{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:EXCJ46A36RRDDDRSYKYUUXUV6T","short_pith_number":"pith:EXCJ46A3","canonical_record":{"source":{"id":"1204.0815","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-04-03T21:24:38Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"497014abb80e1c6b1d66ee52edd7f01a318fe47f6ebf4583c2a4ab432d82f9b0","abstract_canon_sha256":"246d2693daec430d90381ee4570001401d5545230148749edde0a79b3c0b835c"},"schema_version":"1.0"},"canonical_sha256":"25c49e781bf462318e32c2b14a5e95f4e1fb0823b39406417db368926f56c82d","source":{"kind":"arxiv","id":"1204.0815","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0815","created_at":"2026-05-18T03:58:37Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0815v1","created_at":"2026-05-18T03:58:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0815","created_at":"2026-05-18T03:58:37Z"},{"alias_kind":"pith_short_12","alias_value":"EXCJ46A36RRD","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EXCJ46A36RRDDDRS","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EXCJ46A3","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:EXCJ46A36RRDDDRSYKYUUXUV6T","target":"record","payload":{"canonical_record":{"source":{"id":"1204.0815","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-04-03T21:24:38Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"497014abb80e1c6b1d66ee52edd7f01a318fe47f6ebf4583c2a4ab432d82f9b0","abstract_canon_sha256":"246d2693daec430d90381ee4570001401d5545230148749edde0a79b3c0b835c"},"schema_version":"1.0"},"canonical_sha256":"25c49e781bf462318e32c2b14a5e95f4e1fb0823b39406417db368926f56c82d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:37.693735Z","signature_b64":"WnAQtmFwyb5GEEohd1psSLSGVHBQbb+1XDWTdU0Q5Rg/Xg35NxDZFNRcEQnLcIgG6sNGiqrMAKJhWCNAOT9vAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25c49e781bf462318e32c2b14a5e95f4e1fb0823b39406417db368926f56c82d","last_reissued_at":"2026-05-18T03:58:37.693005Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:37.693005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.0815","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":"2026-05-18T03:58:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KAzG42ykStPQNwUFlEghVCMJGV7gMSjidNx5GepWu8Lnlly8qZasRYcIts6sahshlxAM4LUkJ8GyeLVP+NXbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:57:15.077035Z"},"content_sha256":"0c57341915d1279d62b7dc3d5a76f51775f33a9127d04b954c59507fb86a5726","schema_version":"1.0","event_id":"sha256:0c57341915d1279d62b7dc3d5a76f51775f33a9127d04b954c59507fb86a5726"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:EXCJ46A36RRDDDRSYKYUUXUV6T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Polyharmonic Hardy Spaces on the Complexified Annulus and Error Estimates of Cubature Formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.NA","authors_text":"Hermann Render, Ognyan Kounchev","submitted_at":"2012-04-03T21:24:38Z","abstract_excerpt":"The present paper has a twofold contribution: first, we introduce a new concept of Hardy spaces on a multidimensional complexified annular domain which is closely related to the annulus of the Klein-Dirac quadric important in Conformal Quantum Field Theory. Secondly, for functions in these Hardy spaces, we provide error estimate for the polyharmonic Gau\\ss -Jacobi cubature formulas, which have been introduced in previous papers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0815","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":"2026-05-18T03:58:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xl9vF7CD14eXWLmo1cJiznB6JQCPo+Y1dVTqQy+4ruv1iCMUM4hVwopjS890uOwe2sHTAVMKbmIkkkc70zx7Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:57:15.077376Z"},"content_sha256":"b92b310827eae0702c49c738a5efd107383e502594f991ad9f4bef8bb161c7d8","schema_version":"1.0","event_id":"sha256:b92b310827eae0702c49c738a5efd107383e502594f991ad9f4bef8bb161c7d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EXCJ46A36RRDDDRSYKYUUXUV6T/bundle.json","state_url":"https://pith