{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5Z2OQPGQYWRZSQN5SFBPEVU4FG","short_pith_number":"pith:5Z2OQPGQ","canonical_record":{"source":{"id":"1512.02337","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-12-08T05:49:07Z","cross_cats_sorted":["cs.CC","cs.LG","stat.ML"],"title_canon_sha256":"c9bab099d6f8a5854c6bff89dadf84b7f1080c523b9f029378b7b8efc6620cbb","abstract_canon_sha256":"a16f4b3c45b5d4ebf369544b9f6a6c10e354d050285c53641c0d6e8c4ec48d25"},"schema_version":"1.0"},"canonical_sha256":"ee74e83cd0c5a39941bd9142f2569c29910a69d67c0228197750004bada25ed5","source":{"kind":"arxiv","id":"1512.02337","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02337","created_at":"2026-05-18T01:21:21Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02337v2","created_at":"2026-05-18T01:21:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02337","created_at":"2026-05-18T01:21:21Z"},{"alias_kind":"pith_short_12","alias_value":"5Z2OQPGQYWRZ","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5Z2OQPGQYWRZSQN5","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5Z2OQPGQ","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5Z2OQPGQYWRZSQN5SFBPEVU4FG","target":"record","payload":{"canonical_record":{"source":{"id":"1512.02337","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-12-08T05:49:07Z","cross_cats_sorted":["cs.CC","cs.LG","stat.ML"],"title_canon_sha256":"c9bab099d6f8a5854c6bff89dadf84b7f1080c523b9f029378b7b8efc6620cbb","abstract_canon_sha256":"a16f4b3c45b5d4ebf369544b9f6a6c10e354d050285c53641c0d6e8c4ec48d25"},"schema_version":"1.0"},"canonical_sha256":"ee74e83cd0c5a39941bd9142f2569c29910a69d67c0228197750004bada25ed5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:21.138532Z","signature_b64":"MwIb2QtAVS6CCWBa5jL3x8fdJpf/qSn43Q3S0KtEDpQlsSkeTTdikdV/rog2GfftqDLyLUy+v2qFolKjtohoAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee74e83cd0c5a39941bd9142f2569c29910a69d67c0228197750004bada25ed5","last_reissued_at":"2026-05-18T01:21:21.138019Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:21.138019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.02337","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oDSOFeoHEuBiyh9PGLNAxyAvSwgX9x5AIer8ABO5LGjaPypkoOH7FJHAT0X3u3h90hO8fNiXcA8eSahoxqSdCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:26:19.622854Z"},"content_sha256":"ce90add3521c65365d62cd517b9681cf83602bbed6d6ebfd986235f24f105878","schema_version":"1.0","event_id":"sha256:ce90add3521c65365d62cd517b9681cf83602bbed6d6ebfd986235f24f105878"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5Z2OQPGQYWRZSQN5SFBPEVU4FG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast spectral algorithms from sum-of-squares proofs: tensor decomposition and planted sparse vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"David Steurer, Jonathan Shi, Samuel B. Hopkins, Tselil Schramm","submitted_at":"2015-12-08T05:49:07Z","abstract_excerpt":"We consider two problems that arise in machine learning applications: the problem of recovering a planted sparse vector in a random linear subspace and the problem of decomposing a random low-rank overcomplete 3-tensor. For both problems, the best known guarantees are based on the sum-of-squares method. We develop new algorithms inspired by analyses of the sum-of-squares method. Our algorithms achieve the same or similar guarantees as sum-of-squares for these problems but the running time is significantly faster.\n  For the planted sparse vector problem, we give an algorithm with running time n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02337","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T01:21:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tW1FoOy6jcGXROH2kBgtU7Qt2WzFT1WrXYzAalK/aOJFDhmTSddgMkEz/iZoi3kmdkKQbNl2Jn9kiTJiVudsBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:26:19.623552Z"},"content_sha256":"d7a8a150691381c594c15c977eda815eabe0ee6dbd05cd85cbdfeae6ac15a224","schema_version":"1.0","event_id":"sha256:d7a8a150691381c594c15c977eda815eabe0ee6dbd05cd85cbdfeae6ac15a224"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5Z2OQPGQYWRZSQN5SFBPEVU4FG/bundle.json","state_url":"https://pith.science/pith/5Z2OQPGQYWRZSQN5SFBPEVU4FG