{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:HA4U6KGUMC4ZU2FOOYUCHFXYNA","short_pith_number":"pith:HA4U6KGU","canonical_record":{"source":{"id":"1012.5409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-24T16:41:57Z","cross_cats_sorted":[],"title_canon_sha256":"4b43f96d5e7df69d0bc7b4e19812d78b910a0145fe740f6839bd2f2713fe3a31","abstract_canon_sha256":"f99a28f62db92b4f03335e863e27fb5257af74eab416608e2d0cd46fb8fa05c0"},"schema_version":"1.0"},"canonical_sha256":"38394f28d460b99a68ae76282396f8680feb9dcacddacc31cc4a008bb08b4490","source":{"kind":"arxiv","id":"1012.5409","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5409","created_at":"2026-05-18T04:32:34Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5409v1","created_at":"2026-05-18T04:32:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5409","created_at":"2026-05-18T04:32:34Z"},{"alias_kind":"pith_short_12","alias_value":"HA4U6KGUMC4Z","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HA4U6KGUMC4ZU2FO","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HA4U6KGU","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:HA4U6KGUMC4ZU2FOOYUCHFXYNA","target":"record","payload":{"canonical_record":{"source":{"id":"1012.5409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-24T16:41:57Z","cross_cats_sorted":[],"title_canon_sha256":"4b43f96d5e7df69d0bc7b4e19812d78b910a0145fe740f6839bd2f2713fe3a31","abstract_canon_sha256":"f99a28f62db92b4f03335e863e27fb5257af74eab416608e2d0cd46fb8fa05c0"},"schema_version":"1.0"},"canonical_sha256":"38394f28d460b99a68ae76282396f8680feb9dcacddacc31cc4a008bb08b4490","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:34.960773Z","signature_b64":"lmvYqF3Di9eybopH2Mr1XYnovxwm7W3E0HUXwfAHsIJh9hZfaCUkhqytlQIzXc450VoeS09udIRqf9A1fX2iBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38394f28d460b99a68ae76282396f8680feb9dcacddacc31cc4a008bb08b4490","last_reissued_at":"2026-05-18T04:32:34.960274Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:34.960274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.5409","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":"2026-05-18T04:32:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t8PEWqwSVUNlVlTSNLzT38KBBOhb/3SgtbzxdO3pHRdHmywjarOWm5iT4ZjKbdvCRxhsL6EZ9zhwTjQrcbAnDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T09:07:41.134650Z"},"content_sha256":"a749f5ba0fb72d85111a73794bc6629269acca5663d7c8e29b7ab3c51aac3c48","schema_version":"1.0","event_id":"sha256:a749f5ba0fb72d85111a73794bc6629269acca5663d7c8e29b7ab3c51aac3c48"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:HA4U6KGUMC4ZU2FOOYUCHFXYNA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quadrature rules and distribution of points on manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christine Choirat, Giacomo Gigante, Giancarlo Travaglini, Leonardo Colzani, Luca Brandolini, Raffaello Seri","submitted_at":"2010-12-24T16:41:57Z","abstract_excerpt":"We study the error in quadrature rules on a compact manifold. As in the Koksma-Hlawka inequality, we consider a discrepancy of the sampling points and a generalized variation of the function. In particular, we give sharp quantitative estimates for quadrature rules of functions in Sobolev classes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5409","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":"2026-05-18T04:32:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+xycBebv3LupOrDYcoewGEOoLisa/q893dxZj+ZYHpueIJ+8xODIwjlwchbEV31JlKzfoaSwf9+dncJjdLOgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T09:07:41.135376Z"},"content_sha256":"ad13ac60b31f9ce5d83cccbfb41f60cb2f5b6568d0f3cf8690a21e8045eccabf","schema_version":"1.0","event_id":"sha256:ad13ac60b31f9ce5d83cccbfb41f60cb2f5b6568d0f3cf8690a21e8045eccabf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HA4U6KGUMC4ZU2FOOYUCHFXYNA/bundle.json","state_url":"https://pith