{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FR6KGQIFYQI3EQ6CQY4KP7J2BI","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":"aa073bc6ef257f7af5ecaa05f24295b58ab219b5baf8ddadba3477c6563cc173","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-04-21T13:31:27Z","title_canon_sha256":"bb619d93af1b8a94bba53cd252b877a4015101986e730a840bdc4e88dcda884f"},"schema_version":"1.0","source":{"id":"2504.15096","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.15096","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"arxiv_version","alias_value":"2504.15096v2","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.15096","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"pith_short_12","alias_value":"FR6KGQIFYQI3","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"pith_short_16","alias_value":"FR6KGQIFYQI3EQ6C","created_at":"2026-06-19T16:11:10Z"},{"alias_kind":"pith_short_8","alias_value":"FR6KGQIF","created_at":"2026-06-19T16:11:10Z"}],"graph_snapshots":[{"event_id":"sha256:33c1fc01c3ec7dd5dbe24b5231b8efd45e130bc5076e824c64f4b24686254f65","target":"graph","created_at":"2026-06-19T16:11:10Z","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/2504.15096/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we investigate the problem of finding {\\it bisections} (i.e., balanced bipartitions) in graphs. We prove the following two results for {\\it all} graphs $G$: (1). $G$ has a bisection where each vertex $v$ has at least $(1/4 - o(1))d_G(v)$ neighbors in its own part; (2). $G$ also has a bisection where each vertex $v$ has at least $(1/4 - o(1))d_G(v)$ neighbors in the opposite part. These results are asymptotically optimal up to a factor of $1/2$, aligning with what is expected from random constructions, and provide the first systematic understanding of bisections in general graphs","authors_text":"Hehui Wu, Jie Ma","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-04-21T13:31:27Z","title":"Bisections of graphs under degree constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.15096","kind":"arxiv","version":2},"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:e0284d9a90150052dbea2a81a26895b1b178a49574b101774f5f2f6839a05276","target":"record","created_at":"2026-06-19T16:11:10Z","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":"aa073bc6ef257f7af5ecaa05f24295b58ab219b5baf8ddadba3477c6563cc173","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-04-21T13:31:27Z","title_canon_sha256":"bb619d93af1b8a94bba53cd252b877a4015101986e730a840bdc4e88dcda884f"},"schema_version":"1.0","source":{"id":"2504.15096","kind":"arxiv","version":2}},"canonical_sha256":"2c7ca34105c411b243c28638a7fd3a0a361a4beb88092a5d34ad6be229dfa57f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c7ca34105c411b243c28638a7fd3a0a361a4beb88092a5d34ad6be229dfa57f","first_computed_at":"2026-06-19T16:11:10.649263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:10.649263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YrSuV0Z/czwsPU4vMz5WHghbKEfbFzHQjjkZHsWRYyI6wVINOJWkdMgzfSuObKkvjg923TGIedSWxYi7rV+jCA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:10.649663Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.15096","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0284d9a90150052dbea2a81a26895b1b178a49574b101774f5f2f6839a05276","sha256:33c1fc01c3ec7dd5dbe24b5231b8efd45e130bc5076e824c64f4b24686254f65"],"state_sha256":"91b1f96cd05a0eb3209fe7c1a6be2e5ccc413081f0c44cb46fa5d022907da7db"}