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5Z2OQPGQYWRZSQN5SFBPEVU4FG/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":"2026-05-27T21:26:19Z","links":{"resolver":"https://pith.science/pith/5Z2OQPGQYWRZSQN5SFBPEVU4FG","bundle":"https://pith.science/pith/5Z2OQPGQYWRZSQN5SFBPEVU4FG/bundle.json","state":"https://pith.science/pith/5Z2OQPGQYWRZSQN5SFBPEVU4FG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5Z2OQPGQYWRZSQN5SFBPEVU4FG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5Z2OQPGQYWRZSQN5SFBPEVU4FG","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":"a16f4b3c45b5d4ebf369544b9f6a6c10e354d050285c53641c0d6e8c4ec48d25","cross_cats_sorted":["cs.CC","cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-12-08T05:49:07Z","title_canon_sha256":"c9bab099d6f8a5854c6bff89dadf84b7f1080c523b9f029378b7b8efc6620cbb"},"schema_version":"1.0","source":{"id":"1512.02337","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02337","created_at":"2026-05-18T01:21:21Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02337v2","created_at":"2026-05-18T01:21:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02337","created_at":"2026-05-18T01:21:21Z"},{"alias_kind":"pith_short_12","alias_value":"5Z2OQPGQYWRZ","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"5Z2OQPGQYWRZSQN5","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"5Z2OQPGQ","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:d7a8a150691381c594c15c977eda815eabe0ee6dbd05cd85cbdfeae6ac15a224","target":"graph","created_at":"2026-05-18T01:21:21Z","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 two problems that arise in machine learning applications: the problem of recovering a planted sparse vector in a random linear subspace and the problem of decomposing a random low-rank overcomplete 3-tensor. For both problems, the best known guarantees are based on the sum-of-squares method. We develop new algorithms inspired by analyses of the sum-of-squares method. Our algorithms achieve the same or similar guarantees as sum-of-squares for these problems but the running time is significantly faster.\n  For the planted sparse vector problem, we give an algorithm with running time n","authors_text":"David Steurer, Jonathan Shi, Samuel B. Hopkins, Tselil Schramm","cross_cats":["cs.CC","cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-12-08T05:49:07Z","title":"Fast spectral algorithms from sum-of-squares proofs: tensor decomposition and planted sparse vectors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02337","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:ce90add3521c65365d62cd517b9681cf83602bbed6d6ebfd986235f24f105878","target":"record","created_at":"2026-05-18T01:21:21Z","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":"a16f4b3c45b5d4ebf369544b9f6a6c10e354d050285c53641c0d6e8c4ec48d25","cross_cats_sorted":["cs.CC","cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-12-08T05:49:07Z","title_canon_sha256":"c9bab099d6f8a5854c6bff89dadf84b7f1080c523b9f029378b7b8efc6620cbb"},"schema_version":"1.0","source":{"id":"1512.02337","kind":"arxiv","version":2}},"canonical_sha256":"ee74e83cd0c5a39941bd9142f2569c29910a69d67c0228197750004bada25ed5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee74e83cd0c5a39941bd9142f2569c29910a69d67c0228197750004bada25ed5","first_computed_at":"2026-05-18T01:21:21.138019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:21.138019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MwIb2QtAVS6CCWBa5jL3x8fdJpf/qSn43Q3S0KtEDpQlsSkeTTdikdV/rog2GfftqDLyLUy+v2qFolKjtohoAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:21.138532Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.02337","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce90add3521c65365d62cd517b9681cf83602bbed6d6ebfd986235f24f105878","sha256:d7a8a150691381c594c15c977eda815eabe0ee6dbd05cd85cbdfeae6ac15a224"],"state_sha256":"81b1571858e927bec599037b8c860cbfa244d2c3a1e1578cccc54360542e72c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qatkZt3OtPlYG9yIEAfY29M5F4jBNffVad67juwasqE9CHpxayRAJeK5sTigEnq8M0btgQy2GbV3T44mLn07Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T21:26:19.626081Z","bundle_sha256":"d7a7f237ba19ab218bbd989926bc0cd25d63ed6e736777806c06e5d0caba1b43"}}