{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3EGYX7A7CSUQKDBOWWZ6WES6UL","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":"ef729dd4d55581928e6e2d267e657144d6feb518e30f50403e58d220b9c3de2a","cross_cats_sorted":["cs.DS","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-11-28T00:00:59Z","title_canon_sha256":"23bcaf3ec1ffaf7b7e996893bcd620f4c56055b8f1109c88ed52a184fec6c35d"},"schema_version":"1.0","source":{"id":"1311.7178","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7178","created_at":"2026-05-18T03:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7178v1","created_at":"2026-05-18T03:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7178","created_at":"2026-05-18T03:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"3EGYX7A7CSUQ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3EGYX7A7CSUQKDBO","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3EGYX7A7","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:ac935c799cb3a6a1fa4063a4f540f6d9ea1ec0aa39716045e1ba619cc75cc1a8","target":"graph","created_at":"2026-05-18T03:05:57Z","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":"We give a deterministic algorithm for approximately counting satisfying assignments of a degree-$d$ polynomial threshold function (PTF). Given a degree-$d$ input polynomial $p(x_1,\\dots,x_n)$ over $R^n$ and a parameter $\\epsilon> 0$, our algorithm approximates $\\Pr_{x \\sim \\{-1,1\\}^n}[p(x) \\geq 0]$ to within an additive $\\pm \\epsilon$ in time $O_{d,\\epsilon}(1)\\cdot \\mathop{poly}(n^d)$. (Any sort of efficient multiplicative approximation is impossible even for randomized algorithms assuming $NP\\not=RP$.) Note that the running time of our algorithm (as a function of $n^d$, the number of coeffic","authors_text":"Anindya De, Rocco Servedio","cross_cats":["cs.DS","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-11-28T00:00:59Z","title":"Efficient deterministic approximate counting for low-degree polynomial threshold functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7178","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":"sha256:215cc86e088a1d46c8f6c3f2d46e2d049aec6d12df20a99569a4fd170ea4e350","target":"record","created_at":"2026-05-18T03:05:57Z","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":"ef729dd4d55581928e6e2d267e657144d6feb518e30f50403e58d220b9c3de2a","cross_cats_sorted":["cs.DS","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-11-28T00:00:59Z","title_canon_sha256":"23bcaf3ec1ffaf7b7e996893bcd620f4c56055b8f1109c88ed52a184fec6c35d"},"schema_version":"1.0","source":{"id":"1311.7178","kind":"arxiv","version":1}},"canonical_sha256":"d90d8bfc1f14a9050c2eb5b3eb125ea2c19df7308cb1ce303047a6e6c35a40aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d90d8bfc1f14a9050c2eb5b3eb125ea2c19df7308cb1ce303047a6e6c35a40aa","first_computed_at":"2026-05-18T03:05:57.043531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:57.043531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VcIofHDfH4tjCGyN3Uo35QTFDHXv2ahbmETvJLN5nTsnRGV7ywLq4WYuAXdv1GUukC3DZGsd/JaPJ1f7is1eCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:57.044181Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.7178","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:215cc86e088a1d46c8f6c3f2d46e2d049aec6d12df20a99569a4fd170ea4e350","sha256:ac935c799cb3a6a1fa4063a4f540f6d9ea1ec0aa39716045e1ba619cc75cc1a8"],"state_sha256":"080dfd61409dbdd825bb24cdfb786ab35b823a2ccc3714acea60c7b34faf95e9"}