{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TUANSWFSGR6OGOOE2JUDTT6KMD","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":"4cbcb002d76ba3f23294231369a111f3061d84b65f469efccc9c9efb626e1c02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-10-10T19:05:54Z","title_canon_sha256":"886cb117b96a9388d2f2ee0469706b0624515b246cad192c875ce4fb73930bff"},"schema_version":"1.0","source":{"id":"1610.03029","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03029","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03029v1","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03029","created_at":"2026-05-18T01:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"TUANSWFSGR6O","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TUANSWFSGR6OGOOE","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TUANSWFS","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:d4fbcb2b34182f0ba91035f90acf646e99753bfe0ee5a7049453657fa9e7e213","target":"graph","created_at":"2026-05-18T01:02:50Z","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":"For a $k$-ary predicate $P$, a random instance of CSP$(P)$ with $n$ variables and $m$ constraints is unsatisfiable with high probability when $m \\gg n$. The natural algorithmic task in this regime is \\emph{refutation}: finding a proof that a given random instance is unsatisfiable. Recent work of Allen et al. suggests that the difficulty of refuting CSP$(P)$ using an SDP is determined by a parameter $\\mathrm{cmplx}(P)$, the smallest $t$ for which there does not exist a $t$-wise uniform distribution over satisfying assignments to $P$. In particular they show that random instances of CSP$(P)$ wit","authors_text":"David Witmer, Ryuhei Mori","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-10-10T19:05:54Z","title":"Lower bounds for CSP refutation by SDP hierarchies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03029","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:e0640834b2f98bd1cc0e471385275ff82e9bdde4cedc3ca22be32109f8900639","target":"record","created_at":"2026-05-18T01:02:50Z","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":"4cbcb002d76ba3f23294231369a111f3061d84b65f469efccc9c9efb626e1c02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-10-10T19:05:54Z","title_canon_sha256":"886cb117b96a9388d2f2ee0469706b0624515b246cad192c875ce4fb73930bff"},"schema_version":"1.0","source":{"id":"1610.03029","kind":"arxiv","version":1}},"canonical_sha256":"9d00d958b2347ce339c4d26839cfca60e912f951d8def369c82a42f41f54d2d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d00d958b2347ce339c4d26839cfca60e912f951d8def369c82a42f41f54d2d5","first_computed_at":"2026-05-18T01:02:50.159355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:50.159355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I3L7VyAhG5601CUr1wrcBgfK46UCusYeMC2xJsVvurCdRFgaR/KhYJIHUuIwJLsFuSEHa74rIrqIH4bkPmcvCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:50.159755Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03029","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0640834b2f98bd1cc0e471385275ff82e9bdde4cedc3ca22be32109f8900639","sha256:d4fbcb2b34182f0ba91035f90acf646e99753bfe0ee5a7049453657fa9e7e213"],"state_sha256":"a4a720c40472e5cc4dcee4050dacabad0ca977f1f84bf2639660eea15af45e10"}