{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ZXIJGA4PPJNTLG7TKG7RNVSM63","short_pith_number":"pith:ZXIJGA4P","schema_version":"1.0","canonical_sha256":"cdd093038f7a5b359bf351bf16d64cf6f4edb7c1e10147a787faf3a8fc9d17b9","source":{"kind":"arxiv","id":"1801.06338","version":2},"attestation_state":"computed","paper":{"title":"Boolean constant degree functions on the slice are juntas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Ferdinand Ihringer, Yuval Filmus","submitted_at":"2018-01-19T09:27:27Z","abstract_excerpt":"We show that a Boolean degree $d$ function on the slice $\\binom{[n]}{k} = \\{ (x_1,\\ldots,x_n) \\in \\{0,1\\} : \\sum_{i=1}^n x_i = k \\}$ is a junta, assuming that $k,n-k$ are large enough. This generalizes a classical result of Nisan and Szegedy on the hypercube. Moreover, we show that the maximum number of coordinates that a Boolean degree $d$ function can depend on is the same on the slice and the hypercube."},"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":"1801.06338","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-19T09:27:27Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"d4db47155f9c52d4b47a00785bd1f9290211cf71d034dce1639b843824cc42b9","abstract_canon_sha256":"fb9ba9b7a429e972ab0aae72a1d502a5fdf2b8c1c4712fae2a1abe2d51ba51e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:23.079040Z","signature_b64":"/3ln76/KtF9Pe6Qh2/akZcJjG/5sa0guVwjm1CHJFXQBPi/wjwd2WfEvka3z073Q1d2LHuMI28W80ViCKVELAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdd093038f7a5b359bf351bf16d64cf6f4edb7c1e10147a787faf3a8fc9d17b9","last_reissued_at":"2026-05-18T00:25:23.078442Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:23.078442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Boolean constant degree functions on the slice are juntas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Ferdinand Ihringer, Yuval Filmus","submitted_at":"2018-01-19T09:27:27Z","abstract_excerpt":"We show that a Boolean degree $d$ function on the slice $\\binom{[n]}{k} = \\{ (x_1,\\ldots,x_n) \\in \\{0,1\\} : \\sum_{i=1}^n x_i = k \\}$ is a junta, assuming that $k,n-k$ are large enough. This generalizes a classical result of Nisan and Szegedy on the hypercube. Moreover, we show that the maximum number of coordinates that a Boolean degree $d$ function can depend on is the same on the slice and the hypercube."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06338","kind":"arxiv","version":2},"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":"1801.06338","created_at":"2026-05-18T00:25:23.078527+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.06338v2","created_at":"2026-05-18T00:25:23.078527+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.06338","created_at":"2026-05-18T00:25:23.078527+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZXIJGA4PPJNT","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZXIJGA4PPJNTLG7T","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZXIJGA4P","created_at":"2026-05-18T12:33:07.085635+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/ZXIJGA4PPJNTLG7TKG7RNVSM63","json":"https://pith.science/pith/ZXIJGA4PPJNTLG7TKG7RNVSM63.json","graph_json":"https://pith.science/api/pith-number/ZXIJGA4PPJNTLG7TKG7RNVSM63/graph.json","events_json":"https://pith.science/api/pith-number/ZXIJGA4PPJNTLG7TKG7RNVSM63/events.json","paper":"https://pith.science/paper/ZXIJGA4P"},"agent_actions":{"view_html":"https://pith.science/pith/ZXIJGA4PPJNTLG7TKG7RNVSM63","download_json":"https://pith.science/pith/ZXIJGA4PPJNTLG7TKG7RNVSM63.json","view_paper":"https://pith.science/paper/ZXIJGA4P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.06338&json=true","fetch_graph":"https://pith.science/api/pith-number/ZXIJGA4PPJNTLG7TKG7RNVSM63/graph.json","fetch_events":"https://pith.science/api/pith-number/ZXIJGA4PPJNTLG7TKG7RNVSM63/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZXIJGA4PPJNTLG7TKG7RNVSM63/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZXIJGA4PPJNTLG7TKG7RNVSM63/action/storage_attestation","attest_author":"https://pith.science/pith/ZXIJGA4PPJNTLG7TKG7RNVSM63/action/author_attestation","sign_citation":"https://pith.science/pith/ZXIJGA4PPJNTLG7TKG7RNVSM63/action/citation_signature","submit_replication":"https://pith.science/pith/ZXIJGA4PPJNTLG7TKG7RNVSM63/action/replication_record"}},"created_at":"2026-05-18T00:25:23.078527+00:00","updated_at":"2026-05-18T00:25:23.078527+00:00"}