{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:6AI7JNPBSLLIOBLCEESGSFHUCP","short_pith_number":"pith:6AI7JNPB","schema_version":"1.0","canonical_sha256":"f011f4b5e192d687056221246914f413d61a5b58935689296ba835b3240314bb","source":{"kind":"arxiv","id":"2606.30612","version":1},"attestation_state":"computed","paper":{"title":"Nearly-uniform degree distributions in spanning subgraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexey Pokrovskiy, Benny Sudakov, Richard Montgomery","submitted_at":"2026-06-29T17:47:05Z","abstract_excerpt":"We show that, when $d=o(n)$, every $d$-regular $n$-vertex graph contains a spanning subgraph whose degree distribution is nearly uniform, i.e., for each $0\\leq i\\leq d$, there are $(1+o(1))n/(d+1)$ vertices with degree $i$. This proves a conjecture of Alon and Wei on irregular subgraphs and strengthens a previous result of Fox, Luo and Pham."},"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":"2606.30612","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-29T17:47:05Z","cross_cats_sorted":[],"title_canon_sha256":"f753a988ea4525e9b022e790a8da15682456cbb976a7233fa79b06187cb7e841","abstract_canon_sha256":"d834264663a03b3944ccd0d52c17101dc09fb4c91a9ad89f7a96f72c22ed38dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:18:22.619619Z","signature_b64":"MTNU4OQRjfBoKQQICxJ4RNshw0GwgbTCrbktGh2nEV6W0Ye8Jr9O9J38SkCrzvSazkoasc8yO7Bq1PJ9tnaoAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f011f4b5e192d687056221246914f413d61a5b58935689296ba835b3240314bb","last_reissued_at":"2026-06-30T02:18:22.619117Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:18:22.619117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nearly-uniform degree distributions in spanning subgraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexey Pokrovskiy, Benny Sudakov, Richard Montgomery","submitted_at":"2026-06-29T17:47:05Z","abstract_excerpt":"We show that, when $d=o(n)$, every $d$-regular $n$-vertex graph contains a spanning subgraph whose degree distribution is nearly uniform, i.e., for each $0\\leq i\\leq d$, there are $(1+o(1))n/(d+1)$ vertices with degree $i$. This proves a conjecture of Alon and Wei on irregular subgraphs and strengthens a previous result of Fox, Luo and Pham."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30612","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/2606.30612/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":"2606.30612","created_at":"2026-06-30T02:18:22.619183+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.30612v1","created_at":"2026-06-30T02:18:22.619183+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30612","created_at":"2026-06-30T02:18:22.619183+00:00"},{"alias_kind":"pith_short_12","alias_value":"6AI7JNPBSLLI","created_at":"2026-06-30T02:18:22.619183+00:00"},{"alias_kind":"pith_short_16","alias_value":"6AI7JNPBSLLIOBLC","created_at":"2026-06-30T02:18:22.619183+00:00"},{"alias_kind":"pith_short_8","alias_value":"6AI7JNPB","created_at":"2026-06-30T02:18:22.619183+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/6AI7JNPBSLLIOBLCEESGSFHUCP","json":"https://pith.science/pith/6AI7JNPBSLLIOBLCEESGSFHUCP.json","graph_json":"https://pith.science/api/pith-number/6AI7JNPBSLLIOBLCEESGSFHUCP/graph.json","events_json":"https://pith.science/api/pith-number/6AI7JNPBSLLIOBLCEESGSFHUCP/events.json","paper":"https://pith.science/paper/6AI7JNPB"},"agent_actions":{"view_html":"https://pith.science/pith/6AI7JNPBSLLIOBLCEESGSFHUCP","download_json":"https://pith.science/pith/6AI7JNPBSLLIOBLCEESGSFHUCP.json","view_paper":"https://pith.science/paper/6AI7JNPB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.30612&json=true","fetch_graph":"https://pith.science/api/pith-number/6AI7JNPBSLLIOBLCEESGSFHUCP/graph.json","fetch_events":"https://pith.science/api/pith-number/6AI7JNPBSLLIOBLCEESGSFHUCP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6AI7JNPBSLLIOBLCEESGSFHUCP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6AI7JNPBSLLIOBLCEESGSFHUCP/action/storage_attestation","attest_author":"https://pith.science/pith/6AI7JNPBSLLIOBLCEESGSFHUCP/action/author_attestation","sign_citation":"https://pith.science/pith/6AI7JNPBSLLIOBLCEESGSFHUCP/action/citation_signature","submit_replication":"https://pith.science/pith/6AI7JNPBSLLIOBLCEESGSFHUCP/action/replication_record"}},"created_at":"2026-06-30T02:18:22.619183+00:00","updated_at":"2026-06-30T02:18:22.619183+00:00"}