{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:SSU2LHGLIIDKL4CNOW6IJSN3EK","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":"3e5b7a3b5d8b3a300cca2f57771c1240045d921f265168e99542c962ee181062","cross_cats_sorted":["cs.IR","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2009-03-26T08:39:45Z","title_canon_sha256":"5d14dae453da5b30736d8a04fbbe0822cbd3a25d18ec9ecd9a79f1a6776ccccb"},"schema_version":"1.0","source":{"id":"0903.4530","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.4530","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"arxiv_version","alias_value":"0903.4530v2","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.4530","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"pith_short_12","alias_value":"SSU2LHGLIIDK","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"pith_short_16","alias_value":"SSU2LHGLIIDKL4CN","created_at":"2026-06-03T23:06:25Z"},{"alias_kind":"pith_short_8","alias_value":"SSU2LHGL","created_at":"2026-06-03T23:06:25Z"}],"graph_snapshots":[{"event_id":"sha256:c2b98facbd728e4849b3548c77a10dbf66dabeda3cde30569bc053c591577570","target":"graph","created_at":"2026-06-03T23:06:25Z","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/0903.4530/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the decomposition of a nonnegative tensor into a minimal sum of outer product of nonnegative vectors and the associated parsimonious naive Bayes probabilistic model. We show that the corresponding approximation problem, which is central to nonnegative PARAFAC, will always have optimal solutions. The result holds for any choice of norms and, under a mild assumption, even Bregman divergences.","authors_text":"Lek-Heng Lim, Pierre Comon","cross_cats":["cs.IR","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2009-03-26T08:39:45Z","title":"Nonnegative approximations of nonnegative tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.4530","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:d98b9c88de84d3155c9bcd6244d99571f5c49a82f74eb93c1bb6e72cd7fa5b1d","target":"record","created_at":"2026-06-03T23:06:25Z","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":"3e5b7a3b5d8b3a300cca2f57771c1240045d921f265168e99542c962ee181062","cross_cats_sorted":["cs.IR","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2009-03-26T08:39:45Z","title_canon_sha256":"5d14dae453da5b30736d8a04fbbe0822cbd3a25d18ec9ecd9a79f1a6776ccccb"},"schema_version":"1.0","source":{"id":"0903.4530","kind":"arxiv","version":2}},"canonical_sha256":"94a9a59ccb4206a5f04d75bc84c9bb2291f533ea857927d8579a8f6808dfeef3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94a9a59ccb4206a5f04d75bc84c9bb2291f533ea857927d8579a8f6808dfeef3","first_computed_at":"2026-06-03T23:06:25.228569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T23:06:25.228569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qcQOU4e9NenDF8KkRoS8JOuF5ni5ROf6NNvBJSmkxPc7SsZmzYZm+vZOnNeP47cnTQ8ZoueHVhqHwTzmyYCzCg==","signature_status":"signed_v1","signed_at":"2026-06-03T23:06:25.229102Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.4530","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d98b9c88de84d3155c9bcd6244d99571f5c49a82f74eb93c1bb6e72cd7fa5b1d","sha256:c2b98facbd728e4849b3548c77a10dbf66dabeda3cde30569bc053c591577570"],"state_sha256":"0cc848ee7a8ba72359d1270175a019d6b06df65546d8bf992299e77dd5d203dd"}