{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:7BRKMZIBNTP5434VP2BNVWJA6M","short_pith_number":"pith:7BRKMZIB","canonical_record":{"source":{"id":"1012.5022","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"physics.comp-ph","submitted_at":"2010-12-22T16:05:07Z","cross_cats_sorted":["cond-mat.str-el","nucl-th"],"title_canon_sha256":"a348aa5a3054c9944e48f3aa7ab135b075d3d0038aca4e9b8819a4aa015b4a53","abstract_canon_sha256":"5b76f76eeb6cb6b1cc46d91194c08ad7cb94b3173286f43cf5c7cbf79a79975f"},"schema_version":"1.0"},"canonical_sha256":"f862a665016cdfde6f957e82dad920f3132a4670aae06c0fb540ebca04662615","source":{"kind":"arxiv","id":"1012.5022","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5022","created_at":"2026-05-18T02:04:18Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5022v1","created_at":"2026-05-18T02:04:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5022","created_at":"2026-05-18T02:04:18Z"},{"alias_kind":"pith_short_12","alias_value":"7BRKMZIBNTP5","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7BRKMZIBNTP5434V","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7BRKMZIB","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:7BRKMZIBNTP5434VP2BNVWJA6M","target":"record","payload":{"canonical_record":{"source":{"id":"1012.5022","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"physics.comp-ph","submitted_at":"2010-12-22T16:05:07Z","cross_cats_sorted":["cond-mat.str-el","nucl-th"],"title_canon_sha256":"a348aa5a3054c9944e48f3aa7ab135b075d3d0038aca4e9b8819a4aa015b4a53","abstract_canon_sha256":"5b76f76eeb6cb6b1cc46d91194c08ad7cb94b3173286f43cf5c7cbf79a79975f"},"schema_version":"1.0"},"canonical_sha256":"f862a665016cdfde6f957e82dad920f3132a4670aae06c0fb540ebca04662615","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:18.520615Z","signature_b64":"wgzW1ZYvxviGGb3sSIhSCNetmWzFcG9xz0UGMesbX63mYujARqAjUvHNeiG+gQNzK8pDpWEjLvazOCbDRS41CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f862a665016cdfde6f957e82dad920f3132a4670aae06c0fb540ebca04662615","last_reissued_at":"2026-05-18T02:04:18.519761Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:18.519761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.5022","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":"2026-05-18T02:04:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5RaEdUJQTypclvxR2keBODzwRH6/Fn4xwDTcAfqXxcQI0DxInsUoDY+ZpgHIdHEbng+73Zj7TOca4RR/6nclCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T10:21:44.282546Z"},"content_sha256":"a5413cd05b37cc4ac142cf768190482c83ef621579075b690111662c231cd2c2","schema_version":"1.0","event_id":"sha256:a5413cd05b37cc4ac142cf768190482c83ef621579075b690111662c231cd2c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:7BRKMZIBNTP5434VP2BNVWJA6M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numeric and symbolic evaluation of the pfaffian of general skew-symmetric matrices","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["cond-mat.str-el","nucl-th"],"primary_cat":"physics.comp-ph","authors_text":"C. Gonz\\'alez-Ballestero, G. F. Bertsch, L.M. Robledo","submitted_at":"2010-12-22T16:05:07Z","abstract_excerpt":"Evaluation of pfaffians arises in a number of physics applications, and for some of them a direct method is preferable to using the determinantal formula. We discuss two methods for the numerical evaluation of pfaffians. The first is tridiagonalization based on Householder transformations. The main advantage of this method is its numerical stability that makes unnecessary the implementation of a pivoting strategy. The second method considered is based on Aitken's block diagonalization formula. It yields to a kind of LU (similar to Cholesky's factorization) decomposition (under