{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:EXTGHEPS2UTUTTUS7BV6JUALI4","short_pith_number":"pith:EXTGHEPS","canonical_record":{"source":{"id":"2606.04267","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-02T22:35:54Z","cross_cats_sorted":["cs.NA","math.NA","stat.TH"],"title_canon_sha256":"76b6bee1fe567f00dc404cb3227545217754ebb26fd6788eee946d18e71bb65e","abstract_canon_sha256":"39e4b6acda5095a22e97cd4217d27a015029e3855b3a27e173d54a1550867d2a"},"schema_version":"1.0"},"canonical_sha256":"25e66391f2d52749ce92f86be4d00b4720dc67214df404f8900d4bfee8296a98","source":{"kind":"arxiv","id":"2606.04267","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04267","created_at":"2026-06-04T01:09:01Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04267v1","created_at":"2026-06-04T01:09:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04267","created_at":"2026-06-04T01:09:01Z"},{"alias_kind":"pith_short_12","alias_value":"EXTGHEPS2UTU","created_at":"2026-06-04T01:09:01Z"},{"alias_kind":"pith_short_16","alias_value":"EXTGHEPS2UTUTTUS","created_at":"2026-06-04T01:09:01Z"},{"alias_kind":"pith_short_8","alias_value":"EXTGHEPS","created_at":"2026-06-04T01:09:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:EXTGHEPS2UTUTTUS7BV6JUALI4","target":"record","payload":{"canonical_record":{"source":{"id":"2606.04267","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-02T22:35:54Z","cross_cats_sorted":["cs.NA","math.NA","stat.TH"],"title_canon_sha256":"76b6bee1fe567f00dc404cb3227545217754ebb26fd6788eee946d18e71bb65e","abstract_canon_sha256":"39e4b6acda5095a22e97cd4217d27a015029e3855b3a27e173d54a1550867d2a"},"schema_version":"1.0"},"canonical_sha256":"25e66391f2d52749ce92f86be4d00b4720dc67214df404f8900d4bfee8296a98","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:09:01.047763Z","signature_b64":"YbKIAsfgRCrv7AOfq0pmPqEetoV7eAsL3IwI6kt+AXnWDVNxmTGDxJMv+3ZUVix6nX+9fyjZur6J79nxkKgqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25e66391f2d52749ce92f86be4d00b4720dc67214df404f8900d4bfee8296a98","last_reissued_at":"2026-06-04T01:09:01.047081Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:09:01.047081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.04267","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":"2026-06-04T01:09:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MNYJOUs/lQZy4k0oU+zIHCneHb5Z/wIDCxPmTe7Ws5bLcQeciTw6jLPXPyKG+fHLLwCiv81oOAA/jnQM1ATMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T07:58:56.889604Z"},"content_sha256":"6d98fc94c5ac397a99952c4656b1cc142b44d813c0f51dd3876444682a003cd2","schema_version":"1.0","event_id":"sha256:6d98fc94c5ac397a99952c4656b1cc142b44d813c0f51dd3876444682a003cd2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:EXTGHEPS2UTUTTUS7BV6JUALI4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unbiased estimation of squared concentration in the Fisher-von Mises-Langevin distribution and the impossibility of unbiased concentration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","stat.TH"],"primary_cat":"math.ST","authors_text":"Andrey A. Popov, Yuqin Jiang, Zain Jabbar","submitted_at":"2026-06-02T22:35:54Z","abstract_excerpt":"The estimation of concentration parameter in Fisher-von Mises-Langevin distribution is the directional statistics analogue of the estimation of the precision matrix for the Gaussian distribution. In this work we show that unbiased estimation of this parameter is impossible. With this realization in hand, we provide an alternative parameterization of the Fisher-von Mises-Langevin distribution in terms of the squared concentration, which we term the intensity. We fruther show that unbiased estimation of thereof is possible, and provide (almost) unbiased estimators thereof in terms of a partial s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04267","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.04267/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-04T01:09:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zdmy4Z2XLwOLLJ0I/AkNMEp3zm6terlOysdOUkniOUyGkn8MhkdvqLerIJF5+DYFYfklmW714o7uw9Figb81Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T07:58:56.890510Z"},"content_sha256":"31dd851546e6c82e54d22fee4ee29761695e20c5a12d54f9c19649afa29a64db","schema_version":"1.0","event_id":"sha256:31dd851546e6c82e54d22fee4ee29761695e20c5a12d54f9c19649afa29a64db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EXTGHEPS2UTUTTUS7BV6JUALI4/bundle.json","state_url":"https://pith.science/pith