{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:4D72TPPKBU3BT6VZZPJ6IZAWR7","short_pith_number":"pith:4D72TPPK","schema_version":"1.0","canonical_sha256":"e0ffa9bdea0d3619fab9cbd3e464168ff2ad6067c5178e1f3af36fc483272f1f","source":{"kind":"arxiv","id":"1404.6535","version":1},"attestation_state":"computed","paper":{"title":"Quadratization of Symmetric Pseudo-Boolean Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.CV","math.CO"],"primary_cat":"math.OC","authors_text":"Aritanan Gruber, Endre Boros, Martin Anthony, Yves Crama","submitted_at":"2014-04-25T20:00:22Z","abstract_excerpt":"A pseudo-Boolean function is a real-valued function $f(x)=f(x_1,x_2,\\ldots,x_n)$ of $n$ binary variables; that is, a mapping from $\\{0,1\\}^n$ to $\\mathbb{R}$. For a pseudo-Boolean function $f(x)$ on $\\{0,1\\}^n$, we say that $g(x,y)$ is a quadratization of $f$ if $g(x,y)$ is a quadratic polynomial depending on $x$ and on $m$ auxiliary binary variables $y_1,y_2,\\ldots,y_m$ such that $f(x)= \\min \\{g(x,y) : y \\in \\{0,1\\}^m \\}$ for all $x \\in \\{0,1\\}^n$. By means of quadratizations, minimization of $f$ is reduced to minimization (over its extended set of variables) of the quadratic function $g(x,y)"},"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":"1404.6535","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-04-25T20:00:22Z","cross_cats_sorted":["cs.CC","cs.CV","math.CO"],"title_canon_sha256":"9af42e8d09b1959e751186932389cdd2a6a019f40519e36b13fabed7a638fc27","abstract_canon_sha256":"e10af07b2c402b6b8721942f6b15a20146e707e5ba2dd52ba793aab3443c8f42"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:06.821516Z","signature_b64":"ZQhEPnmtUikKqde6V4e4dE1oUqE0Kx0njwUEGGGE55UH+tocm9o6sZc3VNvKceAWQGNHW6SEggelagESEl5hDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0ffa9bdea0d3619fab9cbd3e464168ff2ad6067c5178e1f3af36fc483272f1f","last_reissued_at":"2026-05-18T02:53:06.820881Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:06.820881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quadratization of Symmetric Pseudo-Boolean Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.CV","math.CO"],"primary_cat":"math.OC","authors_text":"Aritanan Gruber, Endre Boros, Martin Anthony, Yves Crama","submitted_at":"2014-04-25T20:00:22Z","abstract_excerpt":"A pseudo-Boolean function is a real-valued function $f(x)=f(x_1,x_2,\\ldots,x_n)$ of $n$ binary variables; that is, a mapping from $\\{0,1\\}^n$ to $\\mathbb{R}$. For a pseudo-Boolean function $f(x)$ on $\\{0,1\\}^n$, we say that $g(x,y)$ is a quadratization of $f$ if $g(x,y)$ is a quadratic polynomial depending on $x$ and on $m$ auxiliary binary variables $y_1,y_2,\\ldots,y_m$ such that $f(x)= \\min \\{g(x,y) : y \\in \\{0,1\\}^m \\}$ for all $x \\in \\{0,1\\}^n$. By means of quadratizations, minimization of $f$ is reduced to minimization (over its extended set of variables) of the quadratic function $g(x,y)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6535","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":"1404.6535","created_at":"2026-05-18T02:53:06.820993+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.6535v1","created_at":"2026-05-18T02:53:06.820993+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6535","created_at":"2026-05-18T02:53:06.820993+00:00"},{"alias_kind":"pith_short_12","alias_value":"4D72TPPKBU3B","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4D72TPPKBU3BT6VZ","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4D72TPPK","created_at":"2026-05-18T12:28:14.216126+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/4D72TPPKBU3BT6VZZPJ6IZAWR7","json":"https://pith.science/pith/4D72TPPKBU3BT6VZZPJ6IZAWR7.json","graph_json":"https://pith.science/api/pith-number/4D72TPPKBU3BT6VZZPJ6IZAWR7/graph.json","events_json":"https://pith.science/api/pith-number/4D72TPPKBU3BT6VZZPJ6IZAWR7/events.json","paper":"https://pith.science/paper/4D72TPPK"},"agent_actions":{"view_html":"https://pith.science/pith/4D72TPPKBU3BT6VZZPJ6IZAWR7","download_json":"https://pith.science/pith/4D72TPPKBU3BT6VZZPJ6IZAWR7.json","view_paper":"https://pith.science/paper/4D72TPPK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.6535&json=true","fetch_graph":"https://pith.science/api/pith-number/4D72TPPKBU3BT6VZZPJ6IZAWR7/graph.json","fetch_events":"https://pith.science/api/pith-number/4D72TPPKBU3BT6VZZPJ6IZAWR7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4D72TPPKBU3BT6VZZPJ6IZAWR7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4D72TPPKBU3BT6VZZPJ6IZAWR7/action/storage_attestation","attest_author":"https://pith.science/pith/4D72TPPKBU3BT6VZZPJ6IZAWR7/action/author_attestation","sign_citation":"https://pith.science/pith/4D72TPPKBU3BT6VZZPJ6IZAWR7/action/citation_signature","submit_replication":"https://pith.science/pith/4D72TPPKBU3BT6VZZPJ6IZAWR7/action/replication_record"}},"created_at":"2026-05-18T02:53:06.820993+00:00","updated_at":"2026-05-18T02:53:06.820993+00:00"}