{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PHULMFHIRUBNKYPLOBGTKSVOLP","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":"46e8839e2bd5c9ed01eb9ada39fad7f75cb141388b2e98eca34ec35d3bfe92d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-10-28T07:45:34Z","title_canon_sha256":"2076eaf5cc45c6c6a8f75f8197acd1a0cb57822ee8b123f1845b44c09161c7a6"},"schema_version":"1.0","source":{"id":"1110.6271","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6271","created_at":"2026-05-18T03:59:13Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6271v2","created_at":"2026-05-18T03:59:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6271","created_at":"2026-05-18T03:59:13Z"},{"alias_kind":"pith_short_12","alias_value":"PHULMFHIRUBN","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PHULMFHIRUBNKYPL","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PHULMFHI","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:b358c77378775f0a814c44184e09edb4c6b633b5962afaaaab8bedd394374e14","target":"graph","created_at":"2026-05-18T03:59:13Z","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 consider the complexity of two questions on polynomials given by arithmetic circuits: testing whether a monomial is present and counting the number of monomials. We show that these problems are complete for subclasses of the counting hierarchy which had few or no known natural complete problems. We also study these questions for circuits computing multilinear polynomials.","authors_text":"Guillaume Malod, Herv\\'e Fournier, Stefan Mengel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-10-28T07:45:34Z","title":"Monomials in arithmetic circuits: Complete problems in the counting hierarchy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6271","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":"sha256:8120e6a1ba7f7e96ed64d6d91a31b8fe990f0b559816b59ff7912270e5b3ccd3","target":"record","created_at":"2026-05-18T03:59:13Z","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":"46e8839e2bd5c9ed01eb9ada39fad7f75cb141388b2e98eca34ec35d3bfe92d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-10-28T07:45:34Z","title_canon_sha256":"2076eaf5cc45c6c6a8f75f8197acd1a0cb57822ee8b123f1845b44c09161c7a6"},"schema_version":"1.0","source":{"id":"1110.6271","kind":"arxiv","version":2}},"canonical_sha256":"79e8b614e88d02d561eb704d354aae5bdc78ff463a8b124e9a30af4a8187bbe2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79e8b614e88d02d561eb704d354aae5bdc78ff463a8b124e9a30af4a8187bbe2","first_computed_at":"2026-05-18T03:59:13.696109Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:13.696109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NIZ0fCJPVJxwiba0bt0BVRooI+UwJU9vqXeDMa3A0mP/lr2MCp8c1qRA/nCY01SECym5casAyTcy6APJq9iwAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:13.696916Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6271","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8120e6a1ba7f7e96ed64d6d91a31b8fe990f0b559816b59ff7912270e5b3ccd3","sha256:b358c77378775f0a814c44184e09edb4c6b633b5962afaaaab8bedd394374e14"],"state_sha256":"2d197d974225dc58f0d7e7dcf5810b7521dc8b5f53215f6664f847550d84381c"}