{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:XTGOB3A5C7CHDBQ6H5KVFBUNM5","short_pith_number":"pith:XTGOB3A5","canonical_record":{"source":{"id":"math/0410110","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2004-10-05T17:13:46Z","cross_cats_sorted":[],"title_canon_sha256":"35e4d864a487fd6d564072639f63b5c4d4a40c529a4374580d09e9217fbc1cb1","abstract_canon_sha256":"260f501b325dd08ae92d7526fab0abf19916ef85846320508a68d645e8720076"},"schema_version":"1.0"},"canonical_sha256":"bccce0ec1d17c471861e3f5552868d675b33cec326bb45709ffafc283c776c80","source":{"kind":"arxiv","id":"math/0410110","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0410110","created_at":"2026-05-18T01:05:25Z"},{"alias_kind":"arxiv_version","alias_value":"math/0410110v1","created_at":"2026-05-18T01:05:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0410110","created_at":"2026-05-18T01:05:25Z"},{"alias_kind":"pith_short_12","alias_value":"XTGOB3A5C7CH","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XTGOB3A5C7CHDBQ6","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XTGOB3A5","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:XTGOB3A5C7CHDBQ6H5KVFBUNM5","target":"record","payload":{"canonical_record":{"source":{"id":"math/0410110","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2004-10-05T17:13:46Z","cross_cats_sorted":[],"title_canon_sha256":"35e4d864a487fd6d564072639f63b5c4d4a40c529a4374580d09e9217fbc1cb1","abstract_canon_sha256":"260f501b325dd08ae92d7526fab0abf19916ef85846320508a68d645e8720076"},"schema_version":"1.0"},"canonical_sha256":"bccce0ec1d17c471861e3f5552868d675b33cec326bb45709ffafc283c776c80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:25.893397Z","signature_b64":"o9HMKY/Xi0nSMCuPwawojqE4bT3eWXrKEA1DH+onAT8OU1CiU2zYKvHdaIYi2PZQaT89nI/SZbUaA/2uIsP1Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bccce0ec1d17c471861e3f5552868d675b33cec326bb45709ffafc283c776c80","last_reissued_at":"2026-05-18T01:05:25.892888Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:25.892888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0410110","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":"2026-05-18T01:05:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iAGHbUUXrc5Vkw6VxGjKxcxRVD0rqIAiKyEW2sAPh4fJLMQ5eNtdar8HhyFlPt97+dNgTweUOom0lLOZhkzoDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:06:12.580779Z"},"content_sha256":"0b15407a616ce5eba1904b0bcb3cd93694686fc9e39d4f26044e80b265e1fb51","schema_version":"1.0","event_id":"sha256:0b15407a616ce5eba1904b0bcb3cd93694686fc9e39d4f26044e80b265e1fb51"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:XTGOB3A5C7CHDBQ6H5KVFBUNM5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Potential theory for hyperbolic SPDEs","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eulalia Nualart, Robert C. Dalang","submitted_at":"2004-10-05T17:13:46Z","abstract_excerpt":"We give general sufficient conditions which imply upper and lower bounds for the probability that a multiparameter process hits a given set E in terms of a capacity of E related to the process. This extends a result of Khoshnevisan and Shi [Ann. Probab. 27 (1999) 1135-1159], where estimates for the hitting probabilities of the (N,d) Brownian sheet in terms of the\n (d-2N) Newtonian capacity are obtained, and readily applies to a wide class of Gaussian processes. Using Malliavin calculus and, in particular, a result of Kohatsu-Higa [Probab. Theory Related Fields 126 (2003) 421-457], we apply the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410110","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":"2026-05-18T01:05:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"efnG0AG/tHsw0HUfMXggFEu2//m2qsxvhSJ+v3d6YRtOLDDD33jBMk/D69QtxEN2YKMz51Z/tYaNrsZ9dS8MBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:06:12.581115Z"},"content_sha256":"6907dcf22d68d20d1d40a38be597931c9b659f409e8d454798b0329f0909422f","schema_version":"1.0","event_id":"sha256:6907dcf22d68d20d1d40a38be597931c9b659f409e8d454798b0329f0909422f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XTGOB3A5C7CHDBQ6H5KVFBUNM5/bundle.json","state_url":"https://pith.science