{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:AU47RCJSLRNNI7SJFAOI6BA2RG","short_pith_number":"pith:AU47RCJS","canonical_record":{"source":{"id":"2011.04253","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2020-11-09T08:58:38Z","cross_cats_sorted":[],"title_canon_sha256":"b603790b1c79f370c1de7b7d570107b565a57c630adc844284deffeb99eb3a24","abstract_canon_sha256":"d53e590f8c8bbc9344fde5c6732e260124b1124870cfc979a91acd09be4204fa"},"schema_version":"1.0"},"canonical_sha256":"0539f889325c5ad47e49281c8f041a89a46e7c6477c9f85fbcaf26bca67559f1","source":{"kind":"arxiv","id":"2011.04253","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.04253","created_at":"2026-07-05T05:40:19Z"},{"alias_kind":"arxiv_version","alias_value":"2011.04253v2","created_at":"2026-07-05T05:40:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.04253","created_at":"2026-07-05T05:40:19Z"},{"alias_kind":"pith_short_12","alias_value":"AU47RCJSLRNN","created_at":"2026-07-05T05:40:19Z"},{"alias_kind":"pith_short_16","alias_value":"AU47RCJSLRNNI7SJ","created_at":"2026-07-05T05:40:19Z"},{"alias_kind":"pith_short_8","alias_value":"AU47RCJS","created_at":"2026-07-05T05:40:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:AU47RCJSLRNNI7SJFAOI6BA2RG","target":"record","payload":{"canonical_record":{"source":{"id":"2011.04253","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2020-11-09T08:58:38Z","cross_cats_sorted":[],"title_canon_sha256":"b603790b1c79f370c1de7b7d570107b565a57c630adc844284deffeb99eb3a24","abstract_canon_sha256":"d53e590f8c8bbc9344fde5c6732e260124b1124870cfc979a91acd09be4204fa"},"schema_version":"1.0"},"canonical_sha256":"0539f889325c5ad47e49281c8f041a89a46e7c6477c9f85fbcaf26bca67559f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:40:19.704522Z","signature_b64":"x3NbjjaxPFgF+qxnB04JbLqTbStLqw3MdVTFspp6GR1x2hCKGs5leS7mQR0vnKxyct774MKblzA06vbONc1cCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0539f889325c5ad47e49281c8f041a89a46e7c6477c9f85fbcaf26bca67559f1","last_reissued_at":"2026-07-05T05:40:19.704105Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:40:19.704105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2011.04253","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":"2026-07-05T05:40:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hGLxlJg63uxT92JfpK8B6JhIXHrVpcKdf2rV0YA/VFhB9ET9dulNrLfH2iyhBBc/+DbUNKVEVuoHMKsVwdsdAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:25:01.517383Z"},"content_sha256":"99a289b35322b05e0ba93693143cad3058f319c1b78141003eb218f17c10cda3","schema_version":"1.0","event_id":"sha256:99a289b35322b05e0ba93693143cad3058f319c1b78141003eb218f17c10cda3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:AU47RCJSLRNNI7SJFAOI6BA2RG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Machinery for Proving Sum-of-Squares Lower Bounds on Certification Problems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Aaron Potechin, Goutham Rajendran","submitted_at":"2020-11-09T08:58:38Z","abstract_excerpt":"In this paper, we construct general machinery for proving Sum-of-Squares lower bounds on certification problems by generalizing the techniques used by Barak et al. [FOCS 2016] to prove Sum-of-Squares lower bounds for planted clique. Using this machinery, we prove degree $n^{\\epsilon}$ Sum-of-Squares lower bounds for tensor PCA, the Wishart model of sparse PCA, and a variant of planted clique which we call planted slightly denser subgraph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.04253","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2011.04253/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":"2026-07-05T05:40:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FZ6aZq9F+42hHJm70jvqdcLWtUmFd9iF5Xwezn81XPVz7sKAwNNvoKl+6bev9R5Gf5RnffReZ/NApoiloy9/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:25:01.517984Z"},"content_sha256":"3093813f7fd653281845024d1f616097b64db42d0f3e84ca673c69c77e13f69d","schema_version":"1.0","event_id":"sha256:3093813f7fd653281845024d1f616097b64db42d0f3e84ca673c69c77e13f69d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AU47RCJSLRNNI7SJFAOI6BA2RG/bundle.json","state_url":"https://