{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2BDBURHH2BSIADIR2Q5MBENOBV","short_pith_number":"pith:2BDBURHH","canonical_record":{"source":{"id":"1306.1598","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-06-07T03:24:56Z","cross_cats_sorted":[],"title_canon_sha256":"d3dcea1c65a00f7911fb72759b954f3fef46c8124f7b4219b4464215c1d05429","abstract_canon_sha256":"55b9966c9cf01e69e3165b9319c3eb5f432d3f39bb5023038df2a74af4c39402"},"schema_version":"1.0"},"canonical_sha256":"d0461a44e7d064800d11d43ac091ae0d788e718a0a0870883ec032497f8464f2","source":{"kind":"arxiv","id":"1306.1598","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1598","created_at":"2026-05-18T03:21:33Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1598v1","created_at":"2026-05-18T03:21:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1598","created_at":"2026-05-18T03:21:33Z"},{"alias_kind":"pith_short_12","alias_value":"2BDBURHH2BSI","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2BDBURHH2BSIADIR","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2BDBURHH","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2BDBURHH2BSIADIR2Q5MBENOBV","target":"record","payload":{"canonical_record":{"source":{"id":"1306.1598","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-06-07T03:24:56Z","cross_cats_sorted":[],"title_canon_sha256":"d3dcea1c65a00f7911fb72759b954f3fef46c8124f7b4219b4464215c1d05429","abstract_canon_sha256":"55b9966c9cf01e69e3165b9319c3eb5f432d3f39bb5023038df2a74af4c39402"},"schema_version":"1.0"},"canonical_sha256":"d0461a44e7d064800d11d43ac091ae0d788e718a0a0870883ec032497f8464f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:33.014678Z","signature_b64":"9QmP0gEKv1Lf56js50GuakMZGXrXmiLeuKDB4iLBRwJQz6KExVhK2APM+Smhry2G7TLs7ycwHdiTBylzG57WCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0461a44e7d064800d11d43ac091ae0d788e718a0a0870883ec032497f8464f2","last_reissued_at":"2026-05-18T03:21:33.013929Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:33.013929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.1598","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":"2026-05-18T03:21:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tyqafqis88Xza73eTcDoBBb2Wu1/yAXW3aAgj73DzO3DCoNCBEr7gPF+gvSipXff/cMDp/HPC8dWO9XtlM9XBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:58:19.757636Z"},"content_sha256":"8224b2648b4d546ddbcfe442ed3372c494aee8480a8778884ca5c784c0f5a488","schema_version":"1.0","event_id":"sha256:8224b2648b4d546ddbcfe442ed3372c494aee8480a8778884ca5c784c0f5a488"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2BDBURHH2BSIADIR2Q5MBENOBV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bayesian factorizations of big sparse tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Amy Herring, Anirban Bhattacharya, David Dunson, Jing Zhou","submitted_at":"2013-06-07T03:24:56Z","abstract_excerpt":"It has become routine to collect data that are structured as multiway arrays (tensors). There is an enormous literature on low rank and sparse matrix factorizations, but limited consideration of extensions to the tensor case in statistics. The most common low rank tensor factorization relies on parallel factor analysis (PARAFAC), which expresses a rank $k$ tensor as a sum of rank one tensors. When observations are only available for a tiny subset of the cells of a big tensor, the low rank assumption is not sufficient and PARAFAC has poor performance. We induce an additional layer of dimension "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1598","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":"2026-05-18T03:21:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B/HCORFLnOB+gTzTwPjWEvwtzssNFcW0E/8XDPQ5BJjg0VGUQwF3b7ThrWEo58adwrwkzEKfQAEdsf9A2ALVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:58:19.757994Z"},"content_sha256":"6980cdb80f9ce56aa886902748dbbb5cc9889e2b33828ed982048945e27723c4","schema_version":"1.0","event_id":"sha256:6980cdb80f9ce56aa886902748dbbb5cc9889e2b33828ed982048945e27723c4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2BDBURHH2BSIADIR2Q5MBENOBV/bundle.json","state_url":"https://pith.science/pith