{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:LINBA7KZ2GSXZD6FK3SU7JYWNB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b5602301872aff216c7e67e16fc5685be79e66d52d0871651c2b01a86552edcb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-02-10T16:26:18Z","title_canon_sha256":"b8721a0fe119edf0a779ab00e7456791a120d953dc2f36e9c6b9635fda084a70"},"schema_version":"1.0","source":{"id":"2502.06629","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.06629","created_at":"2026-07-05T10:12:09Z"},{"alias_kind":"arxiv_version","alias_value":"2502.06629v1","created_at":"2026-07-05T10:12:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.06629","created_at":"2026-07-05T10:12:09Z"},{"alias_kind":"pith_short_12","alias_value":"LINBA7KZ2GSX","created_at":"2026-07-05T10:12:09Z"},{"alias_kind":"pith_short_16","alias_value":"LINBA7KZ2GSXZD6F","created_at":"2026-07-05T10:12:09Z"},{"alias_kind":"pith_short_8","alias_value":"LINBA7KZ","created_at":"2026-07-05T10:12:09Z"}],"graph_snapshots":[{"event_id":"sha256:12bce52e775c91a2dbe824f88f2ad062a7b938d8748e6b54c3766c3216425826","target":"graph","created_at":"2026-07-05T10:12:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2502.06629/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Benjamini, Kalifa and Tzalik recently proved that there is an absolute constant $c>0$ such that any graph with at most $c\\cdot2^d/d$ edges and no isolated vertices is a minor of the $d$-dimensional hypercube $Q_d$, while there is an absolute constant $K > 0$ such that $Q_d$ is not $(K\\cdot2^d/\\sqrt{d})$-minor-universal. We show that $Q_d$ does not contain 3-uniform expander graphs with $C\\cdot2^d/d$ edges as minors. This matches the lower bound up to a constant factor and answers one of their questions.","authors_text":"Alex Scott, Dmitry Tsarev, Emma Hogan, Jane Tan, Lukas Michel, Youri Tamitegama","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-02-10T16:26:18Z","title":"Tight Bounds for Hypercube Minor-Universality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06629","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:165bf65885bbe5bbd289826ed91c1e683b002405ae671c754e346f43b7a35252","target":"record","created_at":"2026-07-05T10:12:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b5602301872aff216c7e67e16fc5685be79e66d52d0871651c2b01a86552edcb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-02-10T16:26:18Z","title_canon_sha256":"b8721a0fe119edf0a779ab00e7456791a120d953dc2f36e9c6b9635fda084a70"},"schema_version":"1.0","source":{"id":"2502.06629","kind":"arxiv","version":1}},"canonical_sha256":"5a1a107d59d1a57c8fc556e54fa71668715adfff811a0b93df5bbb512e23597a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a1a107d59d1a57c8fc556e54fa71668715adfff811a0b93df5bbb512e23597a","first_computed_at":"2026-07-05T10:12:09.768156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:12:09.768156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hWiT/hjidd13yIJaJDU8Yfflw0O/AA2OZJDI6CBTYDcSzQgQgjocxaTTu3YZDnRs9mSGZ8LdWDo6UhXKVA5fAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:12:09.768667Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.06629","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:165bf65885bbe5bbd289826ed91c1e683b002405ae671c754e346f43b7a35252","sha256:12bce52e775c91a2dbe824f88f2ad062a7b938d8748e6b54c3766c3216425826"],"state_sha256":"218cc922d964f00487dbfb813ba05af4876c4098993ea37964fcc419f92e32ce"}