{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AEJOHS35EFGXGLVK3AFNQYZM7D","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":"abeb42fe30ffb80ce6d2efa56c860300278323fb580066f8c221546f5d79d94b","cross_cats_sorted":["cs.CC","cs.DS","cs.IT","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-02-21T02:14:31Z","title_canon_sha256":"cbb3a2e024ca66e0cce2f1fe4579f0ee07f09937523097a81238fe140bddc96e"},"schema_version":"1.0","source":{"id":"1702.06237","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.06237","created_at":"2026-05-18T00:41:47Z"},{"alias_kind":"arxiv_version","alias_value":"1702.06237v3","created_at":"2026-05-18T00:41:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.06237","created_at":"2026-05-18T00:41:47Z"},{"alias_kind":"pith_short_12","alias_value":"AEJOHS35EFGX","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AEJOHS35EFGXGLVK","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AEJOHS35","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:0b1c24092375f94996ac88e77de5e718dd7c5ba2b20e2d98d1db4bba34e4ff62","target":"graph","created_at":"2026-05-18T00:41:47Z","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":"We obtain the first polynomial-time algorithm for exact tensor completion that improves over the bound implied by reduction to matrix completion. The algorithm recovers an unknown 3-tensor with $r$ incoherent, orthogonal components in $\\mathbb R^n$ from $r\\cdot \\tilde O(n^{1.5})$ randomly observed entries of the tensor. This bound improves over the previous best one of $r\\cdot \\tilde O(n^{2})$ by reduction to exact matrix completion. Our bound also matches the best known results for the easier problem of approximate tensor completion (Barak & Moitra, 2015).\n  Our algorithm and analysis extends","authors_text":"Aaron Potechin, David Steurer","cross_cats":["cs.CC","cs.DS","cs.IT","math.IT","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-02-21T02:14:31Z","title":"Exact tensor completion with sum-of-squares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06237","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":"sha256:0e76c3cc4264d0991c2145fc22198a245c53a25f02cdc555cf4f10ccaf26b129","target":"record","created_at":"2026-05-18T00:41:47Z","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":"abeb42fe30ffb80ce6d2efa56c860300278323fb580066f8c221546f5d79d94b","cross_cats_sorted":["cs.CC","cs.DS","cs.IT","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-02-21T02:14:31Z","title_canon_sha256":"cbb3a2e024ca66e0cce2f1fe4579f0ee07f09937523097a81238fe140bddc96e"},"schema_version":"1.0","source":{"id":"1702.06237","kind":"arxiv","version":3}},"canonical_sha256":"0112e3cb7d214d732eaad80ad8632cf8e41e6508fcd29512eeb254a31706b40b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0112e3cb7d214d732eaad80ad8632cf8e41e6508fcd29512eeb254a31706b40b","first_computed_at":"2026-05-18T00:41:47.756818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:47.756818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"187xnUFdWuKzFr4LjrSuaWAqoMR51YeuzyhkEVv86P3FZs4Jvt88SmCWJoMOsopmL8mqBwfcsf8Lg9ytl6cYBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:47.757415Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.06237","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e76c3cc4264d0991c2145fc22198a245c53a25f02cdc555cf4f10ccaf26b129","sha256:0b1c24092375f94996ac88e77de5e718dd7c5ba2b20e2d98d1db4bba34e4ff62"],"state_sha256":"e1f3eb323e8c02337dd3f7851b9ba90b8946809af81f26c187e22509e6d7271f"}