{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:6KWI2DQGEMCQAZQNXWOWQQIJ7N","short_pith_number":"pith:6KWI2DQG","schema_version":"1.0","canonical_sha256":"f2ac8d0e06230500660dbd9d684109fb68b47d789b2b9adc2d070a8533b2bfa9","source":{"kind":"arxiv","id":"1810.02729","version":1},"attestation_state":"computed","paper":{"title":"Intersection sizes of linear subspaces with the hypercube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carla Groenland, Tom Johnston","submitted_at":"2018-10-05T14:52:23Z","abstract_excerpt":"We continue the study by Melo and Winter [arXiv:1712.01763, 2017] on the possible intersection sizes of a $k$-dimensional subspace with the vertices of the $n$-dimensional hypercube in Euclidean space. Melo and Winter conjectured that all intersection sizes larger than $2^{k-1}$ (the \"large\" sizes) are of the form $2^{k-1}+2^i$. We show that this is almost true: the large intersection sizes are either of this form or of the form $35\\cdot 2^{k-6}$. We also disprove a second conjecture of Melo and Winter by proving that a positive fraction of the \"small\" values is missing."},"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":"1810.02729","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-05T14:52:23Z","cross_cats_sorted":[],"title_canon_sha256":"4f66869785caf515e925e39951c407e70b4a0e2e44f5726f5b1604d8f161ac4f","abstract_canon_sha256":"770c1ca069ed23cf8e2e60128547648473b73645e27b538bb16e0da90dbd3fb7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:00.819116Z","signature_b64":"lKUQGNEXvWZLFF7ULuVkzUXpUDfnfr+N2F2q4QMq46rdBilRE9Zz6UjG6ff6JVpWSmcgoZulkVbLyRcBLQ2ACg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2ac8d0e06230500660dbd9d684109fb68b47d789b2b9adc2d070a8533b2bfa9","last_reissued_at":"2026-05-18T00:04:00.818477Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:00.818477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intersection sizes of linear subspaces with the hypercube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carla Groenland, Tom Johnston","submitted_at":"2018-10-05T14:52:23Z","abstract_excerpt":"We continue the study by Melo and Winter [arXiv:1712.01763, 2017] on the possible intersection sizes of a $k$-dimensional subspace with the vertices of the $n$-dimensional hypercube in Euclidean space. Melo and Winter conjectured that all intersection sizes larger than $2^{k-1}$ (the \"large\" sizes) are of the form $2^{k-1}+2^i$. We show that this is almost true: the large intersection sizes are either of this form or of the form $35\\cdot 2^{k-6}$. We also disprove a second conjecture of Melo and Winter by proving that a positive fraction of the \"small\" values is missing."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02729","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":"1810.02729","created_at":"2026-05-18T00:04:00.818571+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.02729v1","created_at":"2026-05-18T00:04:00.818571+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02729","created_at":"2026-05-18T00:04:00.818571+00:00"},{"alias_kind":"pith_short_12","alias_value":"6KWI2DQGEMCQ","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_16","alias_value":"6KWI2DQGEMCQAZQN","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_8","alias_value":"6KWI2DQG","created_at":"2026-05-18T12:32:08.215937+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/6KWI2DQGEMCQAZQNXWOWQQIJ7N","json":"https://pith.science/pith/6KWI2DQGEMCQAZQNXWOWQQIJ7N.json","graph_json":"https://pith.science/api/pith-number/6KWI2DQGEMCQAZQNXWOWQQIJ7N/graph.json","events_json":"https://pith.science/api/pith-number/6KWI2DQGEMCQAZQNXWOWQQIJ7N/events.json","paper":"https://pith.science/paper/6KWI2DQG"},"agent_actions":{"view_html":"https://pith.science/pith/6KWI2DQGEMCQAZQNXWOWQQIJ7N","download_json":"https://pith.science/pith/6KWI2DQGEMCQAZQNXWOWQQIJ7N.json","view_paper":"https://pith.science/paper/6KWI2DQG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.02729&json=true","fetch_graph":"https://pith.science/api/pith-number/6KWI2DQGEMCQAZQNXWOWQQIJ7N/graph.json","fetch_events":"https://pith.science/api/pith-number/6KWI2DQGEMCQAZQNXWOWQQIJ7N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6KWI2DQGEMCQAZQNXWOWQQIJ7N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6KWI2DQGEMCQAZQNXWOWQQIJ7N/action/storage_attestation","attest_author":"https://pith.science/pith/6KWI2DQGEMCQAZQNXWOWQQIJ7N/action/author_attestation","sign_citation":"https://pith.science/pith/6KWI2DQGEMCQAZQNXWOWQQIJ7N/action/citation_signature","submit_replication":"https://pith.science/pith/6KWI2DQGEMCQAZQNXWOWQQIJ7N/action/replication_record"}},"created_at":"2026-05-18T00:04:00.818571+00:00","updated_at":"2026-05-18T00:04:00.818571+00:00"}