{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TU4Y7IE7YIANBDHKGUERUWJINS","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":"d9f432acfa6e3b81439131e7160f73a1c7dbbc02b9f013546fc00ec4e65334ac","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-01-16T12:58:33Z","title_canon_sha256":"512ff57e21854b0298108e2dab03c2a9b72bbda21b9225b3cf22f0e9624d0580"},"schema_version":"1.0","source":{"id":"1201.3239","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3239","created_at":"2026-05-18T03:20:18Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3239v5","created_at":"2026-05-18T03:20:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3239","created_at":"2026-05-18T03:20:18Z"},{"alias_kind":"pith_short_12","alias_value":"TU4Y7IE7YIAN","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TU4Y7IE7YIANBDHK","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TU4Y7IE7","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:c613a6a7e1e39a76022b7f9d4396212d6330734c2ef267d573398ef1d878a8ff","target":"graph","created_at":"2026-05-18T03:20:18Z","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":"We propose an accelerated version of the holonomic gradient descent and apply it to calculating the maximum likelihood estimate (MLE) of the Fisher-Bingham distribution on a $d$-dimensional sphere. We derive a Pfaffian system (an integrable connection) and a series expansion associated with the normalizing constant with an error estimation. These enable us to solve some MLE problems up to dimension $d=7$ with a specified accuracy.","authors_text":"Hiromasa Nakayama, Kenta Nishiyama, Nobuki Takayama, Tamio Koyama","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-01-16T12:58:33Z","title":"Holonomic Gradient Descent for the Fisher-Bingham Distribution on the $d$-dimensional Sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3239","kind":"arxiv","version":5},"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":"sha256:57922c06b3eb3699a00d10fff9e6596abf6ce2eeb396b54fae5df1b897a0fc3c","target":"record","created_at":"2026-05-18T03:20:18Z","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":"d9f432acfa6e3b81439131e7160f73a1c7dbbc02b9f013546fc00ec4e65334ac","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-01-16T12:58:33Z","title_canon_sha256":"512ff57e21854b0298108e2dab03c2a9b72bbda21b9225b3cf22f0e9624d0580"},"schema_version":"1.0","source":{"id":"1201.3239","kind":"arxiv","version":5}},"canonical_sha256":"9d398fa09fc200d08cea35091a59286cb438356c2183bdd031de932443632efc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d398fa09fc200d08cea35091a59286cb438356c2183bdd031de932443632efc","first_computed_at":"2026-05-18T03:20:18.736600Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:18.736600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IdVsSObWEo82fWQIA1DxSsX6oyrWLffnC/Qon0xzpYlAh50rrwBaJyC0vBH2EJPuXY/hqr7Lk2aLZP2OokmxAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:18.737380Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3239","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57922c06b3eb3699a00d10fff9e6596abf6ce2eeb396b54fae5df1b897a0fc3c","sha256:c613a6a7e1e39a76022b7f9d4396212d6330734c2ef267d573398ef1d878a8ff"],"state_sha256":"176a41a1079f78920eddcee57590fd919003b9154e77a86089180ed7e2285a3c"}