{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:SWIWLUDJFVUV4COOJRFZA5TOOR","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":"a532c760ca7e03bb5e6f4b9191e0fb28135256cdb27f9dc8290637f07135a79b","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2024-11-22T18:58:08Z","title_canon_sha256":"803f631135dfdf6ac7bd15f9cd2f276f23eb077218488fc7c97927187123aa9d"},"schema_version":"1.0","source":{"id":"2411.15136","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15136","created_at":"2026-07-05T09:39:16Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15136v1","created_at":"2026-07-05T09:39:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15136","created_at":"2026-07-05T09:39:16Z"},{"alias_kind":"pith_short_12","alias_value":"SWIWLUDJFVUV","created_at":"2026-07-05T09:39:16Z"},{"alias_kind":"pith_short_16","alias_value":"SWIWLUDJFVUV4COO","created_at":"2026-07-05T09:39:16Z"},{"alias_kind":"pith_short_8","alias_value":"SWIWLUDJ","created_at":"2026-07-05T09:39:16Z"}],"graph_snapshots":[{"event_id":"sha256:ec9587d12d22588317895ac7246e1028a68eb403dc55835d4ed7b1f9c46b8fb3","target":"graph","created_at":"2026-07-05T09:39:16Z","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/2411.15136/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\Sigma_1,\\ldots,\\Sigma_k$ be finite alphabets, and let $\\mu$ be a distribution over $\\Sigma_1 \\times \\dots \\times \\Sigma_k$ in which the probability of each atom is at least $\\alpha$. We prove that if $\\mu$ does not admit Abelian embeddings, and $f_i: \\Sigma_i \\to \\mathbb{C}$ are $1$-bounded functions (for $i=1,\\ldots,k$) such that \\[ \\left|\\mathbb{E}_{(x_1,\\dots,x_k) \\sim \\mu^{\\otimes n}}\\Big[f_1(x_1) \\dots f_k(x_k)\\Big]\\right| \\geq \\varepsilon, \\] then there exists $L\\colon \\Sigma_1^n\\to\\mathbb{C}$ of degree at most $d$ and $\\|L\\|_2\\leq 1$ such that $|\\langle f_1, L\\rangle|\\geq \\delta$,","authors_text":"Amey Bhangale, Dor Minzer, Subhash Khot, Yang P. Liu","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2024-11-22T18:58:08Z","title":"On Approximability of Satisfiable $k$-CSPs: VII"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15136","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:ed5b42dca9e194b4012ad86978aa47e83b833dca1b002a77bbce8261669313cb","target":"record","created_at":"2026-07-05T09:39:16Z","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":"a532c760ca7e03bb5e6f4b9191e0fb28135256cdb27f9dc8290637f07135a79b","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2024-11-22T18:58:08Z","title_canon_sha256":"803f631135dfdf6ac7bd15f9cd2f276f23eb077218488fc7c97927187123aa9d"},"schema_version":"1.0","source":{"id":"2411.15136","kind":"arxiv","version":1}},"canonical_sha256":"959165d0692d695e09ce4c4b90766e747b774bba345d0e542809d517b54446f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"959165d0692d695e09ce4c4b90766e747b774bba345d0e542809d517b54446f1","first_computed_at":"2026-07-05T09:39:16.740767Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:39:16.740767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vvmdYSTzGbTq8KYs4rllBXWgklG/QqQrV6cxsFvkWfWtMIgyw9k1ePqIr/CwbOsiPRz0YhOoPrYk+LxTGY57BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:39:16.741182Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.15136","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed5b42dca9e194b4012ad86978aa47e83b833dca1b002a77bbce8261669313cb","sha256:ec9587d12d22588317895ac7246e1028a68eb403dc55835d4ed7b1f9c46b8fb3"],"state_sha256":"528a93982eda6de1fb06b06c65bbc76e3357d694de8dbe33b9a2974f8fa50ce8"}