{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:V7XY6QUJA552VY64HHKE2WCXGC","short_pith_number":"pith:V7XY6QUJ","canonical_record":{"source":{"id":"1207.3143","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-07-13T04:50:18Z","cross_cats_sorted":["math.AC","stat.TH"],"title_canon_sha256":"ccb6222c9fa68b0ba54472f64415480c664d934cbb6dad51acae5e5adce7fb2d","abstract_canon_sha256":"d99b2d8c5bd1e664d9358954bcedf26edd4e02329a0829e0d2c1fa2841c57ff6"},"schema_version":"1.0"},"canonical_sha256":"afef8f4289077baae3dc39d44d585730bd5357869be932f9816c02c2d981b04d","source":{"kind":"arxiv","id":"1207.3143","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3143","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3143v3","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3143","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"pith_short_12","alias_value":"V7XY6QUJA552","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"V7XY6QUJA552VY64","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"V7XY6QUJ","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:V7XY6QUJA552VY64HHKE2WCXGC","target":"record","payload":{"canonical_record":{"source":{"id":"1207.3143","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-07-13T04:50:18Z","cross_cats_sorted":["math.AC","stat.TH"],"title_canon_sha256":"ccb6222c9fa68b0ba54472f64415480c664d934cbb6dad51acae5e5adce7fb2d","abstract_canon_sha256":"d99b2d8c5bd1e664d9358954bcedf26edd4e02329a0829e0d2c1fa2841c57ff6"},"schema_version":"1.0"},"canonical_sha256":"afef8f4289077baae3dc39d44d585730bd5357869be932f9816c02c2d981b04d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:06.720419Z","signature_b64":"Rt/sI6inUValgg9myUiyBec6MDp8SSwvSEwwbESxNLVkBNK08wHV+HD31nf/s3dfEO430MeEuPXyQeKiIlMBBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afef8f4289077baae3dc39d44d585730bd5357869be932f9816c02c2d981b04d","last_reissued_at":"2026-05-18T03:31:06.719567Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:06.719567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.3143","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:31:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QrtU7H33360qPKkXCyXFooPWyyamjNmNaS8zfEiHcJNihrHF3EuwLUDnexgrxshf/38C5IYi4H20q3TuxkOFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:22:39.733560Z"},"content_sha256":"63070ccbb4d52b3a48ad7182f8312c734ab4caa7f1b5d7b17ef3ca0489e21d24","schema_version":"1.0","event_id":"sha256:63070ccbb4d52b3a48ad7182f8312c734ab4caa7f1b5d7b17ef3ca0489e21d24"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:V7XY6QUJA552VY64HHKE2WCXGC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The algebra of interpolatory cubature formulae for generic nodes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","stat.TH"],"primary_cat":"math.ST","authors_text":"Claudia Fassino, Eva Riccomagno, Giovanni Pistone","submitted_at":"2012-07-13T04:50:18Z","abstract_excerpt":"We consider the classical problem of computing the expected value of a real function $f$ of the $d$-variate random variable $X$ using cubature formul\\ae. We use in synergy tools from Commutative Algebra for cubature rul\\ae, from elementary orthogonal polynomial theory and from Probability."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3143","kind":"arxiv","version":3},"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":"2026-05-18T03:31:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S7uKD1XnE82Cs76f9XmlUgaNJd6R81zzXtdPxBIc8QlhwVF796SpqsTjgWJJFlwaMKEYZOqMQR0d/ns6gQX0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:22:39.734119Z"},"content_sha256":"95f7e46d9b3f298e9e89ba0517bc72f11b63a81907ec7e514d2ac88f997b8ce3","schema_version":"1.0","event_id":"sha256:95f7e46d9b3f298e9e89ba0517bc72f11b63a81907ec7e514d2ac88f997b8ce3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V7XY6QUJA552VY64HHKE2WCXGC/bundle.json","state_url":"https://pith.science/pith/V7XY6QUJA552VY64HHKE2WCXGC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V7XY6QUJA552VY64HHKE2WCXGC/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":"2026-05-30T19:22:39Z","links":{"resolver":"https://pith.science/pith/V7XY6QUJA552VY64HHKE2WCXGC","bundle":"https://pith.science/pith/V7XY6QUJA552VY64HHKE2WCXGC/bundle.json","state":"https://pith.science/pith/V7XY6QUJA552VY64HHKE2WCXGC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V7XY6QUJA552VY64HHKE2WCXGC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:V7XY6QUJA552VY64HHKE2WCXGC","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":"d99b2d8c5bd1e664d9358954bcedf26edd4e02329a0829e0d2c1fa2841c57ff6","cross_cats_sorted":["math.AC","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-07-13T04:50:18Z","title_canon_sha256":"ccb6222c9fa68b0ba54472f64415480c664d934cbb6dad51acae5e5adce7fb2d"},"schema_version":"1.0","source":{"id":"1207.3143","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3143","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3143v3","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3143","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"pith_short_12","alias_value":"V7XY6QUJA552","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"V7XY6QUJA552VY64","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"V7XY6QUJ","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:95f7e46d9b3f298e9e89ba0517bc72f11b63a81907ec7e514d2ac88f997b8ce3","target":"graph","created_at":"2026-05-18T03:31:06Z","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 consider the classical problem of computing the expected value of a real function $f$ of the $d$-variate random variable $X$ using cubature formul\\ae. We use in synergy tools from Commutative Algebra for cubature rul\\ae, from elementary orthogonal polynomial theory and from Probability.","authors_text":"Claudia Fassino, Eva Riccomagno, Giovanni Pistone","cross_cats":["math.AC","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-07-13T04:50:18Z","title":"The algebra of interpolatory cubature formulae for generic nodes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3143","kind":"arxiv","version":3},"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":"sha256:63070ccbb4d52b3a48ad7182f8312c734ab4caa7f1b5d7b17ef3ca0489e21d24","target":"record","created_at":"2026-05-18T03:31:06Z","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":"d99b2d8c5bd1e664d9358954bcedf26edd4e02329a0829e0d2c1fa2841c57ff6","cross_cats_sorted":["math.AC","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-07-13T04:50:18Z","title_canon_sha256":"ccb6222c9fa68b0ba54472f64415480c664d934cbb6dad51acae5e5adce7fb2d"},"schema_version":"1.0","source":{"id":"1207.3143","kind":"arxiv","version":3}},"canonical_sha256":"afef8f4289077baae3dc39d44d585730bd5357869be932f9816c02c2d981b04d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afef8f4289077baae3dc39d44d585730bd5357869be932f9816c02c2d981b04d","first_computed_at":"2026-05-18T03:31:06.719567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:06.719567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rt/sI6inUValgg9myUiyBec6MDp8SSwvSEwwbESxNLVkBNK08wHV+HD31nf/s3dfEO430MeEuPXyQeKiIlMBBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:06.720419Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3143","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63070ccbb4d52b3a48ad7182f8312c734ab4caa7f1b5d7b17ef3ca0489e21d24","sha256:95f7e46d9b3f298e9e89ba0517bc72f11b63a81907ec7e514d2ac88f997b8ce3"],"state_sha256":"8cdb77b84f410fe57d4fccbd7407439ace0cedc1d5c153e2e9b508bd31e1fbea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/azuAauo1g4sBOFbqsqdy/vGdaFiHgHb2uwyy0snYJiHIDakMkxZ+VmlDqWSCQKu55c7fUFF8VmUo/0tuHpSCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T19:22:39.736876Z","bundle_sha256":"e1fe726a5b84b3983391f7e42ac433fb4dad93d51c425dded89d145f99d8d272"}}