{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:LZGOTFADN5GDQ5LLQBMQQ3GVQJ","short_pith_number":"pith:LZGOTFAD","schema_version":"1.0","canonical_sha256":"5e4ce994036f4c38756b8059086cd5826a889618f0ad6fde94100404f884e1fe","source":{"kind":"arxiv","id":"2102.04703","version":4},"attestation_state":"computed","paper":{"title":"Inapproximability of a Pair of Forms Defining a Partial Boolean Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","math.OC"],"primary_cat":"cs.LG","authors_text":"Bjoern Andres, David Stein","submitted_at":"2021-02-09T08:46:50Z","abstract_excerpt":"We consider the problem of jointly minimizing forms of two Boolean functions $f, g \\colon \\{0,1\\}^J \\to \\{0,1\\}$ such that $f + g \\leq 1$ and so as to separate disjoint sets $A \\cup B \\subseteq \\{0,1\\}^J$ such that $f(A) = \\{1\\}$ and $g(B) = \\{1\\}$. We hypothesize that this problem is easier to solve or approximate than the well-understood problem of minimizing the form of one Boolean function $h: \\{0,1\\}^J \\to \\{0,1\\}$ such that $h(A) = \\{1\\}$ and $h(B) = \\{0\\}$. For a large class of forms, including binary decision trees and ordered binary decision diagrams, we refute this hypothesis. For di"},"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":"2102.04703","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-02-09T08:46:50Z","cross_cats_sorted":["cs.CC","cs.DM","math.OC"],"title_canon_sha256":"8d0f4bfd1eb129a501c9a0fe1cfd6efc2e3dbd3b3300308cd53a5d74b919b688","abstract_canon_sha256":"aba3ae25acc6b4779c0efa96d4e09c4c26950a4ab543bd7a627eb4c9958cc9fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:55:35.697836Z","signature_b64":"Z7gSbTAu1bn0Irm+FyJIB2exdM13lzW0C/uJw5MoyhgP8RXVjkyxnl7wesxUeWw+ELsQS8QRfycbIUHYYwK/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e4ce994036f4c38756b8059086cd5826a889618f0ad6fde94100404f884e1fe","last_reissued_at":"2026-07-05T04:55:35.697375Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:55:35.697375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inapproximability of a Pair of Forms Defining a Partial Boolean Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","math.OC"],"primary_cat":"cs.LG","authors_text":"Bjoern Andres, David Stein","submitted_at":"2021-02-09T08:46:50Z","abstract_excerpt":"We consider the problem of jointly minimizing forms of two Boolean functions $f, g \\colon \\{0,1\\}^J \\to \\{0,1\\}$ such that $f + g \\leq 1$ and so as to separate disjoint sets $A \\cup B \\subseteq \\{0,1\\}^J$ such that $f(A) = \\{1\\}$ and $g(B) = \\{1\\}$. We hypothesize that this problem is easier to solve or approximate than the well-understood problem of minimizing the form of one Boolean function $h: \\{0,1\\}^J \\to \\{0,1\\}$ such that $h(A) = \\{1\\}$ and $h(B) = \\{0\\}$. For a large class of forms, including binary decision trees and ordered binary decision diagrams, we refute this hypothesis. For di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.04703","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2102.04703/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2102.04703","created_at":"2026-07-05T04:55:35.697433+00:00"},{"alias_kind":"arxiv_version","alias_value":"2102.04703v4","created_at":"2026-07-05T04:55:35.697433+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.04703","created_at":"2026-07-05T04:55:35.697433+00:00"},{"alias_kind":"pith_short_12","alias_value":"LZGOTFADN5GD","created_at":"2026-07-05T04:55:35.697433+00:00"},{"alias_kind":"pith_short_16","alias_value":"LZGOTFADN5GDQ5LL","created_at":"2026-07-05T04:55:35.697433+00:00"},{"alias_kind":"pith_short_8","alias_value":"LZGOTFAD","created_at":"2026-07-05T04:55:35.697433+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/LZGOTFADN5GDQ5LLQBMQQ3GVQJ","json":"https://pith.science/pith/LZGOTFADN5GDQ5LLQBMQQ3GVQJ.json","graph_json":"https://pith.science/api/pith-number/LZGOTFADN5GDQ5LLQBMQQ3GVQJ/graph.json","events_json":"https://pith.science/api/pith-number/LZGOTFADN5GDQ5LLQBMQQ3GVQJ/events.json","paper":"https://pith.science/paper/LZGOTFAD"},"agent_actions":{"view_html":"https://pith.science/pith/LZGOTFADN5GDQ5LLQBMQQ3GVQJ","download_json":"https://pith.science/pith/LZGOTFADN5GDQ5LLQBMQQ3GVQJ.json","view_paper":"https://pith.science/paper/LZGOTFAD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2102.04703&json=true","fetch_graph":"https://pith.science/api/pith-number/LZGOTFADN5GDQ5LLQBMQQ3GVQJ/graph.json","fetch_events":"https://pith.science/api/pith-number/LZGOTFADN5GDQ5LLQBMQQ3GVQJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LZGOTFADN5GDQ5LLQBMQQ3GVQJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LZGOTFADN5GDQ5LLQBMQQ3GVQJ/action/storage_attestation","attest_author":"https://pith.science/pith/LZGOTFADN5GDQ5LLQBMQQ3GVQJ/action/author_attestation","sign_citation":"https://pith.science/pith/LZGOTFADN5GDQ5LLQBMQQ3GVQJ/action/citation_signature","submit_replication":"https://pith.science/pith/LZGOTFADN5GDQ5LLQBMQQ3GVQJ/action/replication_record"}},"created_at":"2026-07-05T04:55:35.697433+00:00","updated_at":"2026-07-05T04:55:35.697433+00:00"}