/EXTGHEPS2UTUTTUS7BV6JUALI4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EXTGHEPS2UTUTTUS7BV6JUALI4/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":"2026-08-11T07:58:56Z","links":{"resolver":"https://pith.science/pith/EXTGHEPS2UTUTTUS7BV6JUALI4","bundle":"https://pith.science/pith/EXTGHEPS2UTUTTUS7BV6JUALI4/bundle.json","state":"https://pith.science/pith/EXTGHEPS2UTUTTUS7BV6JUALI4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EXTGHEPS2UTUTTUS7BV6JUALI4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EXTGHEPS2UTUTTUS7BV6JUALI4","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":"39e4b6acda5095a22e97cd4217d27a015029e3855b3a27e173d54a1550867d2a","cross_cats_sorted":["cs.NA","math.NA","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-02T22:35:54Z","title_canon_sha256":"76b6bee1fe567f00dc404cb3227545217754ebb26fd6788eee946d18e71bb65e"},"schema_version":"1.0","source":{"id":"2606.04267","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04267","created_at":"2026-06-04T01:09:01Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04267v1","created_at":"2026-06-04T01:09:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04267","created_at":"2026-06-04T01:09:01Z"},{"alias_kind":"pith_short_12","alias_value":"EXTGHEPS2UTU","created_at":"2026-06-04T01:09:01Z"},{"alias_kind":"pith_short_16","alias_value":"EXTGHEPS2UTUTTUS","created_at":"2026-06-04T01:09:01Z"},{"alias_kind":"pith_short_8","alias_value":"EXTGHEPS","created_at":"2026-06-04T01:09:01Z"}],"graph_snapshots":[{"event_id":"sha256:31dd851546e6c82e54d22fee4ee29761695e20c5a12d54f9c19649afa29a64db","target":"graph","created_at":"2026-06-04T01:09:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.04267/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The estimation of concentration parameter in Fisher-von Mises-Langevin distribution is the directional statistics analogue of the estimation of the precision matrix for the Gaussian distribution. In this work we show that unbiased estimation of this parameter is impossible. With this realization in hand, we provide an alternative parameterization of the Fisher-von Mises-Langevin distribution in terms of the squared concentration, which we term the intensity. We fruther show that unbiased estimation of thereof is possible, and provide (almost) unbiased estimators thereof in terms of a partial s","authors_text":"Andrey A. Popov, Yuqin Jiang, Zain Jabbar","cross_cats":["cs.NA","math.NA","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-02T22:35:54Z","title":"Unbiased estimation of squared concentration in the Fisher-von Mises-Langevin distribution and the impossibility of unbiased concentration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04267","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":"sha256:6d98fc94c5ac397a99952c4656b1cc142b44d813c0f51dd3876444682a003cd2","target":"record","created_at":"2026-06-04T01:09:01Z","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":"39e4b6acda5095a22e97cd4217d27a015029e3855b3a27e173d54a1550867d2a","cross_cats_sorted":["cs.NA","math.NA","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-02T22:35:54Z","title_canon_sha256":"76b6bee1fe567f00dc404cb3227545217754ebb26fd6788eee946d18e71bb65e"},"schema_version":"1.0","source":{"id":"2606.04267","kind":"arxiv","version":1}},"canonical_sha256":"25e66391f2d52749ce92f86be4d00b4720dc67214df404f8900d4bfee8296a98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25e66391f2d52749ce92f86be4d00b4720dc67214df404f8900d4bfee8296a98","first_computed_at":"2026-06-04T01:09:01.047081Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T01:09:01.047081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YbKIAsfgRCrv7AOfq0pmPqEetoV7eAsL3IwI6kt+AXnWDVNxmTGDxJMv+3ZUVix6nX+9fyjZur6J79nxkKgqDQ==","signature_status":"signed_v1","signed_at":"2026-06-04T01:09:01.047763Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.04267","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d98fc94c5ac397a99952c4656b1cc142b44d813c0f51dd3876444682a003cd2","sha256:31dd851546e6c82e54d22fee4ee29761695e20c5a12d54f9c19649afa29a64db"],"state_sha256":"4aad9463f80854599ebfc556a3148c572b4d8d7eecf2999365b6099e07ce66da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p+bkpFmhQeaXLQSDFu6xnFcoA052lVD4QoxWPlyife6E0DfX69WmfRk+CQcE8S5nYdqCxpFip1KmceadXPKTAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T07:58:56.899869Z","bundle_sha256":"fd0fafa474fffb957e7d871f91aa9c3440211c7eb2f07792a467533134edf53f"}}