{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:AUEJZWLWJ57CWAOLDEZ4MVHX2F","short_pith_number":"pith:AUEJZWLW","canonical_record":{"source":{"id":"2505.12713","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-19T05:08:37Z","cross_cats_sorted":["cs.LG","cs.NA","eess.SP","stat.ML"],"title_canon_sha256":"596969d76c98f555a32147c96d5efe820fedbb0bc94f694f80c6b606cdcceeef","abstract_canon_sha256":"f9e15fb54e1d08fc0590d48336eb3d5cd519432daba11a16d8b4fa37a4a141a7"},"schema_version":"1.0"},"canonical_sha256":"05089cd9764f7e2b01cb1933c654f7d15ae4bb494f49702af91cdc151c863d81","source":{"kind":"arxiv","id":"2505.12713","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.12713","created_at":"2026-07-05T11:05:08Z"},{"alias_kind":"arxiv_version","alias_value":"2505.12713v1","created_at":"2026-07-05T11:05:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.12713","created_at":"2026-07-05T11:05:08Z"},{"alias_kind":"pith_short_12","alias_value":"AUEJZWLWJ57C","created_at":"2026-07-05T11:05:08Z"},{"alias_kind":"pith_short_16","alias_value":"AUEJZWLWJ57CWAOL","created_at":"2026-07-05T11:05:08Z"},{"alias_kind":"pith_short_8","alias_value":"AUEJZWLW","created_at":"2026-07-05T11:05:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:AUEJZWLWJ57CWAOLDEZ4MVHX2F","target":"record","payload":{"canonical_record":{"source":{"id":"2505.12713","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-19T05:08:37Z","cross_cats_sorted":["cs.LG","cs.NA","eess.SP","stat.ML"],"title_canon_sha256":"596969d76c98f555a32147c96d5efe820fedbb0bc94f694f80c6b606cdcceeef","abstract_canon_sha256":"f9e15fb54e1d08fc0590d48336eb3d5cd519432daba11a16d8b4fa37a4a141a7"},"schema_version":"1.0"},"canonical_sha256":"05089cd9764f7e2b01cb1933c654f7d15ae4bb494f49702af91cdc151c863d81","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:05:08.635814Z","signature_b64":"+0XJKoz30L6nzRKy+0j/63xQ12aKPQVEvdz409zEemU6ToyjLRWpXEpVrra8WhLsp9lhjCzEI9RiGdEs7wzlAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05089cd9764f7e2b01cb1933c654f7d15ae4bb494f49702af91cdc151c863d81","last_reissued_at":"2026-07-05T11:05:08.635397Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:05:08.635397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.12713","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":"2026-07-05T11:05:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lm7b7CQCN1psJ0+6MD8Y8+pKgx7stl8ZEd47/AaH5p76U84ZHTdVvdOvwlFKmWIO1ugiLxNP9aj2T6TmeGb1Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T05:48:55.391653Z"},"content_sha256":"fb0c4d0c4c168b633a567d5a3ff422fbcf942ad58ee1f82ccb83bb089d1f6679","schema_version":"1.0","event_id":"sha256:fb0c4d0c4c168b633a567d5a3ff422fbcf942ad58ee1f82ccb83bb089d1f6679"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:AUEJZWLWJ57CWAOLDEZ4MVHX2F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Identifiability of Nonnegative Tucker Decompositions -- Part I: Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","eess.SP","stat.ML"],"primary_cat":"math.NA","authors_text":"Giovanni Barbarino, Nicolas Gillis, Subhayan Saha","submitted_at":"2025-05-19T05:08:37Z","abstract_excerpt":"Tensor decompositions have become a central tool in data science, with applications in areas such as data analysis, signal processing, and machine learning. A key property of many tensor decompositions, such as the canonical polyadic decomposition, is identifiability: the factors are unique, up to trivial scaling and permutation ambiguities. This allows one to recover the groundtruth sources that generated the data. The Tucker decomposition (TD) is a central and widely used tensor decomposition model. However, it is in general not identifiable. In this paper, we study the identifiability of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.12713","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/2505.12713/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":"2026-07-05T11:05:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o1TAAsoho/AIjEUX+/vl6+IU6LZPwuY2+jgvUpEMkgm8+1vnVaC2aXRlMlnETPzMW3UZ+IQx7eFbErBnoPDtAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T05:48:55.392497Z"},"content_sha256":"ecd3af40147b0ab478d05c02abf1aaf1311b0391602facb112eb1670f31856e2","schema_version":"1.0","event_id":"sha256:ecd3af40147b0ab478d05c02abf1aaf1311b0391602facb112eb1670f31856e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AUEJZWLWJ57CWAOLDEZ4MVHX2F/bundle.json","state_url":"https://pith