{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:LFQEZOR6FCL3SY3QW32JRPHSB3","short_pith_number":"pith:LFQEZOR6","canonical_record":{"source":{"id":"1904.03858","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-08T06:26:35Z","cross_cats_sorted":["cond-mat.stat-mech","cs.LG","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"1ede8f06d5313813bbf1a4ee6c6ee6c696733daba2a0eecd7c925a4b9b5ba41c","abstract_canon_sha256":"acba4fffce1ca1cf2fe990592af1c3fa52630034367a4061cd3780aa32c09e25"},"schema_version":"1.0"},"canonical_sha256":"59604cba3e2897b96370b6f498bcf20eec36f8bd21ac39ed66e96bba959f401e","source":{"kind":"arxiv","id":"1904.03858","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.03858","created_at":"2026-07-05T11:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1904.03858v3","created_at":"2026-07-05T11:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03858","created_at":"2026-07-05T11:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"LFQEZOR6FCL3","created_at":"2026-07-05T11:56:11Z"},{"alias_kind":"pith_short_16","alias_value":"LFQEZOR6FCL3SY3Q","created_at":"2026-07-05T11:56:11Z"},{"alias_kind":"pith_short_8","alias_value":"LFQEZOR6","created_at":"2026-07-05T11:56:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:LFQEZOR6FCL3SY3QW32JRPHSB3","target":"record","payload":{"canonical_record":{"source":{"id":"1904.03858","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-08T06:26:35Z","cross_cats_sorted":["cond-mat.stat-mech","cs.LG","math.ST","stat.ML","stat.TH"],"title_canon_sha256":"1ede8f06d5313813bbf1a4ee6c6ee6c696733daba2a0eecd7c925a4b9b5ba41c","abstract_canon_sha256":"acba4fffce1ca1cf2fe990592af1c3fa52630034367a4061cd3780aa32c09e25"},"schema_version":"1.0"},"canonical_sha256":"59604cba3e2897b96370b6f498bcf20eec36f8bd21ac39ed66e96bba959f401e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:56:11.586395Z","signature_b64":"lJgGLcNFDDbuCav0kt6jl2I8qDMHpybMWncdn4jYGuNRTen32DAKmsutxFZaqX46CVZa4PJSFrHFawhFWOB7Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59604cba3e2897b96370b6f498bcf20eec36f8bd21ac39ed66e96bba959f401e","last_reissued_at":"2026-07-05T11:56:11.585783Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:56:11.585783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.03858","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:56:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r8oqxPjTS2ffr6YyFTEp2sHOAdrxl4+lVCZJpIbYpc4i20PduwFFW3YIVg/tmpJFQ5T9hKeO41oqP5R0wylnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T20:33:21.239876Z"},"content_sha256":"ae75cfaf7a9ab4b9ca7dfae867ebc1cf1f4d790ed303fb994b406ef9ebdcfe13","schema_version":"1.0","event_id":"sha256:ae75cfaf7a9ab4b9ca7dfae867ebc1cf1f4d790ed303fb994b406ef9ebdcfe13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:LFQEZOR6FCL3SY3QW32JRPHSB3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Kikuchi Hierarchy and Tensor PCA","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.LG","math.ST","stat.ML","stat.TH"],"primary_cat":"cs.DS","authors_text":"Ahmed El Alaoui, Alexander S. Wein, Cristopher Moore","submitted_at":"2019-04-08T06:26:35Z","abstract_excerpt":"For the tensor PCA (principal component analysis) problem, we propose a new hierarchy of increasingly powerful algorithms with increasing runtime. Our hierarchy is analogous to the sum-of-squares (SOS) hierarchy but is instead inspired by statistical physics and related algorithms such as belief propagation and AMP (approximate message passing). Our level-$\\ell$ algorithm can be thought of as a linearized message-passing algorithm that keeps track of $\\ell$-wise dependencies among the hidden variables. Specifically, our algorithms are spectral methods based on the Kikuchi Hessian, which genera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03858","kind":"arxiv","version":3},"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/1904.03858/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":"2026-07-05T11:56:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jkonEL8w6zXYmY9JTvi5Q+B2ILK5+tJphGzlUW8Y/OOvCLqnrldtuVqHdzqyoPd5+K9KXjoCulzMuVtN1qb3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T20:33:21.240511Z"},"content_sha256":"19f2e14fc29b2a2f287b9761c7c6f175eff37f84da0d73f7a2f77d05f30a148f","schema_version":"1.0","event_id":"sha256:19f2e14fc29b2a2f287b9761c7c6f175eff37f84da0d73f7a2f77d05f30a148f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LFQEZOR6FCL3SY3QW32JRPHSB3/bundle.json","