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We prove Feige's 2008 conjecture on the hypergraph Moore bound: there are absolute constants $A$ and $C$ (independent of $k$) such that for every $k\\ge3$ and every $1\\le\\ell\\le n$, any $k$-uniform hypergraph on $n$ vertices with more than $C\\,n^{k/2}/\\ell^{k/2-1}$ hyperedges contains an even cover of size at most $A\\,\\ell\\log(en/\\ell"},"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":"2607.26028","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-07-28T17:38:31Z","cross_cats_sorted":["cs.DM","quant-ph"],"title_canon_sha256":"baf59a67cbbeb1c5721d4acacb8ea854c5dedb98dc7f533326bcbf39f6adfc04","abstract_canon_sha256":"2268c81f1f62484c206fc3dbd3aa88a3c49a6bea10662166e9fdae4c1496c2fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-29T01:26:20.580339Z","signature_b64":"fqtcyCzJF40mJyzhcfMmPUlVKEjNEa30/obMlgHLdZ8IcHPijaXbRydR00Dl3hWAwDnN43Z0T7jpsmGFejCICg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92eb2f6422b2911dbe5aacdd3edc022893b9795cd2fdc6792a5e522ba02cebe6","last_reissued_at":"2026-07-29T01:26:20.579452Z","signature_status":"signed_v1","first_computed_at":"2026-07-29T01:26:20.579452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Spectral Proof of the Hypergraph Moore Bound","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","quant-ph"],"primary_cat":"math.CO","authors_text":"Alexander Schmidhuber, Matthew B. 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We prove Feige's 2008 conjecture on the hypergraph Moore bound: there are absolute constants $A$ and $C$ (independent of $k$) such that for every $k\\ge3$ and every $1\\le\\ell\\le n$, any $k$-uniform hypergraph on $n$ vertices with more than $C\\,n^{k/2}/\\ell^{k/2-1}$ hyperedges contains an even cover of size at most $A\\,\\ell\\log(en/\\ell"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26028","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.26028/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":"2607.26028","created_at":"2026-07-29T01:26:20.579887+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.26028v1","created_at":"2026-07-29T01:26:20.579887+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.26028","created_at":"2026-07-29T01:26:20.579887+00:00"},{"alias_kind":"pith_short_12","alias_value":"SLVS6ZBCWKIR","created_at":"2026-07-29T01:26:20.579887+00:00"},{"alias_kind":"pith_short_16","alias_value":"SLVS6ZBCWKIR3PS2","created_at":"2026-07-29T01:26:20.579887+00:00"},{"alias_kind":"pith_short_8","alias_value":"SLVS6ZBC","created_at":"2026-07-29T01:26:20.579887+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/SLVS6ZBCWKIR3PS2VTOT5XACFC","json":"https://pith.science/pith/SLVS6ZBCWKIR3PS2VTOT5XACFC.json","graph_json":"https://pith.science/api/pith-number/SLVS6ZBCWKIR3PS2VTOT5XACFC/graph.json","events_json":"https://pith.science/api/pith-number/SLVS6ZBCWKIR3PS2VTOT5XACFC/events.json","paper":"https://pith.science/paper/SLVS6ZBC"},"agent_actions":{"view_html":"https://pith.science/pith/SLVS6ZBCWKIR3PS2VTOT5XACFC","download_json":"https://pith.science/pith/SLVS6ZBCWKIR3PS2VTOT5XACFC.json","view_paper":"https://pith.science/paper/SLVS6ZBC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.26028&json=true","fetch_graph":"https://pith.science/api/pith-number/SLVS6ZBCWKIR3PS2VTOT5XACFC/graph.json","fetch_events":"https://pith.science/api/pith-number/SLVS6ZBCWKIR3PS2VTOT5XACFC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SLVS6ZBCWKIR3PS2VTOT5XACFC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SLVS6ZBCWKIR3PS2VTOT5XACFC/action/storage_attestation","attest_author":"https://pith.science/pith/SLVS6ZBCWKIR3PS2VTOT5XACFC/action/author_attestation","sign_citation":"https://pith.science/pith/SLVS6ZBCWKIR3PS2VTOT5XACFC/action/citation_signature","submit_replication":"https://pith.science/pith/SLVS6ZBCWKIR3PS2VTOT5XACFC/action/replication_record"}},"created_at":"2026-07-29T01:26:20.579887+00:00","updated_at":"2026-07-29T01:26:20.579887+00:00"}