{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:SGI2OXSLY7PGYKQMQWY6BEZLCG","short_pith_number":"pith:SGI2OXSL","canonical_record":{"source":{"id":"1303.5101","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-03-20T21:35:02Z","cross_cats_sorted":[],"title_canon_sha256":"06aa97acbc6db79fe9870bc2a5699f38e9dff3716dfc9d737f13388eff28f9eb","abstract_canon_sha256":"19056befd3379453a2b98f94709b7a12c375e575cc4d9e6592f896ecc3b13fb9"},"schema_version":"1.0"},"canonical_sha256":"9191a75e4bc7de6c2a0c85b1e0932b118ff39727c50f1823ac72a794c6d2f66a","source":{"kind":"arxiv","id":"1303.5101","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.5101","created_at":"2026-05-18T03:30:14Z"},{"alias_kind":"arxiv_version","alias_value":"1303.5101v1","created_at":"2026-05-18T03:30:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5101","created_at":"2026-05-18T03:30:14Z"},{"alias_kind":"pith_short_12","alias_value":"SGI2OXSLY7PG","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SGI2OXSLY7PGYKQM","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SGI2OXSL","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:SGI2OXSLY7PGYKQMQWY6BEZLCG","target":"record","payload":{"canonical_record":{"source":{"id":"1303.5101","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-03-20T21:35:02Z","cross_cats_sorted":[],"title_canon_sha256":"06aa97acbc6db79fe9870bc2a5699f38e9dff3716dfc9d737f13388eff28f9eb","abstract_canon_sha256":"19056befd3379453a2b98f94709b7a12c375e575cc4d9e6592f896ecc3b13fb9"},"schema_version":"1.0"},"canonical_sha256":"9191a75e4bc7de6c2a0c85b1e0932b118ff39727c50f1823ac72a794c6d2f66a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:14.583137Z","signature_b64":"RbgbB7/Cl/uYICuUPM1vTOgS7xw1M5BbIxRE12A4hRCEx9hg2wMBHgOjYLo1dfW2C6WKNNqo4PCeZn3vgFLrBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9191a75e4bc7de6c2a0c85b1e0932b118ff39727c50f1823ac72a794c6d2f66a","last_reissued_at":"2026-05-18T03:30:14.582326Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:14.582326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.5101","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":"2026-05-18T03:30:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ScX+CtgH+bntbRjqB3xeA0VQK3DxZFcAqFSF0O4ybGLeANTVgx6aF+59jevYtpLhpWmNasADvrIigEuXfxo/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T14:14:34.673385Z"},"content_sha256":"c992353db2c428c2d94ca3fbd86b4d14e7ef4ad2530c6aa19fa2b7eb064dd535","schema_version":"1.0","event_id":"sha256:c992353db2c428c2d94ca3fbd86b4d14e7ef4ad2530c6aa19fa2b7eb064dd535"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:SGI2OXSLY7PGYKQMQWY6BEZLCG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gaussian Quadrature of int_0^1 f(x) log^m(x) dx and int_(-1)^1 f(x) cos(pi*x/2) dx","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Richard J. Mathar","submitted_at":"2013-03-20T21:35:02Z","abstract_excerpt":"We tabulate the abscissae and associated weights for numerical integration of integrals with either the singular weight function (-log x)^m for exponents m=1, 2 or 3, or the symmetric weight function cos(pi*x/2). Standard brute force arithmetics generates explicit pairs of these values for up to 128 nodes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5101","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":"2026-05-18T03:30:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fVsb7T+zrjQjYtrqU8KxoyioKS5IqyY1R6LXrjb5JEAGd7TtvU7nCkmRHVCgEpASDOcIFGecp5QRIhmmij2zDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T14:14:34.673751Z"},"content_sha256":"b9fb8e5dea3145a318a5478b666fe6eec14117981d1dbc1c203fdf6f5884f198","schema_version":"1.0","event_id":"sha256:b9fb8e5dea3145a318a5478b666fe6eec14117981d1dbc1c203fdf6f5884f198"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SGI2OXSLY7PGYKQMQWY6BEZLCG/bundle.json","state_url":"https://pith.science/pith/SGI2OXSLY7PGYKQMQWY6BEZLCG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SGI2OXSLY7PGYKQMQWY6BEZLCG/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":"2026-06-29T14:14:34Z","links":{"resolver":"https://pith.science/pith/SGI2OXSLY7PGYKQMQWY6BEZLCG","bundle":"https://pith.science/pith/SGI2OXSLY7PGYKQMQWY6BEZLCG/bundle.json","state":"https://pith.science/pith/SGI2OXSLY7PGYKQMQWY6BEZLCG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SGI2OXSLY7PGYKQMQWY6BEZLCG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SGI2OXSLY7PGYKQMQWY6BEZLCG","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":"19056befd3379453a2b98f94709b7a12c375e575cc4d9e6592f896ecc3b13fb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-03-20T21:35:02Z","title_canon_sha256":"06aa97acbc6db79fe9870bc2a5699f38e9dff3716dfc9d737f13388eff28f9eb"},"schema_version":"1.0","source":{"id":"1303.5101","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.5101","created_at":"2026-05-18T03:30:14Z"},{"alias_kind":"arxiv_version","alias_value":"1303.5101v1","created_at":"2026-05-18T03:30:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5101","created_at":"2026-05-18T03:30:14Z"},{"alias_kind":"pith_short_12","alias_value":"SGI2OXSLY7PG","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SGI2OXSLY7PGYKQM","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SGI2OXSL","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:b9fb8e5dea3145a318a5478b666fe6eec14117981d1dbc1c203fdf6f5884f198","target":"graph","created_at":"2026-05-18T03:30:14Z","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 tabulate the abscissae and associated weights for numerical integration of integrals with either the singular weight function (-log x)^m for exponents m=1, 2 or 3, or the symmetric weight function cos(pi*x/2). Standard brute force arithmetics generates explicit pairs of these values for up to 128 nodes.","authors_text":"Richard J. Mathar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-03-20T21:35:02Z","title":"Gaussian Quadrature of int_0^1 f(x) log^m(x) dx and int_(-1)^1 f(x) cos(pi*x/2) dx"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5101","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:c992353db2c428c2d94ca3fbd86b4d14e7ef4ad2530c6aa19fa2b7eb064dd535","target":"record","created_at":"2026-05-18T03:30:14Z","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":"19056befd3379453a2b98f94709b7a12c375e575cc4d9e6592f896ecc3b13fb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-03-20T21:35:02Z","title_canon_sha256":"06aa97acbc6db79fe9870bc2a5699f38e9dff3716dfc9d737f13388eff28f9eb"},"schema_version":"1.0","source":{"id":"1303.5101","kind":"arxiv","version":1}},"canonical_sha256":"9191a75e4bc7de6c2a0c85b1e0932b118ff39727c50f1823ac72a794c6d2f66a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9191a75e4bc7de6c2a0c85b1e0932b118ff39727c50f1823ac72a794c6d2f66a","first_computed_at":"2026-05-18T03:30:14.582326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:14.582326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RbgbB7/Cl/uYICuUPM1vTOgS7xw1M5BbIxRE12A4hRCEx9hg2wMBHgOjYLo1dfW2C6WKNNqo4PCeZn3vgFLrBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:14.583137Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.5101","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c992353db2c428c2d94ca3fbd86b4d14e7ef4ad2530c6aa19fa2b7eb064dd535","sha256:b9fb8e5dea3145a318a5478b666fe6eec14117981d1dbc1c203fdf6f5884f198"],"state_sha256":"612eaf64f641115c84b62f6402d24a3790e0b2146218d7034edc0a88754a7a50"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XzEa0cuZvQ8kNZLQmTz0BgPNnao46KZ0BW0Q3LIdm5WV+QnQDyX+yoeHISO90T3iMkEDokbdTHr5R7GzYE13DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T14:14:34.675740Z","bundle_sha256":"25e322d5c0cbcfe2c3fb5d3eb946ff9799c50992ca73804025e75a7290fdcdad"}}