{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:NENTF4X4OWXEMVRSTUKA6WE5QS","short_pith_number":"pith:NENTF4X4","schema_version":"1.0","canonical_sha256":"691b32f2fc75ae4656329d140f589d849f7c99d5e055f7b39685384630947b77","source":{"kind":"arxiv","id":"1611.04548","version":1},"attestation_state":"computed","paper":{"title":"Real Stable Polynomials and Matroids: Optimization and Counting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.OC","math.PR"],"primary_cat":"cs.DS","authors_text":"Damian Straszak, Nisheeth K. Vishnoi","submitted_at":"2016-11-14T20:11:38Z","abstract_excerpt":"A great variety of fundamental optimization and counting problems arising in computer science, mathematics and physics can be reduced to one of the following computational tasks involving polynomials and set systems: given an $m$-variate real polynomial $g$ and a family of subsets $B$ of $[m]$, (1) find $S\\in B$ such that the monomial in $g$ corresponding to $S$ has the largest coefficient in $g$, or (2) compute the sum of coefficients of monomials in $g$ corresponding to all the sets in $B$. Special cases of these problems, such as computing permanents, sampling from DPPs and maximizing subde"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1611.04548","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-14T20:11:38Z","cross_cats_sorted":["math.CO","math.OC","math.PR"],"title_canon_sha256":"52e8a8d30e79fc40325b6d9b8e5861f45ab7cba7a45c6f3228db05a8904f7a7c","abstract_canon_sha256":"8b0bb6c2da0f68b7218eef3ca4ba0e9f230548041243249cc44d9452ae437b00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:12.815377Z","signature_b64":"61FtUFXLl47zK1RRGUeLE0Gq8WDmjWD8UQvDKI/gGF3F8r9sN+IV+YlI2KDrmNYqAm9isqTlsWBoZbh/Ag2JDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"691b32f2fc75ae4656329d140f589d849f7c99d5e055f7b39685384630947b77","last_reissued_at":"2026-05-18T00:59:12.814736Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:12.814736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Real Stable Polynomials and Matroids: Optimization and Counting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.OC","math.PR"],"primary_cat":"cs.DS","authors_text":"Damian Straszak, Nisheeth K. Vishnoi","submitted_at":"2016-11-14T20:11:38Z","abstract_excerpt":"A great variety of fundamental optimization and counting problems arising in computer science, mathematics and physics can be reduced to one of the following computational tasks involving polynomials and set systems: given an $m$-variate real polynomial $g$ and a family of subsets $B$ of $[m]$, (1) find $S\\in B$ such that the monomial in $g$ corresponding to $S$ has the largest coefficient in $g$, or (2) compute the sum of coefficients of monomials in $g$ corresponding to all the sets in $B$. Special cases of these problems, such as computing permanents, sampling from DPPs and maximizing subde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04548","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1611.04548","created_at":"2026-05-18T00:59:12.814828+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.04548v1","created_at":"2026-05-18T00:59:12.814828+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04548","created_at":"2026-05-18T00:59:12.814828+00:00"},{"alias_kind":"pith_short_12","alias_value":"NENTF4X4OWXE","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"NENTF4X4OWXEMVRS","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"NENTF4X4","created_at":"2026-05-18T12:30:32.724797+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NENTF4X4OWXEMVRSTUKA6WE5QS","json":"https://pith.science/pith/NENTF4X4OWXEMVRSTUKA6WE5QS.json","graph_json":"https://pith.science/api/pith-number/NENTF4X4OWXEMVRSTUKA6WE5QS/graph.json","events_json":"https://pith.science/api/pith-number/NENTF4X4OWXEMVRSTUKA6WE5QS/events.json","paper":"https://pith.science/paper/NENTF4X4"},"agent_actions":{"view_html":"https://pith.science/pith/NENTF4X4OWXEMVRSTUKA6WE5QS","download_json":"https://pith.science/pith/NENTF4X4OWXEMVRSTUKA6WE5QS.json","view_paper":"https://pith.science/paper/NENTF4X4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.04548&json=true","fetch_graph":"https://pith.science/api/pith-number/NENTF4X4OWXEMVRSTUKA6WE5QS/graph.json","fetch_events":"https://pith.science/api/pith-number/NENTF4X4OWXEMVRSTUKA6WE5QS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NENTF4X4OWXEMVRSTUKA6WE5QS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NENTF4X4OWXEMVRSTUKA6WE5QS/action/storage_attestation","attest_author":"https://pith.science/pith/NENTF4X4OWXEMVRSTUKA6WE5QS/action/author_attestation","sign_citation":"https://pith.science/pith/NENTF4X4OWXEMVRSTUKA6WE5QS/action/citation_signature","submit_replication":"https://pith.science/pith/NENTF4X4OWXEMVRSTUKA6WE5QS/action/replication_record"}},"created_at":"2026-05-18T00:59:12.814828+00:00","updated_at":"2026-05-18T00:59:12.814828+00:00"}