{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:B6PS6OFIGE2XOSTEYFCMT7HRS2","short_pith_number":"pith:B6PS6OFI","canonical_record":{"source":{"id":"1709.00651","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-03T01:17:51Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"ec7331147f5f02deb4866d8ad44f19d9283fa47b10792f06fac737d5e74fdd79","abstract_canon_sha256":"27ee1b1647aeed636e5c0659bb3addc22f7b1b5123fb44a2c7e70613a287d2d8"},"schema_version":"1.0"},"canonical_sha256":"0f9f2f38a83135774a64c144c9fcf1968cddd97d2e0c12fb50fdf09c8977482f","source":{"kind":"arxiv","id":"1709.00651","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.00651","created_at":"2026-05-18T00:36:05Z"},{"alias_kind":"arxiv_version","alias_value":"1709.00651v1","created_at":"2026-05-18T00:36:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00651","created_at":"2026-05-18T00:36:05Z"},{"alias_kind":"pith_short_12","alias_value":"B6PS6OFIGE2X","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"B6PS6OFIGE2XOSTE","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"B6PS6OFI","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:B6PS6OFIGE2XOSTEYFCMT7HRS2","target":"record","payload":{"canonical_record":{"source":{"id":"1709.00651","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-03T01:17:51Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"ec7331147f5f02deb4866d8ad44f19d9283fa47b10792f06fac737d5e74fdd79","abstract_canon_sha256":"27ee1b1647aeed636e5c0659bb3addc22f7b1b5123fb44a2c7e70613a287d2d8"},"schema_version":"1.0"},"canonical_sha256":"0f9f2f38a83135774a64c144c9fcf1968cddd97d2e0c12fb50fdf09c8977482f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:05.535395Z","signature_b64":"JEX+4H9/fyDB/8F7vCSRgEGgcES2RgFPQwNMN6tFSuCOMNJPTUD94L7bizvrE/CQ1L+eo+xBTbDp7e7UhxCpAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f9f2f38a83135774a64c144c9fcf1968cddd97d2e0c12fb50fdf09c8977482f","last_reissued_at":"2026-05-18T00:36:05.534963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:05.534963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.00651","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":"2026-05-18T00:36:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L4+SPMQjqGTC2DsV53W4ycgGH35LgM1W8N0TYrvpM5AQLiQxi+gVOryNxdgFB3FAf5DFeOnKvu3ZNW9Nh83/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:37:26.069530Z"},"content_sha256":"300aeead3f9e27e5a32a62af8569efe1f523dcfe3837400c1f9357a2636d7903","schema_version":"1.0","event_id":"sha256:300aeead3f9e27e5a32a62af8569efe1f523dcfe3837400c1f9357a2636d7903"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:B6PS6OFIGE2XOSTEYFCMT7HRS2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Points for Cubature Rules and Polynomial Interpolation on a Square","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NA","authors_text":"Yuan Xu","submitted_at":"2017-09-03T01:17:51Z","abstract_excerpt":"The nodes of certain minimal cubature rule are real common zeros of a set of orthogonal polynomials of degree $n$. They often consist of a well distributed set of points and interpolation polynomials based on them have desired convergence behavior. We report what is known and the theory behind by explaining the situation when the domain of integrals is a square."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00651","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":"2026-05-18T00:36:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PDy6m/BJotjAdYYbnPV0uuv/xwkjEE7UlgIae9XIvKDa2OsvPHdlrlzKOvhwW0+jmrenWKa4qZMARTEBNVN+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:37:26.069864Z"},"content_sha256":"cdd8646c0d68900a9a2ea18037499c4c3118ea1a33d916d1132416c7851a2b6b","schema_version":"1.0","event_id":"sha256:cdd8646c0d68900a9a2ea18037499c4c3118ea1a33d916d1132416c7851a2b6b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B6PS6OFIGE2XOSTEYFCMT7HRS2/bundle.json","state_url":"https://pith.science/pith/B6PS6OFIGE2XOSTEYFCMT7HRS2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B6PS6OFIGE2XOSTEYFCMT7HRS2/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":"2026-06-05T11:37:26Z","links":{"resolver":"https://pith.science/pith/B6PS6OFIGE2XOSTEYFCMT7HRS2","bundle":"https://pith.science/pith/B6PS6OFIGE2XOSTEYFCMT7HRS2/bundle.json","state":"https://pith.science/pith/B6PS6OFIGE2XOSTEYFCMT7HRS2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B6PS6OFIGE2XOSTEYFCMT7HRS2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:B6PS6OFIGE2XOSTEYFCMT7HRS2","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":"27ee1b1647aeed636e5c0659bb3addc22f7b1b5123fb44a2c7e70613a287d2d8","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-03T01:17:51Z","title_canon_sha256":"ec7331147f5f02deb4866d8ad44f19d9283fa47b10792f06fac737d5e74fdd79"},"schema_version":"1.0","source":{"id":"1709.00651","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.00651","created_at":"2026-05-18T00:36:05Z"},{"alias_kind":"arxiv_version","alias_value":"1709.00651v1","created_at":"2026-05-18T00:36:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.00651","created_at":"2026-05-18T00:36:05Z"},{"alias_kind":"pith_short_12","alias_value":"B6PS6OFIGE2X","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"B6PS6OFIGE2XOSTE","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"B6PS6OFI","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:cdd8646c0d68900a9a2ea18037499c4c3118ea1a33d916d1132416c7851a2b6b","target":"graph","created_at":"2026-05-18T00:36:05Z","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 nodes of certain minimal cubature rule are real common zeros of a set of orthogonal polynomials of degree $n$. They often consist of a well distributed set of points and interpolation polynomials based on them have desired convergence behavior. We report what is known and the theory behind by explaining the situation when the domain of integrals is a square.","authors_text":"Yuan Xu","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-03T01:17:51Z","title":"Optimal Points for Cubature Rules and Polynomial Interpolation on a Square"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00651","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":"sha256:300aeead3f9e27e5a32a62af8569efe1f523dcfe3837400c1f9357a2636d7903","target":"record","created_at":"2026-05-18T00:36:05Z","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":"27ee1b1647aeed636e5c0659bb3addc22f7b1b5123fb44a2c7e70613a287d2d8","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-03T01:17:51Z","title_canon_sha256":"ec7331147f5f02deb4866d8ad44f19d9283fa47b10792f06fac737d5e74fdd79"},"schema_version":"1.0","source":{"id":"1709.00651","kind":"arxiv","version":1}},"canonical_sha256":"0f9f2f38a83135774a64c144c9fcf1968cddd97d2e0c12fb50fdf09c8977482f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f9f2f38a83135774a64c144c9fcf1968cddd97d2e0c12fb50fdf09c8977482f","first_computed_at":"2026-05-18T00:36:05.534963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:05.534963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JEX+4H9/fyDB/8F7vCSRgEGgcES2RgFPQwNMN6tFSuCOMNJPTUD94L7bizvrE/CQ1L+eo+xBTbDp7e7UhxCpAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:05.535395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.00651","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:300aeead3f9e27e5a32a62af8569efe1f523dcfe3837400c1f9357a2636d7903","sha256:cdd8646c0d68900a9a2ea18037499c4c3118ea1a33d916d1132416c7851a2b6b"],"state_sha256":"35ca7beb628abe140b7f9425b34978f76888d8b7f140d6226d2c7e6bbdecc91a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"emKC+umnt9Kvi2wbbsYztPbBG+ZIDPhkNyXi9JnITC4emCrjZe81YPBcWEjK/yENBoy6y4SBBapeS4OqFVvuCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T11:37:26.071830Z","bundle_sha256":"1cb25fd5d068a7c05fdd7283735453b11855d78076c733cdebb13fabdfcfc32b"}}