state_url":"https://pith.science/pith/LFQEZOR6FCL3SY3QW32JRPHSB3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LFQEZOR6FCL3SY3QW32JRPHSB3/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":"2026-08-11T20:33:21Z","links":{"resolver":"https://pith.science/pith/LFQEZOR6FCL3SY3QW32JRPHSB3","bundle":"https://pith.science/pith/LFQEZOR6FCL3SY3QW32JRPHSB3/bundle.json","state":"https://pith.science/pith/LFQEZOR6FCL3SY3QW32JRPHSB3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LFQEZOR6FCL3SY3QW32JRPHSB3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LFQEZOR6FCL3SY3QW32JRPHSB3","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":"acba4fffce1ca1cf2fe990592af1c3fa52630034367a4061cd3780aa32c09e25","cross_cats_sorted":["cond-mat.stat-mech","cs.LG","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-08T06:26:35Z","title_canon_sha256":"1ede8f06d5313813bbf1a4ee6c6ee6c696733daba2a0eecd7c925a4b9b5ba41c"},"schema_version":"1.0","source":{"id":"1904.03858","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.03858","created_at":"2026-07-05T11:56:11Z"},{"alias_kind":"arxiv_version","alias_value":"1904.03858v3","created_at":"2026-07-05T11:56:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03858","created_at":"2026-07-05T11:56:11Z"},{"alias_kind":"pith_short_12","alias_value":"LFQEZOR6FCL3","created_at":"2026-07-05T11:56:11Z"},{"alias_kind":"pith_short_16","alias_value":"LFQEZOR6FCL3SY3Q","created_at":"2026-07-05T11:56:11Z"},{"alias_kind":"pith_short_8","alias_value":"LFQEZOR6","created_at":"2026-07-05T11:56:11Z"}],"graph_snapshots":[{"event_id":"sha256:19f2e14fc29b2a2f287b9761c7c6f175eff37f84da0d73f7a2f77d05f30a148f","target":"graph","created_at":"2026-07-05T11:56:11Z","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/1904.03858/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For the tensor PCA (principal component analysis) problem, we propose a new hierarchy of increasingly powerful algorithms with increasing runtime. Our hierarchy is analogous to the sum-of-squares (SOS) hierarchy but is instead inspired by statistical physics and related algorithms such as belief propagation and AMP (approximate message passing). Our level-$\\ell$ algorithm can be thought of as a linearized message-passing algorithm that keeps track of $\\ell$-wise dependencies among the hidden variables. Specifically, our algorithms are spectral methods based on the Kikuchi Hessian, which genera","authors_text":"Ahmed El Alaoui, Alexander S. Wein, Cristopher Moore","cross_cats":["cond-mat.stat-mech","cs.LG","math.ST","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-08T06:26:35Z","title":"The Kikuchi Hierarchy and Tensor PCA"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03858","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:ae75cfaf7a9ab4b9ca7dfae867ebc1cf1f4d790ed303fb994b406ef9ebdcfe13","target":"record","created_at":"2026-07-05T11:56:11Z","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":"acba4fffce1ca1cf2fe990592af1c3fa52630034367a4061cd3780aa32c09e25","cross_cats_sorted":["cond-mat.stat-mech","cs.LG","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-08T06:26:35Z","title_canon_sha256":"1ede8f06d5313813bbf1a4ee6c6ee6c696733daba2a0eecd7c925a4b9b5ba41c"},"schema_version":"1.0","source":{"id":"1904.03858","kind":"arxiv","version":3}},"canonical_sha256":"59604cba3e2897b96370b6f498bcf20eec36f8bd21ac39ed66e96bba959f401e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59604cba3e2897b96370b6f498bcf20eec36f8bd21ac39ed66e96bba959f401e","first_computed_at":"2026-07-05T11:56:11.585783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:56:11.585783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lJgGLcNFDDbuCav0kt6jl2I8qDMHpybMWncdn4jYGuNRTen32DAKmsutxFZaqX46CVZa4PJSFrHFawhFWOB7Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:56:11.586395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.03858","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae75cfaf7a9ab4b9ca7dfae867ebc1cf1f4d790ed303fb994b406ef9ebdcfe13","sha256:19f2e14fc29b2a2f287b9761c7c6f175eff37f84da0d73f7a2f77d05f30a148f"],"state_sha256":"356f4be191902510609c63d1f03689f534c184c096d4266f811e844ceeee02c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DGr/DY9iSmAfU0kKaQiq54bV39/nugnKnhDFFn5IRJJseOQI26ZCfNy3AsMt25z8ChJclcQb6DYfNzVTnoXFDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T20:33:21.244870Z","bundle_sha256":"acabea3848f44124dc5b9e8c34d7b9f53ca7c42256f7535e58d18cbd181bb8d6"}}