{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KQHABRQ3MP7QDDX2GIU45OOUNF","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":"bfad0779e314a5b487feb7a1e9814e5275dfa189c2239b9ac9e3c9190cc34748","cross_cats_sorted":["math.PR","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-11-15T06:23:43Z","title_canon_sha256":"4e3e541345b4a0c49a8a2c7e8b3515949a5defefe087105eb4c7ddc00f252f60"},"schema_version":"1.0","source":{"id":"1711.05424","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.05424","created_at":"2026-05-18T00:25:07Z"},{"alias_kind":"arxiv_version","alias_value":"1711.05424v2","created_at":"2026-05-18T00:25:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05424","created_at":"2026-05-18T00:25:07Z"},{"alias_kind":"pith_short_12","alias_value":"KQHABRQ3MP7Q","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KQHABRQ3MP7QDDX2","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KQHABRQ3","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:3d213084197b94bfe3732a7e1a7bef6ae6e7192dde60c9792b0c55219cf3be65","target":"graph","created_at":"2026-05-18T00:25:07Z","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 consider the problem of estimating a large rank-one tensor ${\\boldsymbol u}^{\\otimes k}\\in({\\mathbb R}^{n})^{\\otimes k}$, $k\\ge 3$ in Gaussian noise. Earlier work characterized a critical signal-to-noise ratio $\\lambda_{Bayes}= O(1)$ above which an ideal estimator achieves strictly positive correlation with the unknown vector of interest. Remarkably no polynomial-time algorithm is known that achieved this goal unless $\\lambda\\ge C n^{(k-2)/4}$ and even powerful semidefinite programming relaxations appear to fail for $1\\ll \\lambda\\ll n^{(k-2)/4}$.\n  In order to elucidate this behavior, we co","authors_text":"Andrea Montanari, Gerard Ben Arous, Mihai Nica, Song Mei","cross_cats":["math.PR","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-11-15T06:23:43Z","title":"The landscape of the spiked tensor model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05424","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":"sha256:3dcaa1171cbab4503584999f1e189977838f45b75c22235f64f353efdc4f8058","target":"record","created_at":"2026-05-18T00:25:07Z","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":"bfad0779e314a5b487feb7a1e9814e5275dfa189c2239b9ac9e3c9190cc34748","cross_cats_sorted":["math.PR","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-11-15T06:23:43Z","title_canon_sha256":"4e3e541345b4a0c49a8a2c7e8b3515949a5defefe087105eb4c7ddc00f252f60"},"schema_version":"1.0","source":{"id":"1711.05424","kind":"arxiv","version":2}},"canonical_sha256":"540e00c61b63ff018efa3229ceb9d46957d99f49b02c2c6ad14ed6477f2fd8d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"540e00c61b63ff018efa3229ceb9d46957d99f49b02c2c6ad14ed6477f2fd8d2","first_computed_at":"2026-05-18T00:25:07.347093Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:07.347093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UayXYAT9gZZ6sYiRcJz7a0m7qpaPb4g7nPfJspRLA/YprC94bFkCB7Y5AAOBr+ALKOmWuePMphzBhbYEMwErAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:07.347635Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.05424","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3dcaa1171cbab4503584999f1e189977838f45b75c22235f64f353efdc4f8058","sha256:3d213084197b94bfe3732a7e1a7bef6ae6e7192dde60c9792b0c55219cf3be65"],"state_sha256":"c399271469afa878f1b6b81211aef7a2d2ac2f885457587973b6fb9f052c83f6"}