{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:CWYZY6QWO6GDERGL2SWCDJH2VO","short_pith_number":"pith:CWYZY6QW","canonical_record":{"source":{"id":"2404.16722","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-04-25T16:34:26Z","cross_cats_sorted":[],"title_canon_sha256":"96d97676c7df51fd7e54e691bcae2d6ddbe1e14a5c9a73c4c702686ec2ffb1e9","abstract_canon_sha256":"6a9a6f81b22494eb65c8e54b77b509eedd73f01a324c71724f691daf6b1b25af"},"schema_version":"1.0"},"canonical_sha256":"15b19c7a16778c3244cbd4ac21a4faab803f11ecad9894f70351e1f06c30c17d","source":{"kind":"arxiv","id":"2404.16722","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.16722","created_at":"2026-07-05T08:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"2404.16722v1","created_at":"2026-07-05T08:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.16722","created_at":"2026-07-05T08:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"CWYZY6QWO6GD","created_at":"2026-07-05T08:12:11Z"},{"alias_kind":"pith_short_16","alias_value":"CWYZY6QWO6GDERGL","created_at":"2026-07-05T08:12:11Z"},{"alias_kind":"pith_short_8","alias_value":"CWYZY6QW","created_at":"2026-07-05T08:12:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:CWYZY6QWO6GDERGL2SWCDJH2VO","target":"record","payload":{"canonical_record":{"source":{"id":"2404.16722","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-04-25T16:34:26Z","cross_cats_sorted":[],"title_canon_sha256":"96d97676c7df51fd7e54e691bcae2d6ddbe1e14a5c9a73c4c702686ec2ffb1e9","abstract_canon_sha256":"6a9a6f81b22494eb65c8e54b77b509eedd73f01a324c71724f691daf6b1b25af"},"schema_version":"1.0"},"canonical_sha256":"15b19c7a16778c3244cbd4ac21a4faab803f11ecad9894f70351e1f06c30c17d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:12:11.766556Z","signature_b64":"4EYAD58GVe//BW4zoGESNjA/adAmb0v7v8OTipAWdmgoy9dmMROqsStqFodBFTiFbzd6JhqCqqPKeYyAZ8BEDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15b19c7a16778c3244cbd4ac21a4faab803f11ecad9894f70351e1f06c30c17d","last_reissued_at":"2026-07-05T08:12:11.766125Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:12:11.766125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.16722","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UJPPbjZYdf4KRpxP7UbduXQMwxlQEnmg2ltHUMMa0yD8OZcGr/dGpoc2n634dp7l7hWeIWkR12L2vVUaL6iSCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T16:08:56.442750Z"},"content_sha256":"4683dcc88a2f3255516ead9f5835c1b4dd9d0c59aef8d746c75140147a4acc18","schema_version":"1.0","event_id":"sha256:4683dcc88a2f3255516ead9f5835c1b4dd9d0c59aef8d746c75140147a4acc18"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:CWYZY6QWO6GDERGL2SWCDJH2VO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Clique Is Hard on Average for Sherali-Adams with Bounded Coefficients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Aaron Potechin, Kilian Risse, Susanna F. de Rezende","submitted_at":"2024-04-25T16:34:26Z","abstract_excerpt":"We prove that Sherali-Adams with polynomially bounded coefficients requires proofs of size $n^{\\Omega(d)}$ to rule out the existence of an $n^{\\Theta(1)}$-clique in Erd\\H{o}s-R\\'{e}nyi random graphs whose maximum clique is of size $d\\leq 2\\log n$. This lower bound is tight up to the multiplicative constant in the exponent. We obtain this result by introducing a technique inspired by pseudo-calibration which may be of independent interest. The technique involves defining a measure on monomials that precisely captures the contribution of a monomial to a refutation. This measure intuitively captu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.16722","kind":"arxiv","version":1},"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/2404.16722/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":"2026-07-05T08:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U5Ir5VcLssOWiQy0ey3AnPTCWmrBG/E0dYVipyx2XYmBZgXdVfKRFm5jNvern43pKLtRgRyPXBykPJPNQc5gDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T16:08:56.443681Z"},"content_sha256":"21f46167bd908aced76881ee0762e6e2f550df5011b1dee8a5756459c22714ac","schema_version":"1.0","event_id":"sha256:21f46167bd908aced76881ee0762e6e2f550df5011b1dee8a5756459c22714ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CWYZY6QWO6GDERGL2SWCDJH2VO/bundle.json","state_url":"https://pith.science/pith/CWYZY6QWO6GDERGL2SWCDJH2VO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CWYZY6QWO6GDERGL2SWCDJH2VO/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":"2026-08-15T16:08:56Z","links":{"resolver":"https://pith.science/pith/CWYZY6QWO6GDERGL2SWCDJH2VO","bundle":"https://pith.science/pith/CWYZY6QWO6GDERGL2SWCDJH2VO/bundle.json","state":"https://pith.science/pith/CWYZY6QWO6GDERGL2SWCDJH2VO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CWYZY6QWO6GDERGL2SWCDJH2VO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:CWYZY6QWO6GDERGL2SWCDJH2VO","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":"6a9a6f81b22494eb65c8e54b77b509eedd73f01a324c71724f691daf6b1b25af","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-04-25T16:34:26Z","title_canon_sha256":"96d97676c7df51fd7e54e691bcae2d6ddbe1e14a5c9a73c4c702686ec2ffb1e9"},"schema_version":"1.0","source":{"id":"2404.16722","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.16722","created_at":"2026-07-05T08:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"2404.16722v1","created_at":"2026-07-05T08:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.16722","created_at":"2026-07-05T08:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"CWYZY6QWO6GD","created_at":"2026-07-05T08:12:11Z"},{"alias_kind":"pith_short_16","alias_value":"CWYZY6QWO6GDERGL","created_at":"2026-07-05T08:12:11Z"},{"alias_kind":"pith_short_8","alias_value":"CWYZY6QW","created_at":"2026-07-05T08:12:11Z"}],"graph_snapshots":[{"event_id":"sha256:21f46167bd908aced76881ee0762e6e2f550df5011b1dee8a5756459c22714ac","target":"graph","created_at":"2026-07-05T08:12:11Z","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/2404.16722/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that Sherali-Adams with polynomially bounded coefficients requires proofs of size $n^{\\Omega(d)}$ to rule out the existence of an $n^{\\Theta(1)}$-clique in Erd\\H{o}s-R\\'{e}nyi random graphs whose maximum clique is of size $d\\leq 2\\log n$. This lower bound is tight up to the multiplicative constant in the exponent. We obtain this result by introducing a technique inspired by pseudo-calibration which may be of independent interest. The technique involves defining a measure on monomials that precisely captures the contribution of a monomial to a refutation. This measure intuitively captu","authors_text":"Aaron Potechin, Kilian Risse, Susanna F. de Rezende","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-04-25T16:34:26Z","title":"Clique Is Hard on Average for Sherali-Adams with Bounded Coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.16722","kind":"arxiv","version":1},"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":"sha256:4683dcc88a2f3255516ead9f5835c1b4dd9d0c59aef8d746c75140147a4acc18","target":"record","created_at":"2026-07-05T08:12:11Z","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":"6a9a6f81b22494eb65c8e54b77b509eedd73f01a324c71724f691daf6b1b25af","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2024-04-25T16:34:26Z","title_canon_sha256":"96d97676c7df51fd7e54e691bcae2d6ddbe1e14a5c9a73c4c702686ec2ffb1e9"},"schema_version":"1.0","source":{"id":"2404.16722","kind":"arxiv","version":1}},"canonical_sha256":"15b19c7a16778c3244cbd4ac21a4faab803f11ecad9894f70351e1f06c30c17d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15b19c7a16778c3244cbd4ac21a4faab803f11ecad9894f70351e1f06c30c17d","first_computed_at":"2026-07-05T08:12:11.766125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:12:11.766125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4EYAD58GVe//BW4zoGESNjA/adAmb0v7v8OTipAWdmgoy9dmMROqsStqFodBFTiFbzd6JhqCqqPKeYyAZ8BEDg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:12:11.766556Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.16722","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4683dcc88a2f3255516ead9f5835c1b4dd9d0c59aef8d746c75140147a4acc18","sha256:21f46167bd908aced76881ee0762e6e2f550df5011b1dee8a5756459c22714ac"],"state_sha256":"1336969580465c3e78fa6a3b1b9baf0d653419a5564bfd3c095593fe7a9081a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HdBg3qoica046ES5lGYoQbfhKhWIsfF8ze7ejIHRWASl7mFutBLkA9BfqnOULsSjwbevTzEm7qkTik0M4ZgBBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T16:08:56.450649Z","bundle_sha256":"e6ae76c818a30c76488796893b29a996758c3fd478cb0a9a1b4ca4ed63bde5cf"}}