pith.science/pith/AU47RCJSLRNNI7SJFAOI6BA2RG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AU47RCJSLRNNI7SJFAOI6BA2RG/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":"2026-08-04T17:25:01Z","links":{"resolver":"https://pith.science/pith/AU47RCJSLRNNI7SJFAOI6BA2RG","bundle":"https://pith.science/pith/AU47RCJSLRNNI7SJFAOI6BA2RG/bundle.json","state":"https://pith.science/pith/AU47RCJSLRNNI7SJFAOI6BA2RG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AU47RCJSLRNNI7SJFAOI6BA2RG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:AU47RCJSLRNNI7SJFAOI6BA2RG","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":"d53e590f8c8bbc9344fde5c6732e260124b1124870cfc979a91acd09be4204fa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2020-11-09T08:58:38Z","title_canon_sha256":"b603790b1c79f370c1de7b7d570107b565a57c630adc844284deffeb99eb3a24"},"schema_version":"1.0","source":{"id":"2011.04253","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.04253","created_at":"2026-07-05T05:40:19Z"},{"alias_kind":"arxiv_version","alias_value":"2011.04253v2","created_at":"2026-07-05T05:40:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.04253","created_at":"2026-07-05T05:40:19Z"},{"alias_kind":"pith_short_12","alias_value":"AU47RCJSLRNN","created_at":"2026-07-05T05:40:19Z"},{"alias_kind":"pith_short_16","alias_value":"AU47RCJSLRNNI7SJ","created_at":"2026-07-05T05:40:19Z"},{"alias_kind":"pith_short_8","alias_value":"AU47RCJS","created_at":"2026-07-05T05:40:19Z"}],"graph_snapshots":[{"event_id":"sha256:3093813f7fd653281845024d1f616097b64db42d0f3e84ca673c69c77e13f69d","target":"graph","created_at":"2026-07-05T05:40:19Z","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/2011.04253/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we construct general machinery for proving Sum-of-Squares lower bounds on certification problems by generalizing the techniques used by Barak et al. [FOCS 2016] to prove Sum-of-Squares lower bounds for planted clique. Using this machinery, we prove degree $n^{\\epsilon}$ Sum-of-Squares lower bounds for tensor PCA, the Wishart model of sparse PCA, and a variant of planted clique which we call planted slightly denser subgraph.","authors_text":"Aaron Potechin, Goutham Rajendran","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2020-11-09T08:58:38Z","title":"Machinery for Proving Sum-of-Squares Lower Bounds on Certification Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.04253","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":"sha256:99a289b35322b05e0ba93693143cad3058f319c1b78141003eb218f17c10cda3","target":"record","created_at":"2026-07-05T05:40:19Z","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":"d53e590f8c8bbc9344fde5c6732e260124b1124870cfc979a91acd09be4204fa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2020-11-09T08:58:38Z","title_canon_sha256":"b603790b1c79f370c1de7b7d570107b565a57c630adc844284deffeb99eb3a24"},"schema_version":"1.0","source":{"id":"2011.04253","kind":"arxiv","version":2}},"canonical_sha256":"0539f889325c5ad47e49281c8f041a89a46e7c6477c9f85fbcaf26bca67559f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0539f889325c5ad47e49281c8f041a89a46e7c6477c9f85fbcaf26bca67559f1","first_computed_at":"2026-07-05T05:40:19.704105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:40:19.704105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x3NbjjaxPFgF+qxnB04JbLqTbStLqw3MdVTFspp6GR1x2hCKGs5leS7mQR0vnKxyct774MKblzA06vbONc1cCA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:40:19.704522Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.04253","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99a289b35322b05e0ba93693143cad3058f319c1b78141003eb218f17c10cda3","sha256:3093813f7fd653281845024d1f616097b64db42d0f3e84ca673c69c77e13f69d"],"state_sha256":"2e46e198b7ce3dae656441c10702e61c57d77747e962d79853aa1bbe82ca26b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RBObxB9ooAjIdFRCd4cx+ipSZnRHkHfTaVHPI6N+Zn56n2i+tlM+rq7z8dV2mw0Fyfjl+mWbsYiZJmv++bhOAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T17:25:01.521868Z","bundle_sha256":"a2ebe1fa4927f91f7a83e792fc0bcf7ce2bfd5b45c3823ba11fa8451779cab48"}}