{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:D3DD3LDKIP3O57ZH2BTNEWH3PB","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":"04aeef61ca21b272bc38e617d8e34d3d14279364381051887c18f76862faebec","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-10-08T08:49:35Z","title_canon_sha256":"a77ff7decac3ea61e419fe1c42c9bbbc403fa10b75fcffe40689501a67bdc7ac"},"schema_version":"1.0","source":{"id":"2110.03975","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.03975","created_at":"2026-07-05T10:45:48Z"},{"alias_kind":"arxiv_version","alias_value":"2110.03975v3","created_at":"2026-07-05T10:45:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.03975","created_at":"2026-07-05T10:45:48Z"},{"alias_kind":"pith_short_12","alias_value":"D3DD3LDKIP3O","created_at":"2026-07-05T10:45:48Z"},{"alias_kind":"pith_short_16","alias_value":"D3DD3LDKIP3O57ZH","created_at":"2026-07-05T10:45:48Z"},{"alias_kind":"pith_short_8","alias_value":"D3DD3LDK","created_at":"2026-07-05T10:45:48Z"}],"graph_snapshots":[{"event_id":"sha256:9953d7b75534b45939c8d81eded0c2b7ebcd59690b72a86dc5b13d38f703aa0b","target":"graph","created_at":"2026-07-05T10:45:48Z","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/2110.03975/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we estimate the number of randomly selected elements of a tensor that with high probability guarantees local convergence of Riemannian gradient descent for tensor train completion. We derive a new bound for the orthogonal projections onto the tangent spaces based on the harmonic mean of the unfoldings' singular values and introduce a notion of core coherence for tensor trains. We also extend the results to tensor train completion with auxiliary subspace information and obtain the corresponding local convergence guarantees.","authors_text":"Nikolai Zamarashkin, Stanislav Budzinskiy","cross_cats":["cs.LG","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-10-08T08:49:35Z","title":"Tensor train completion: local recovery guarantees via Riemannian optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.03975","kind":"arxiv","version":3},"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":"sha256:584184b95340bef419a7ed207c11b530a8c856401053b3044d76a437d4f2775a","target":"record","created_at":"2026-07-05T10:45:48Z","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":"04aeef61ca21b272bc38e617d8e34d3d14279364381051887c18f76862faebec","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-10-08T08:49:35Z","title_canon_sha256":"a77ff7decac3ea61e419fe1c42c9bbbc403fa10b75fcffe40689501a67bdc7ac"},"schema_version":"1.0","source":{"id":"2110.03975","kind":"arxiv","version":3}},"canonical_sha256":"1ec63dac6a43f6eeff27d066d258fb786475a5bc5414210f739a82724a527ea3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ec63dac6a43f6eeff27d066d258fb786475a5bc5414210f739a82724a527ea3","first_computed_at":"2026-07-05T10:45:48.414876Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:45:48.414876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aaL3jWtSuKydaRt/nsZObkNAmze8sADBqcYys4SR0alX6mVALJGGKx9N1cbimpv8xr9jCHJKKmqV1D2QwV40Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:45:48.415378Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.03975","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:584184b95340bef419a7ed207c11b530a8c856401053b3044d76a437d4f2775a","sha256:9953d7b75534b45939c8d81eded0c2b7ebcd59690b72a86dc5b13d38f703aa0b"],"state_sha256":"f26c408cf21303e30d97bc39e62cc06643af5ca1d9ee747994f675ecf72d1895"}