.science/pith/AUEJZWLWJ57CWAOLDEZ4MVHX2F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AUEJZWLWJ57CWAOLDEZ4MVHX2F/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":"2026-08-11T05:48:55Z","links":{"resolver":"https://pith.science/pith/AUEJZWLWJ57CWAOLDEZ4MVHX2F","bundle":"https://pith.science/pith/AUEJZWLWJ57CWAOLDEZ4MVHX2F/bundle.json","state":"https://pith.science/pith/AUEJZWLWJ57CWAOLDEZ4MVHX2F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AUEJZWLWJ57CWAOLDEZ4MVHX2F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:AUEJZWLWJ57CWAOLDEZ4MVHX2F","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":"f9e15fb54e1d08fc0590d48336eb3d5cd519432daba11a16d8b4fa37a4a141a7","cross_cats_sorted":["cs.LG","cs.NA","eess.SP","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-19T05:08:37Z","title_canon_sha256":"596969d76c98f555a32147c96d5efe820fedbb0bc94f694f80c6b606cdcceeef"},"schema_version":"1.0","source":{"id":"2505.12713","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.12713","created_at":"2026-07-05T11:05:08Z"},{"alias_kind":"arxiv_version","alias_value":"2505.12713v1","created_at":"2026-07-05T11:05:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.12713","created_at":"2026-07-05T11:05:08Z"},{"alias_kind":"pith_short_12","alias_value":"AUEJZWLWJ57C","created_at":"2026-07-05T11:05:08Z"},{"alias_kind":"pith_short_16","alias_value":"AUEJZWLWJ57CWAOL","created_at":"2026-07-05T11:05:08Z"},{"alias_kind":"pith_short_8","alias_value":"AUEJZWLW","created_at":"2026-07-05T11:05:08Z"}],"graph_snapshots":[{"event_id":"sha256:ecd3af40147b0ab478d05c02abf1aaf1311b0391602facb112eb1670f31856e2","target":"graph","created_at":"2026-07-05T11:05:08Z","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/2505.12713/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Tensor decompositions have become a central tool in data science, with applications in areas such as data analysis, signal processing, and machine learning. A key property of many tensor decompositions, such as the canonical polyadic decomposition, is identifiability: the factors are unique, up to trivial scaling and permutation ambiguities. This allows one to recover the groundtruth sources that generated the data. The Tucker decomposition (TD) is a central and widely used tensor decomposition model. However, it is in general not identifiable. In this paper, we study the identifiability of th","authors_text":"Giovanni Barbarino, Nicolas Gillis, Subhayan Saha","cross_cats":["cs.LG","cs.NA","eess.SP","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-19T05:08:37Z","title":"Identifiability of Nonnegative Tucker Decompositions -- Part I: Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.12713","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:fb0c4d0c4c168b633a567d5a3ff422fbcf942ad58ee1f82ccb83bb089d1f6679","target":"record","created_at":"2026-07-05T11:05:08Z","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":"f9e15fb54e1d08fc0590d48336eb3d5cd519432daba11a16d8b4fa37a4a141a7","cross_cats_sorted":["cs.LG","cs.NA","eess.SP","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-19T05:08:37Z","title_canon_sha256":"596969d76c98f555a32147c96d5efe820fedbb0bc94f694f80c6b606cdcceeef"},"schema_version":"1.0","source":{"id":"2505.12713","kind":"arxiv","version":1}},"canonical_sha256":"05089cd9764f7e2b01cb1933c654f7d15ae4bb494f49702af91cdc151c863d81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05089cd9764f7e2b01cb1933c654f7d15ae4bb494f49702af91cdc151c863d81","first_computed_at":"2026-07-05T11:05:08.635397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:05:08.635397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+0XJKoz30L6nzRKy+0j/63xQ12aKPQVEvdz409zEemU6ToyjLRWpXEpVrra8WhLsp9lhjCzEI9RiGdEs7wzlAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:05:08.635814Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.12713","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb0c4d0c4c168b633a567d5a3ff422fbcf942ad58ee1f82ccb83bb089d1f6679","sha256:ecd3af40147b0ab478d05c02abf1aaf1311b0391602facb112eb1670f31856e2"],"state_sha256":"fd3d9eadd46689f050e5e046d02f5be1b0718d3651e37e1073a773b8cecec665"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u0YIkTe8HXePydFu5r/uccRiClbmcwk5j4/C4cslVGN9eQaPHq0N3P/AsGONcLJfwB7w4MEs8xXB7nSDRzGrBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T05:48:55.396900Z","bundle_sha256":"1846f9121add276c28117df66ee95c8665e24af7cc65933f3be6ea926682746f"}}