.science/pith/HA4U6KGUMC4ZU2FOOYUCHFXYNA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HA4U6KGUMC4ZU2FOOYUCHFXYNA/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":"2026-05-24T09:07:41Z","links":{"resolver":"https://pith.science/pith/HA4U6KGUMC4ZU2FOOYUCHFXYNA","bundle":"https://pith.science/pith/HA4U6KGUMC4ZU2FOOYUCHFXYNA/bundle.json","state":"https://pith.science/pith/HA4U6KGUMC4ZU2FOOYUCHFXYNA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HA4U6KGUMC4ZU2FOOYUCHFXYNA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HA4U6KGUMC4ZU2FOOYUCHFXYNA","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":"f99a28f62db92b4f03335e863e27fb5257af74eab416608e2d0cd46fb8fa05c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-24T16:41:57Z","title_canon_sha256":"4b43f96d5e7df69d0bc7b4e19812d78b910a0145fe740f6839bd2f2713fe3a31"},"schema_version":"1.0","source":{"id":"1012.5409","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5409","created_at":"2026-05-18T04:32:34Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5409v1","created_at":"2026-05-18T04:32:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5409","created_at":"2026-05-18T04:32:34Z"},{"alias_kind":"pith_short_12","alias_value":"HA4U6KGUMC4Z","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HA4U6KGUMC4ZU2FO","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HA4U6KGU","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:ad13ac60b31f9ce5d83cccbfb41f60cb2f5b6568d0f3cf8690a21e8045eccabf","target":"graph","created_at":"2026-05-18T04:32:34Z","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 study the error in quadrature rules on a compact manifold. As in the Koksma-Hlawka inequality, we consider a discrepancy of the sampling points and a generalized variation of the function. In particular, we give sharp quantitative estimates for quadrature rules of functions in Sobolev classes.","authors_text":"Christine Choirat, Giacomo Gigante, Giancarlo Travaglini, Leonardo Colzani, Luca Brandolini, Raffaello Seri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-24T16:41:57Z","title":"Quadrature rules and distribution of points on manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5409","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:a749f5ba0fb72d85111a73794bc6629269acca5663d7c8e29b7ab3c51aac3c48","target":"record","created_at":"2026-05-18T04:32:34Z","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":"f99a28f62db92b4f03335e863e27fb5257af74eab416608e2d0cd46fb8fa05c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-24T16:41:57Z","title_canon_sha256":"4b43f96d5e7df69d0bc7b4e19812d78b910a0145fe740f6839bd2f2713fe3a31"},"schema_version":"1.0","source":{"id":"1012.5409","kind":"arxiv","version":1}},"canonical_sha256":"38394f28d460b99a68ae76282396f8680feb9dcacddacc31cc4a008bb08b4490","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38394f28d460b99a68ae76282396f8680feb9dcacddacc31cc4a008bb08b4490","first_computed_at":"2026-05-18T04:32:34.960274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:34.960274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lmvYqF3Di9eybopH2Mr1XYnovxwm7W3E0HUXwfAHsIJh9hZfaCUkhqytlQIzXc450VoeS09udIRqf9A1fX2iBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:34.960773Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5409","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a749f5ba0fb72d85111a73794bc6629269acca5663d7c8e29b7ab3c51aac3c48","sha256:ad13ac60b31f9ce5d83cccbfb41f60cb2f5b6568d0f3cf8690a21e8045eccabf"],"state_sha256":"37feacfc8ba0389cf3ac9b6e583293d02e97dafc39f0e3f71fc848eab0671312"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3rtKE5UN/u8xoO5+j7r6z+NlQb4g6KD2gesJAM/hjsnTbe0LWYM6lX2rTqn1nIWMRwyY3S+zAzlXIUYIr9nfBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T09:07:41.139141Z","bundle_sha256":"28ec9aee2b46e05c211a2e36b20cd6dca2aa9920ee0dceff4fdd5dbb24701a3a"}}