/2BDBURHH2BSIADIR2Q5MBENOBV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2BDBURHH2BSIADIR2Q5MBENOBV/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":"2026-06-01T18:58:19Z","links":{"resolver":"https://pith.science/pith/2BDBURHH2BSIADIR2Q5MBENOBV","bundle":"https://pith.science/pith/2BDBURHH2BSIADIR2Q5MBENOBV/bundle.json","state":"https://pith.science/pith/2BDBURHH2BSIADIR2Q5MBENOBV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2BDBURHH2BSIADIR2Q5MBENOBV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2BDBURHH2BSIADIR2Q5MBENOBV","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":"55b9966c9cf01e69e3165b9319c3eb5f432d3f39bb5023038df2a74af4c39402","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-06-07T03:24:56Z","title_canon_sha256":"d3dcea1c65a00f7911fb72759b954f3fef46c8124f7b4219b4464215c1d05429"},"schema_version":"1.0","source":{"id":"1306.1598","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1598","created_at":"2026-05-18T03:21:33Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1598v1","created_at":"2026-05-18T03:21:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1598","created_at":"2026-05-18T03:21:33Z"},{"alias_kind":"pith_short_12","alias_value":"2BDBURHH2BSI","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2BDBURHH2BSIADIR","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2BDBURHH","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:6980cdb80f9ce56aa886902748dbbb5cc9889e2b33828ed982048945e27723c4","target":"graph","created_at":"2026-05-18T03:21:33Z","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":"It has become routine to collect data that are structured as multiway arrays (tensors). There is an enormous literature on low rank and sparse matrix factorizations, but limited consideration of extensions to the tensor case in statistics. The most common low rank tensor factorization relies on parallel factor analysis (PARAFAC), which expresses a rank $k$ tensor as a sum of rank one tensors. When observations are only available for a tiny subset of the cells of a big tensor, the low rank assumption is not sufficient and PARAFAC has poor performance. We induce an additional layer of dimension ","authors_text":"Amy Herring, Anirban Bhattacharya, David Dunson, Jing Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-06-07T03:24:56Z","title":"Bayesian factorizations of big sparse tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1598","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":"sha256:8224b2648b4d546ddbcfe442ed3372c494aee8480a8778884ca5c784c0f5a488","target":"record","created_at":"2026-05-18T03:21:33Z","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":"55b9966c9cf01e69e3165b9319c3eb5f432d3f39bb5023038df2a74af4c39402","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2013-06-07T03:24:56Z","title_canon_sha256":"d3dcea1c65a00f7911fb72759b954f3fef46c8124f7b4219b4464215c1d05429"},"schema_version":"1.0","source":{"id":"1306.1598","kind":"arxiv","version":1}},"canonical_sha256":"d0461a44e7d064800d11d43ac091ae0d788e718a0a0870883ec032497f8464f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0461a44e7d064800d11d43ac091ae0d788e718a0a0870883ec032497f8464f2","first_computed_at":"2026-05-18T03:21:33.013929Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:33.013929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9QmP0gEKv1Lf56js50GuakMZGXrXmiLeuKDB4iLBRwJQz6KExVhK2APM+Smhry2G7TLs7ycwHdiTBylzG57WCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:33.014678Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1598","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8224b2648b4d546ddbcfe442ed3372c494aee8480a8778884ca5c784c0f5a488","sha256:6980cdb80f9ce56aa886902748dbbb5cc9889e2b33828ed982048945e27723c4"],"state_sha256":"0ecbd210535e2d1eb25d50dfd5280dc511e5ba3c9d5e7872467335c01b56a748"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+0avhU8UxHZaN1t4ALNQdomSThYBVVv2RHkGaEID5XQsV8uyk9ytodtqHBro0UVnWCDM7l4fy6yROD5KrVWKAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:58:19.759942Z","bundle_sha256":"a8514682d8c8109bbb2225836b16c4cd0ecf5404ec36e379ede895bc9d25ba19"}}