congruence) of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5022","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":"2026-05-18T02:04:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lIoWubl4AMHe5dGevPTdclyGW259sex5mMAwBQO+vnI2IXjC9cNiFJIy/rlKTaIVGPZIKXY5EHCTn5tphSwPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T10:21:44.282905Z"},"content_sha256":"6d9ca250d66c6a2cd3cca83bd64cc4e82050121d642c833cdc42edf0802db9d6","schema_version":"1.0","event_id":"sha256:6d9ca250d66c6a2cd3cca83bd64cc4e82050121d642c833cdc42edf0802db9d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7BRKMZIBNTP5434VP2BNVWJA6M/bundle.json","state_url":"https://pith.science/pith/7BRKMZIBNTP5434VP2BNVWJA6M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7BRKMZIBNTP5434VP2BNVWJA6M/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":"2026-06-08T10:21:44Z","links":{"resolver":"https://pith.science/pith/7BRKMZIBNTP5434VP2BNVWJA6M","bundle":"https://pith.science/pith/7BRKMZIBNTP5434VP2BNVWJA6M/bundle.json","state":"https://pith.science/pith/7BRKMZIBNTP5434VP2BNVWJA6M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7BRKMZIBNTP5434VP2BNVWJA6M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7BRKMZIBNTP5434VP2BNVWJA6M","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":"5b76f76eeb6cb6b1cc46d91194c08ad7cb94b3173286f43cf5c7cbf79a79975f","cross_cats_sorted":["cond-mat.str-el","nucl-th"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"physics.comp-ph","submitted_at":"2010-12-22T16:05:07Z","title_canon_sha256":"a348aa5a3054c9944e48f3aa7ab135b075d3d0038aca4e9b8819a4aa015b4a53"},"schema_version":"1.0","source":{"id":"1012.5022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5022","created_at":"2026-05-18T02:04:18Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5022v1","created_at":"2026-05-18T02:04:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5022","created_at":"2026-05-18T02:04:18Z"},{"alias_kind":"pith_short_12","alias_value":"7BRKMZIBNTP5","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7BRKMZIBNTP5434V","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7BRKMZIB","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:6d9ca250d66c6a2cd3cca83bd64cc4e82050121d642c833cdc42edf0802db9d6","target":"graph","created_at":"2026-05-18T02:04:18Z","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":"Evaluation of pfaffians arises in a number of physics applications, and for some of them a direct method is preferable to using the determinantal formula. We discuss two methods for the numerical evaluation of pfaffians. The first is tridiagonalization based on Householder transformations. The main advantage of this method is its numerical stability that makes unnecessary the implementation of a pivoting strategy. The second method considered is based on Aitken's block diagonalization formula. It yields to a kind of LU (similar to Cholesky's factorization) decomposition (under congruence) of a","authors_text":"C. Gonz\\'alez-Ballestero, G. F. Bertsch, L.M. Robledo","cross_cats":["cond-mat.str-el","nucl-th"],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"physics.comp-ph","submitted_at":"2010-12-22T16:05:07Z","title":"Numeric and symbolic evaluation of the pfaffian of general skew-symmetric matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5022","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:a5413cd05b37cc4ac142cf768190482c83ef621579075b690111662c231cd2c2","target":"record","created_at":"2026-05-18T02:04:18Z","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":"5b76f76eeb6cb6b1cc46d91194c08ad7cb94b3173286f43cf5c7cbf79a79975f","cross_cats_sorted":["cond-mat.str-el","nucl-th"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"physics.comp-ph","submitted_at":"2010-12-22T16:05:07Z","title_canon_sha256":"a348aa5a3054c9944e48f3aa7ab135b075d3d0038aca4e9b8819a4aa015b4a53"},"schema_version":"1.0","source":{"id":"1012.5022","kind":"arxiv","version":1}},"canonical_sha256":"f862a665016cdfde6f957e82dad920f3132a4670aae06c0fb540ebca04662615","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f862a665016cdfde6f957e82dad920f3132a4670aae06c0fb540ebca04662615","first_computed_at":"2026-05-18T02:04:18.519761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:18.519761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wgzW1ZYvxviGGb3sSIhSCNetmWzFcG9xz0UGMesbX63mYujARqAjUvHNeiG+gQNzK8pDpWEjLvazOCbDRS41CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:18.520615Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5413cd05b37cc4ac142cf768190482c83ef621579075b690111662c231cd2c2","sha256:6d9ca250d66c6a2cd3cca83bd64cc4e82050121d642c833cdc42edf0802db9d6"],"state_sha256":"16e4ffb39777351400a580643f2974b569779fc23d37e3780b739d653c4832f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pladbx43dIkTIyV2aw2WTFTtjz9swkgTEplWU0HvAWHMOJuuWKND9JnVfz/D2ILZJ95rWO4LnkEqQIokmQH0Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T10:21:44.284782Z","bundle_sha256":"2411d72468ee540d5c2799f75cf231a5813ea563f54fe09ceb860ea76b0efb0b"}}