/pith/XTGOB3A5C7CHDBQ6H5KVFBUNM5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XTGOB3A5C7CHDBQ6H5KVFBUNM5/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":"2026-06-26T11:06:12Z","links":{"resolver":"https://pith.science/pith/XTGOB3A5C7CHDBQ6H5KVFBUNM5","bundle":"https://pith.science/pith/XTGOB3A5C7CHDBQ6H5KVFBUNM5/bundle.json","state":"https://pith.science/pith/XTGOB3A5C7CHDBQ6H5KVFBUNM5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XTGOB3A5C7CHDBQ6H5KVFBUNM5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:XTGOB3A5C7CHDBQ6H5KVFBUNM5","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":"260f501b325dd08ae92d7526fab0abf19916ef85846320508a68d645e8720076","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2004-10-05T17:13:46Z","title_canon_sha256":"35e4d864a487fd6d564072639f63b5c4d4a40c529a4374580d09e9217fbc1cb1"},"schema_version":"1.0","source":{"id":"math/0410110","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0410110","created_at":"2026-05-18T01:05:25Z"},{"alias_kind":"arxiv_version","alias_value":"math/0410110v1","created_at":"2026-05-18T01:05:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0410110","created_at":"2026-05-18T01:05:25Z"},{"alias_kind":"pith_short_12","alias_value":"XTGOB3A5C7CH","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XTGOB3A5C7CHDBQ6","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XTGOB3A5","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:6907dcf22d68d20d1d40a38be597931c9b659f409e8d454798b0329f0909422f","target":"graph","created_at":"2026-05-18T01:05:25Z","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 give general sufficient conditions which imply upper and lower bounds for the probability that a multiparameter process hits a given set E in terms of a capacity of E related to the process. This extends a result of Khoshnevisan and Shi [Ann. Probab. 27 (1999) 1135-1159], where estimates for the hitting probabilities of the (N,d) Brownian sheet in terms of the\n (d-2N) Newtonian capacity are obtained, and readily applies to a wide class of Gaussian processes. Using Malliavin calculus and, in particular, a result of Kohatsu-Higa [Probab. Theory Related Fields 126 (2003) 421-457], we apply the","authors_text":"Eulalia Nualart, Robert C. Dalang","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2004-10-05T17:13:46Z","title":"Potential theory for hyperbolic SPDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410110","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":"sha256:0b15407a616ce5eba1904b0bcb3cd93694686fc9e39d4f26044e80b265e1fb51","target":"record","created_at":"2026-05-18T01:05:25Z","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":"260f501b325dd08ae92d7526fab0abf19916ef85846320508a68d645e8720076","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2004-10-05T17:13:46Z","title_canon_sha256":"35e4d864a487fd6d564072639f63b5c4d4a40c529a4374580d09e9217fbc1cb1"},"schema_version":"1.0","source":{"id":"math/0410110","kind":"arxiv","version":1}},"canonical_sha256":"bccce0ec1d17c471861e3f5552868d675b33cec326bb45709ffafc283c776c80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bccce0ec1d17c471861e3f5552868d675b33cec326bb45709ffafc283c776c80","first_computed_at":"2026-05-18T01:05:25.892888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:25.892888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o9HMKY/Xi0nSMCuPwawojqE4bT3eWXrKEA1DH+onAT8OU1CiU2zYKvHdaIYi2PZQaT89nI/SZbUaA/2uIsP1Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:25.893397Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0410110","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b15407a616ce5eba1904b0bcb3cd93694686fc9e39d4f26044e80b265e1fb51","sha256:6907dcf22d68d20d1d40a38be597931c9b659f409e8d454798b0329f0909422f"],"state_sha256":"3c2c98b5589bfbcb90a6f73a8ab2b412d8f18416c5ae5102caa63361781cfc0f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yD01a61i0a8uG7qYsX/k3SKII7RA+sMiMq4NSUy1EN0tdPNEJw3ecQ2uVlpX+TOGoj3HFAJI+WPjB1/8pJJMBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T11:06:12.583071Z","bundle_sha256":"9f7e0039c7ba46e629fc27b4b1555ac6a589e71e829bf555ad55f572a3644f93"}}