot85CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T03:10:40.112057Z"},"content_sha256":"d8662e025e1ef6300a2e1ffc188324e9ac9fd288ad9e8b4c1905bdd805d8b5d6","schema_version":"1.0","event_id":"sha256:d8662e025e1ef6300a2e1ffc188324e9ac9fd288ad9e8b4c1905bdd805d8b5d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J6DJTOIOBNHDYGZN5CT74Q5SQQ/bundle.json","state_url":"https://pith.science/pith/J6DJTOIOBNHDYGZN5CT74Q5SQQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J6DJTOIOBNHDYGZN5CT74Q5SQQ/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":"2026-06-08T03:10:40Z","links":{"resolver":"https://pith.science/pith/J6DJTOIOBNHDYGZN5CT74Q5SQQ","bundle":"https://pith.science/pith/J6DJTOIOBNHDYGZN5CT74Q5SQQ/bundle.json","state":"https://pith.science/pith/J6DJTOIOBNHDYGZN5CT74Q5SQQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J6DJTOIOBNHDYGZN5CT74Q5SQQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:J6DJTOIOBNHDYGZN5CT74Q5SQQ","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":"ffa4538bad881ca357c2d4f0d9d1de279252219362172072689a5d3b4c4cc1dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-17T10:02:09Z","title_canon_sha256":"9faa29d26e2f09143f8f066f4eb97867e821c99322e7f7ef469528e62794fa71"},"schema_version":"1.0","source":{"id":"1011.3919","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3919","created_at":"2026-05-18T04:34:08Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3919v2","created_at":"2026-05-18T04:34:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3919","created_at":"2026-05-18T04:34:08Z"},{"alias_kind":"pith_short_12","alias_value":"J6DJTOIOBNHD","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"J6DJTOIOBNHDYGZN","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"J6DJTOIO","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:d8662e025e1ef6300a2e1ffc188324e9ac9fd288ad9e8b4c1905bdd805d8b5d6","target":"graph","created_at":"2026-05-18T04:34:08Z","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":"We prove optimal dispersive estimates for the wave group $e^{it\\sqrt{-\\Delta+V}}$ for a class of real-valued potentials $V\\in C^{(n-3)/2}({\\bf R}^n)$, $4\\le n\\le 7$, such that $\\partial_x^\\alpha V(x)=O(|x|^{-\\delta})$ for $|x|>1$, where $\\delta>(n+1)/2$.","authors_text":"Fernando Cardoso, Georgi Vodev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-17T10:02:09Z","title":"Optimal dispersive estimates for the wave equation with $C^{(n-3)/2}$ potentials in dimensions $4\\le n\\le 7$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3919","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":"sha256:80e5855bf8bad7cb9729717579e67cd403bd005b1d52a3139133d4e2e3902aa9","target":"record","created_at":"2026-05-18T04:34:08Z","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":"ffa4538bad881ca357c2d4f0d9d1de279252219362172072689a5d3b4c4cc1dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-11-17T10:02:09Z","title_canon_sha256":"9faa29d26e2f09143f8f066f4eb97867e821c99322e7f7ef469528e62794fa71"},"schema_version":"1.0","source":{"id":"1011.3919","kind":"arxiv","version":2}},"canonical_sha256":"4f8699b90e0b4e3c1b2de8a7fe43b2842af0eb849fdc18d4bbfe8e079ef2222c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f8699b90e0b4e3c1b2de8a7fe43b2842af0eb849fdc18d4bbfe8e079ef2222c","first_computed_at":"2026-05-18T04:34:08.614147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:08.614147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vwWmxlkwk20pSLVOGe1l2U7j+T6mC08i74Q4gLb6SZdxSr4CQvZvosqPC/22hzWZDxDkVLOJ+U26THduHOg+CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:08.614761Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.3919","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80e5855bf8bad7cb9729717579e67cd403bd005b1d52a3139133d4e2e3902aa9","sha256:d8662e025e1ef6300a2e1ffc188324e9ac9fd288ad9e8b4c1905bdd805d8b5d6"],"state_sha256":"182b92d8e984d39f8d134f4dd260eb564f028159adccf068eba3c55e0ab51296"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L/hFLtxEjTEa6ZaUa2bGeAlvrN5V4ViBPO30Y5yBUHfoKOIGbf+IRDBPZ1TMi8mP66NUkoEzMQUuVlQXN7PdCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T03:10:40.115753Z","bundle_sha256":"aadbea0615844c392dd1e7c5752ccc410a48b41fcb5d44166794197089e2bfcb"}}