.science/pith/EXCJ46A36RRDDDRSYKYUUXUV6T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EXCJ46A36RRDDDRSYKYUUXUV6T/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":"2026-06-27T04:57:15Z","links":{"resolver":"https://pith.science/pith/EXCJ46A36RRDDDRSYKYUUXUV6T","bundle":"https://pith.science/pith/EXCJ46A36RRDDDRSYKYUUXUV6T/bundle.json","state":"https://pith.science/pith/EXCJ46A36RRDDDRSYKYUUXUV6T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EXCJ46A36RRDDDRSYKYUUXUV6T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EXCJ46A36RRDDDRSYKYUUXUV6T","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":"246d2693daec430d90381ee4570001401d5545230148749edde0a79b3c0b835c","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-04-03T21:24:38Z","title_canon_sha256":"497014abb80e1c6b1d66ee52edd7f01a318fe47f6ebf4583c2a4ab432d82f9b0"},"schema_version":"1.0","source":{"id":"1204.0815","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0815","created_at":"2026-05-18T03:58:37Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0815v1","created_at":"2026-05-18T03:58:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0815","created_at":"2026-05-18T03:58:37Z"},{"alias_kind":"pith_short_12","alias_value":"EXCJ46A36RRD","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EXCJ46A36RRDDDRS","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EXCJ46A3","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:b92b310827eae0702c49c738a5efd107383e502594f991ad9f4bef8bb161c7d8","target":"graph","created_at":"2026-05-18T03:58:37Z","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":"The present paper has a twofold contribution: first, we introduce a new concept of Hardy spaces on a multidimensional complexified annular domain which is closely related to the annulus of the Klein-Dirac quadric important in Conformal Quantum Field Theory. Secondly, for functions in these Hardy spaces, we provide error estimate for the polyharmonic Gau\\ss -Jacobi cubature formulas, which have been introduced in previous papers.","authors_text":"Hermann Render, Ognyan Kounchev","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-04-03T21:24:38Z","title":"Polyharmonic Hardy Spaces on the Complexified Annulus and Error Estimates of Cubature Formulas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0815","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":"sha256:0c57341915d1279d62b7dc3d5a76f51775f33a9127d04b954c59507fb86a5726","target":"record","created_at":"2026-05-18T03:58:37Z","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":"246d2693daec430d90381ee4570001401d5545230148749edde0a79b3c0b835c","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-04-03T21:24:38Z","title_canon_sha256":"497014abb80e1c6b1d66ee52edd7f01a318fe47f6ebf4583c2a4ab432d82f9b0"},"schema_version":"1.0","source":{"id":"1204.0815","kind":"arxiv","version":1}},"canonical_sha256":"25c49e781bf462318e32c2b14a5e95f4e1fb0823b39406417db368926f56c82d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25c49e781bf462318e32c2b14a5e95f4e1fb0823b39406417db368926f56c82d","first_computed_at":"2026-05-18T03:58:37.693005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:37.693005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WnAQtmFwyb5GEEohd1psSLSGVHBQbb+1XDWTdU0Q5Rg/Xg35NxDZFNRcEQnLcIgG6sNGiqrMAKJhWCNAOT9vAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:37.693735Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.0815","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c57341915d1279d62b7dc3d5a76f51775f33a9127d04b954c59507fb86a5726","sha256:b92b310827eae0702c49c738a5efd107383e502594f991ad9f4bef8bb161c7d8"],"state_sha256":"bcbedc21f82add6c7182b10a4a661a3ffd0f77b5426ab044ad9b656452d2f380"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rywiF5x8SAC/4Ulphd7o1jPL3KgmWvkvsJbpVKIF29hOmf+jVZdbVKX2i/JeeTEx5PO26KI6zitV6uVzVk3yAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T04:57:15.079180Z","bundle_sha256":"7745dfde9154231488e213262201688fd303cf1865f3c9ef4c69919834caddcd"}}