{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:WTAO6MCELH7B2K52USAWA3KHSC","short_pith_number":"pith:WTAO6MCE","canonical_record":{"source":{"id":"2112.00816","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2021-12-01T20:27:16Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"16a2a596ef9aec75bade758a41066d04d9fdbced3cee391716b18c9e0e0a8e6d","abstract_canon_sha256":"7787524500ff12e248cbd48cb727da3098c39461ca18f4c841923ea5dfc528bb"},"schema_version":"1.0"},"canonical_sha256":"b4c0ef304459fe1d2bbaa481606d4790a79063adf2f6adfe148babac2c1f3045","source":{"kind":"arxiv","id":"2112.00816","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.00816","created_at":"2026-07-05T05:19:12Z"},{"alias_kind":"arxiv_version","alias_value":"2112.00816v2","created_at":"2026-07-05T05:19:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.00816","created_at":"2026-07-05T05:19:12Z"},{"alias_kind":"pith_short_12","alias_value":"WTAO6MCELH7B","created_at":"2026-07-05T05:19:12Z"},{"alias_kind":"pith_short_16","alias_value":"WTAO6MCELH7B2K52","created_at":"2026-07-05T05:19:12Z"},{"alias_kind":"pith_short_8","alias_value":"WTAO6MCE","created_at":"2026-07-05T05:19:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:WTAO6MCELH7B2K52USAWA3KHSC","target":"record","payload":{"canonical_record":{"source":{"id":"2112.00816","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2021-12-01T20:27:16Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"16a2a596ef9aec75bade758a41066d04d9fdbced3cee391716b18c9e0e0a8e6d","abstract_canon_sha256":"7787524500ff12e248cbd48cb727da3098c39461ca18f4c841923ea5dfc528bb"},"schema_version":"1.0"},"canonical_sha256":"b4c0ef304459fe1d2bbaa481606d4790a79063adf2f6adfe148babac2c1f3045","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:19:12.122841Z","signature_b64":"qhohkrjPW6lZOV/begyHqfAjZ2mg5uy0ky0EFaxnEYPgYTqA/fGJTPceMjBlixKvOcGbUlLZHL5vdVFE4EAxBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4c0ef304459fe1d2bbaa481606d4790a79063adf2f6adfe148babac2c1f3045","last_reissued_at":"2026-07-05T05:19:12.122364Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:19:12.122364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.00816","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:19:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kfra/LwWYqZRA2VTtMumuU8zMuAf8O9/B4TPDnM+he/7rldMJYKqIE3AnX+0v4Wnk514TSwyUwLFQvZkHZxYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T15:30:07.012860Z"},"content_sha256":"52473328388edab571ca9ee0c7b181b5529b34cc4b488aae563f1f8b6e468c9b","schema_version":"1.0","event_id":"sha256:52473328388edab571ca9ee0c7b181b5529b34cc4b488aae563f1f8b6e468c9b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:WTAO6MCELH7B2K52USAWA3KHSC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximum Likelihood Estimation for Brownian Motion Tree Models Based on One Sample","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ME","authors_text":"Caroline Uhler, Chandler Squires, Jan-Christian H\\\"utter, Michael Truell, Piotr Zwiernik","submitted_at":"2021-12-01T20:27:16Z","abstract_excerpt":"We study the problem of maximum likelihood estimation given one data sample ($n=1$) over Brownian Motion Tree Models (BMTMs), a class of Gaussian models on trees. BMTMs are often used as a null model in phylogenetics, where the one-sample regime is common. Specifically, we show that, almost surely, the one-sample BMTM maximum likelihood estimator (MLE) exists, is unique, and corresponds to a fully observed tree. Moreover, we provide a polynomial time algorithm for its exact computation. We also consider the MLE over all possible BMTM tree structures in the one-sample case and show that it exis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.00816","kind":"arxiv","version":2},"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/2112.00816/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":"2026-07-05T05:19:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qfrarC/mEYhRzj+paWqNZfz+cWYPSc0hhVNkOKRLAfMwwKweAIsrNSJVStveXdmgh7HAHhuXAA3XwsNyaaAHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T15:30:07.013478Z"},"content_sha256":"d51d8d1758f2f6800946d8a4f82da16bc18f11aac1c8d25b7f92fbbd7dc92607","schema_version":"1.0","event_id":"sha256:d51d8d1758f2f6800946d8a4f82da16bc18f11aac1c8d25b7f92fbbd7dc92607"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WTAO6MCELH7B2K52USAWA3KHSC/bundle.json","state_url":"https://