{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VJM66YNGL2PBU3XNWWQ27Z6OC6","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":"edf92289014977e4348a415e71f1e7e38de7f77b3a1ad5abc97532e321a6d906","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-15T15:47:18Z","title_canon_sha256":"2cdfe35f68570a0a2618899f7cf3cb25d907f16fa1a7905b25a5f340d14ca1ef"},"schema_version":"1.0","source":{"id":"1603.04724","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04724","created_at":"2026-05-17T23:51:26Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04724v2","created_at":"2026-05-17T23:51:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04724","created_at":"2026-05-17T23:51:26Z"},{"alias_kind":"pith_short_12","alias_value":"VJM66YNGL2PB","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VJM66YNGL2PBU3XN","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VJM66YNG","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:23e20e6743f73319db30321a8a31e7d61f2b4939a7a5473483b39ad40c1d8981","target":"graph","created_at":"2026-05-17T23:51:26Z","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":"We study the $F$-decomposition threshold $\\delta_F$ for a given graph $F$. Here an $F$-decomposition of a graph $G$ is a collection of edge-disjoint copies of $F$ in $G$ which together cover every edge of $G$. (Such an $F$-decomposition can only exist if $G$ is $F$-divisible, i.e. if $e(F)\\mid e(G)$ and each vertex degree of $G$ can be expressed as a linear combination of the vertex degrees of $F$.)\n  The $F$-decomposition threshold $\\delta_F$ is the smallest value ensuring that an $F$-divisible graph $G$ on $n$ vertices with $\\delta(G)\\ge(\\delta_F+o(1))n$ has an $F$-decomposition. Our main re","authors_text":"Allan Lo, Daniela K\\\"uhn, Deryk Osthus, Richard Montgomery, Stefan Glock","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-15T15:47:18Z","title":"On the decomposition threshold of a given graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04724","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":"sha256:196cae6a475c674d527f2afe5d09a7b8e4e4afba4a5caabd46274e8ea978a999","target":"record","created_at":"2026-05-17T23:51:26Z","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":"edf92289014977e4348a415e71f1e7e38de7f77b3a1ad5abc97532e321a6d906","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-15T15:47:18Z","title_canon_sha256":"2cdfe35f68570a0a2618899f7cf3cb25d907f16fa1a7905b25a5f340d14ca1ef"},"schema_version":"1.0","source":{"id":"1603.04724","kind":"arxiv","version":2}},"canonical_sha256":"aa59ef61a65e9e1a6eedb5a1afe7ce1788ef6bb46e8d997467a0ecd40d8c95d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa59ef61a65e9e1a6eedb5a1afe7ce1788ef6bb46e8d997467a0ecd40d8c95d2","first_computed_at":"2026-05-17T23:51:26.323883Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:26.323883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1cKsasN5rDwyZcqP4vmmzoTsoRcQit/8kO6eTFy/bAnefAdnN/Mc6Yp3A9pb+VZT4n3FLW5BCmjCYL2AEBxsAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:26.324451Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04724","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:196cae6a475c674d527f2afe5d09a7b8e4e4afba4a5caabd46274e8ea978a999","sha256:23e20e6743f73319db30321a8a31e7d61f2b4939a7a5473483b39ad40c1d8981"],"state_sha256":"33d9d74f2ab0fa41717f6706a1c6c64b3fcdaa9df847b0fc8b740fe6faaef962"}