{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ODJTYUPOSVFNNMCKYKNIUCLSAG","short_pith_number":"pith:ODJTYUPO","canonical_record":{"source":{"id":"1006.2086","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-10T17:10:26Z","cross_cats_sorted":["cs.NA","math.IT","math.NA"],"title_canon_sha256":"5f489bce5116b409ea30b744f38735eb7960e7bf456780e1f227a130734071c3","abstract_canon_sha256":"ee4582d2a727312def55c61899955769b7aa4dfc890871ad3bcf7299a241cae2"},"schema_version":"1.0"},"canonical_sha256":"70d33c51ee954ad6b04ac29a8a097201a4e04a2f37e3c604d8d41c332d4fe2e6","source":{"kind":"arxiv","id":"1006.2086","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.2086","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"arxiv_version","alias_value":"1006.2086v1","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.2086","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"pith_short_12","alias_value":"ODJTYUPOSVFN","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"pith_short_16","alias_value":"ODJTYUPOSVFNNMCK","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"pith_short_8","alias_value":"ODJTYUPO","created_at":"2026-06-03T23:06:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ODJTYUPOSVFNNMCKYKNIUCLSAG","target":"record","payload":{"canonical_record":{"source":{"id":"1006.2086","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-10T17:10:26Z","cross_cats_sorted":["cs.NA","math.IT","math.NA"],"title_canon_sha256":"5f489bce5116b409ea30b744f38735eb7960e7bf456780e1f227a130734071c3","abstract_canon_sha256":"ee4582d2a727312def55c61899955769b7aa4dfc890871ad3bcf7299a241cae2"},"schema_version":"1.0"},"canonical_sha256":"70d33c51ee954ad6b04ac29a8a097201a4e04a2f37e3c604d8d41c332d4fe2e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T23:06:38.323981Z","signature_b64":"t5HU8fCwOZhwvh2AnZ/fD5mEirfRl7JPIqtJXo/thb0LFOuGm/Vjcp0sBVbMkXmn4+55L1GbpgQFMEBbZLduAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70d33c51ee954ad6b04ac29a8a097201a4e04a2f37e3c604d8d41c332d4fe2e6","last_reissued_at":"2026-06-03T23:06:38.323396Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T23:06:38.323396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.2086","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":"2026-06-03T23:06:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dzpKcA9qfg1uHKgc2oTH9L++mUd+9cB5aSMDgDzLgA63uDxtcql+9OcnaRCaOEizA+ga9w1p7nqDxg1c328lBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:21:15.753590Z"},"content_sha256":"2372df98eb46426b759e1cf237dcf15c58d29b1154c90b02a4537146593e0070","schema_version":"1.0","event_id":"sha256:2372df98eb46426b759e1cf237dcf15c58d29b1154c90b02a4537146593e0070"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ODJTYUPOSVFNNMCKYKNIUCLSAG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Geometric Approach to Low-Rank Matrix Completion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.IT","math.NA"],"primary_cat":"cs.IT","authors_text":"Ely Kerman, Olgica Milenkovic, Wei Dai","submitted_at":"2010-06-10T17:10:26Z","abstract_excerpt":"The low-rank matrix completion problem can be succinctly stated as follows: given a subset of the entries of a matrix, find a low-rank matrix consistent with the observations. While several low-complexity algorithms for matrix completion have been proposed so far, it remains an open problem to devise search procedures with provable performance guarantees for a broad class of matrix models. The standard approach to the problem, which involves the minimization of an objective function defined using the Frobenius metric, has inherent difficulties: the objective function is not continuous and the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2086","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/1006.2086/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":"2026-06-03T23:06:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ctZkREv7h5RCT0rfduC5fxuFnGg435RgYE7yUFQt07zC1LfFN/BwK+sM8ExNRu4K5XO61lYlMTxaf/PmCCdbDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:21:15.753985Z"},"content_sha256":"d441f7abf6320f79fc06c799ded9919903bc0b68813877ad4cd010734e2b6e54","schema_version":"1.0","event_id":"sha256:d441f7abf6320f79fc06c799ded9919903bc0b68813877ad4cd010734e2b6e54"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ODJTYUPOSVFNNMCKYKNIUCLSAG/bundle.json","state_url":"https://pith.science/pith