{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HWAI63GHLKTZG64BXX3DNKN4PO","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":"0168878f2a29351fbf7449d7a445598d746cf2b554556b8b7700b68a251074ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2013-04-30T12:22:17Z","title_canon_sha256":"a95bd344abd5540621abb1fc641a67e4b2183fc4e19f0b7c556a5500624fd9d3"},"schema_version":"1.0","source":{"id":"1304.7973","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7973","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7973v1","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7973","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"pith_short_12","alias_value":"HWAI63GHLKTZ","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HWAI63GHLKTZG64B","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HWAI63GH","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:8faca8596c64ee6cb7ba4279148e829c2d2f98dff9d8f453511ddb7cd2656d6b","target":"graph","created_at":"2026-05-18T03:26:51Z","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":"In this paper we implement the holonomic gradient method to exactly compute the normalising constant of Bingham distributions. This idea is originally applied for general Fisher-Bingham distributions in Nakayama et al. (2011). In this paper we explicitly apply this algorithm to show the exact calculation of the normalising constant; derive explicitly the Pfaffian system for this parametric case; implement the general approach for the maximum likelihood solution search and finally adjust the method for degenerate cases, namely when the parameter values have multiplicities.","authors_text":"Alfred Kume, Tomonari Sei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2013-04-30T12:22:17Z","title":"Calculating the normalising constant of the Bingham distribution on the sphere using the holonomic gradient method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7973","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":"sha256:9567cef3d4f49a459b9233001b3254e7bcab7e6e07c9bf64e4a6c38b077e6ad5","target":"record","created_at":"2026-05-18T03:26:51Z","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":"0168878f2a29351fbf7449d7a445598d746cf2b554556b8b7700b68a251074ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2013-04-30T12:22:17Z","title_canon_sha256":"a95bd344abd5540621abb1fc641a67e4b2183fc4e19f0b7c556a5500624fd9d3"},"schema_version":"1.0","source":{"id":"1304.7973","kind":"arxiv","version":1}},"canonical_sha256":"3d808f6cc75aa7937b81bdf636a9bc7bbe50e57a2b80605a20e387732f2381a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d808f6cc75aa7937b81bdf636a9bc7bbe50e57a2b80605a20e387732f2381a1","first_computed_at":"2026-05-18T03:26:51.275798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:51.275798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WmhGEtQfHztlMBolMzeMG8iMdTnhQ14CxJ5ynR8iDdl/2EpgBjkHT/WYqkHkvDT0UrrwTJ7XwRkAaZvQfwHlCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:51.276551Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.7973","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9567cef3d4f49a459b9233001b3254e7bcab7e6e07c9bf64e4a6c38b077e6ad5","sha256:8faca8596c64ee6cb7ba4279148e829c2d2f98dff9d8f453511ddb7cd2656d6b"],"state_sha256":"5ec41167f63000566bd23f955ede7746de1f04d7aba07ab2e772f8405ff25e01"}