pith.science/pith/WTAO6MCELH7B2K52USAWA3KHSC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WTAO6MCELH7B2K52USAWA3KHSC/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":"2026-08-06T15:30:07Z","links":{"resolver":"https://pith.science/pith/WTAO6MCELH7B2K52USAWA3KHSC","bundle":"https://pith.science/pith/WTAO6MCELH7B2K52USAWA3KHSC/bundle.json","state":"https://pith.science/pith/WTAO6MCELH7B2K52USAWA3KHSC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WTAO6MCELH7B2K52USAWA3KHSC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:WTAO6MCELH7B2K52USAWA3KHSC","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":"7787524500ff12e248cbd48cb727da3098c39461ca18f4c841923ea5dfc528bb","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2021-12-01T20:27:16Z","title_canon_sha256":"16a2a596ef9aec75bade758a41066d04d9fdbced3cee391716b18c9e0e0a8e6d"},"schema_version":"1.0","source":{"id":"2112.00816","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.00816","created_at":"2026-07-05T05:19:12Z"},{"alias_kind":"arxiv_version","alias_value":"2112.00816v2","created_at":"2026-07-05T05:19:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.00816","created_at":"2026-07-05T05:19:12Z"},{"alias_kind":"pith_short_12","alias_value":"WTAO6MCELH7B","created_at":"2026-07-05T05:19:12Z"},{"alias_kind":"pith_short_16","alias_value":"WTAO6MCELH7B2K52","created_at":"2026-07-05T05:19:12Z"},{"alias_kind":"pith_short_8","alias_value":"WTAO6MCE","created_at":"2026-07-05T05:19:12Z"}],"graph_snapshots":[{"event_id":"sha256:d51d8d1758f2f6800946d8a4f82da16bc18f11aac1c8d25b7f92fbbd7dc92607","target":"graph","created_at":"2026-07-05T05:19:12Z","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/2112.00816/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the problem of maximum likelihood estimation given one data sample ($n=1$) over Brownian Motion Tree Models (BMTMs), a class of Gaussian models on trees. BMTMs are often used as a null model in phylogenetics, where the one-sample regime is common. Specifically, we show that, almost surely, the one-sample BMTM maximum likelihood estimator (MLE) exists, is unique, and corresponds to a fully observed tree. Moreover, we provide a polynomial time algorithm for its exact computation. We also consider the MLE over all possible BMTM tree structures in the one-sample case and show that it exis","authors_text":"Caroline Uhler, Chandler Squires, Jan-Christian H\\\"utter, Michael Truell, Piotr Zwiernik","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2021-12-01T20:27:16Z","title":"Maximum Likelihood Estimation for Brownian Motion Tree Models Based on One Sample"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.00816","kind":"arxiv","version":2},"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":"sha256:52473328388edab571ca9ee0c7b181b5529b34cc4b488aae563f1f8b6e468c9b","target":"record","created_at":"2026-07-05T05:19:12Z","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":"7787524500ff12e248cbd48cb727da3098c39461ca18f4c841923ea5dfc528bb","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2021-12-01T20:27:16Z","title_canon_sha256":"16a2a596ef9aec75bade758a41066d04d9fdbced3cee391716b18c9e0e0a8e6d"},"schema_version":"1.0","source":{"id":"2112.00816","kind":"arxiv","version":2}},"canonical_sha256":"b4c0ef304459fe1d2bbaa481606d4790a79063adf2f6adfe148babac2c1f3045","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4c0ef304459fe1d2bbaa481606d4790a79063adf2f6adfe148babac2c1f3045","first_computed_at":"2026-07-05T05:19:12.122364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:19:12.122364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qhohkrjPW6lZOV/begyHqfAjZ2mg5uy0ky0EFaxnEYPgYTqA/fGJTPceMjBlixKvOcGbUlLZHL5vdVFE4EAxBg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:19:12.122841Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.00816","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52473328388edab571ca9ee0c7b181b5529b34cc4b488aae563f1f8b6e468c9b","sha256:d51d8d1758f2f6800946d8a4f82da16bc18f11aac1c8d25b7f92fbbd7dc92607"],"state_sha256":"a28095683f2382c7a9f65a68be4bdc59f4866065fa1e8f526ab1dd64dcd999a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NWmWEH6ossWnPx4nZi6xdzlgJc5a0Bnq3Fx/fvni+3BLtBvmL6hoeTFWXE49VmcOCXCexsEEsQftrakDnJeKCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T15:30:07.018565Z","bundle_sha256":"a1cdf09c69b74f2bcd302e5afcb0bf761c02460bc28a701dde7265a48066046d"}}