{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:B56NDMLJ3MEOADKJOUWVEARE6N","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":"cb2868a223274bde5127a34afd47aaf27a75b0b77d5b6eaf052df2b39299f66d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-07-24T22:54:51Z","title_canon_sha256":"31b72125ff58cda65ec43b6ec3a8c8fb5e807a31c4b88df81efa1fe20afdca09"},"schema_version":"1.0","source":{"id":"1007.4287","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.4287","created_at":"2026-05-18T04:42:03Z"},{"alias_kind":"arxiv_version","alias_value":"1007.4287v3","created_at":"2026-05-18T04:42:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4287","created_at":"2026-05-18T04:42:03Z"},{"alias_kind":"pith_short_12","alias_value":"B56NDMLJ3MEO","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"B56NDMLJ3MEOADKJ","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"B56NDMLJ","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:c4a26c7353fa62d01aa95e6d8b2b9a5ef14f7125dfb98431863f98efb80a2221","target":"graph","created_at":"2026-05-18T04:42:03Z","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"},"paper":{"abstract_excerpt":"Given a bipartite graph $H$ and an integer $n$, let $f(n;H)$ be the smallest integer such that, any set of edge disjoint copies of $H$ on $n$ vertices, can be extended to an $H$-design on at most $n+f(n;H)$ vertices. We establish tight bounds for the growth of $f(n;H)$ as $n \\rightarrow \\infty$. In particular, we prove the conjecture of F\\\"uredi and Lehel \\cite{FuLe} that $f(n;H) = o(n)$. This settles a long-standing open problem.","authors_text":"Ago-Erik Riet, Mykhaylo Tyomkyn, Zolt\\'an F\\\"uredi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-07-24T22:54:51Z","title":"Completing Partial Packings of Bipartite Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4287","kind":"arxiv","version":3},"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:e3cf7720c5e92424ba3b0e0ebbc48e3f931b6999fbb349e084b2aaf86419409e","target":"record","created_at":"2026-05-18T04:42:03Z","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":"cb2868a223274bde5127a34afd47aaf27a75b0b77d5b6eaf052df2b39299f66d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-07-24T22:54:51Z","title_canon_sha256":"31b72125ff58cda65ec43b6ec3a8c8fb5e807a31c4b88df81efa1fe20afdca09"},"schema_version":"1.0","source":{"id":"1007.4287","kind":"arxiv","version":3}},"canonical_sha256":"0f7cd1b169db08e00d49752d520224f36d8bb149ff72a002e3da368337d1dbbd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f7cd1b169db08e00d49752d520224f36d8bb149ff72a002e3da368337d1dbbd","first_computed_at":"2026-05-18T04:42:03.842431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:03.842431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SO1/cnVmQ1SotfSB3+xu4mDYrECsmbMh4+K4grHf6OTAHtWDZEVlneioCzlk2ZI51ygg1ZwpUWS8R2we4GmFDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:03.842957Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.4287","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3cf7720c5e92424ba3b0e0ebbc48e3f931b6999fbb349e084b2aaf86419409e","sha256:c4a26c7353fa62d01aa95e6d8b2b9a5ef14f7125dfb98431863f98efb80a2221"],"state_sha256":"e1ecda767574a9356e04569d683aa395f8ccc9e2cfd8d9bc04e7311ab7a9890f"}