/ODJTYUPOSVFNNMCKYKNIUCLSAG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ODJTYUPOSVFNNMCKYKNIUCLSAG/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":"2026-06-05T11:21:15Z","links":{"resolver":"https://pith.science/pith/ODJTYUPOSVFNNMCKYKNIUCLSAG","bundle":"https://pith.science/pith/ODJTYUPOSVFNNMCKYKNIUCLSAG/bundle.json","state":"https://pith.science/pith/ODJTYUPOSVFNNMCKYKNIUCLSAG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ODJTYUPOSVFNNMCKYKNIUCLSAG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ODJTYUPOSVFNNMCKYKNIUCLSAG","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":"ee4582d2a727312def55c61899955769b7aa4dfc890871ad3bcf7299a241cae2","cross_cats_sorted":["cs.NA","math.IT","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-10T17:10:26Z","title_canon_sha256":"5f489bce5116b409ea30b744f38735eb7960e7bf456780e1f227a130734071c3"},"schema_version":"1.0","source":{"id":"1006.2086","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.2086","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"arxiv_version","alias_value":"1006.2086v1","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.2086","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"pith_short_12","alias_value":"ODJTYUPOSVFN","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"pith_short_16","alias_value":"ODJTYUPOSVFNNMCK","created_at":"2026-06-03T23:06:38Z"},{"alias_kind":"pith_short_8","alias_value":"ODJTYUPO","created_at":"2026-06-03T23:06:38Z"}],"graph_snapshots":[{"event_id":"sha256:d441f7abf6320f79fc06c799ded9919903bc0b68813877ad4cd010734e2b6e54","target":"graph","created_at":"2026-06-03T23:06:38Z","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/1006.2086/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The low-rank matrix completion problem can be succinctly stated as follows: given a subset of the entries of a matrix, find a low-rank matrix consistent with the observations. While several low-complexity algorithms for matrix completion have been proposed so far, it remains an open problem to devise search procedures with provable performance guarantees for a broad class of matrix models. The standard approach to the problem, which involves the minimization of an objective function defined using the Frobenius metric, has inherent difficulties: the objective function is not continuous and the ","authors_text":"Ely Kerman, Olgica Milenkovic, Wei Dai","cross_cats":["cs.NA","math.IT","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-10T17:10:26Z","title":"A Geometric Approach to Low-Rank Matrix Completion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2086","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":"sha256:2372df98eb46426b759e1cf237dcf15c58d29b1154c90b02a4537146593e0070","target":"record","created_at":"2026-06-03T23:06:38Z","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":"ee4582d2a727312def55c61899955769b7aa4dfc890871ad3bcf7299a241cae2","cross_cats_sorted":["cs.NA","math.IT","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-10T17:10:26Z","title_canon_sha256":"5f489bce5116b409ea30b744f38735eb7960e7bf456780e1f227a130734071c3"},"schema_version":"1.0","source":{"id":"1006.2086","kind":"arxiv","version":1}},"canonical_sha256":"70d33c51ee954ad6b04ac29a8a097201a4e04a2f37e3c604d8d41c332d4fe2e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70d33c51ee954ad6b04ac29a8a097201a4e04a2f37e3c604d8d41c332d4fe2e6","first_computed_at":"2026-06-03T23:06:38.323396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T23:06:38.323396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t5HU8fCwOZhwvh2AnZ/fD5mEirfRl7JPIqtJXo/thb0LFOuGm/Vjcp0sBVbMkXmn4+55L1GbpgQFMEBbZLduAQ==","signature_status":"signed_v1","signed_at":"2026-06-03T23:06:38.323981Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.2086","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2372df98eb46426b759e1cf237dcf15c58d29b1154c90b02a4537146593e0070","sha256:d441f7abf6320f79fc06c799ded9919903bc0b68813877ad4cd010734e2b6e54"],"state_sha256":"b2e031d9d4b06728042233695bde2913d6552222e843a146b91c37c804d2a16b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"55DBdqz53XPleYnVpZQbHVKH5Ufk1E9JKktcake8M8KkAkxGIJ00eVltcVYDQtq9pib+utkorfKExZt43PURCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T11:21:15.756176Z","bundle_sha256":"d6bc636a840252a76c62937eba3adcea936e11fc91c4727ce57f91da439dd55b"}}