{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:P2X6TK5DAZD5AK3CQYVVO3S3WA","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":"b3fc716d1d383e32f32ef5ce3194c9b19839a9d0778b6749f269fbaf87abdb16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-07-09T08:37:15Z","title_canon_sha256":"6a58da6d191fc4cc0a3efce6a475399a4a1c3fb9023b23396feed0b2df85e04e"},"schema_version":"1.0","source":{"id":"1207.1985","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1985","created_at":"2026-05-18T03:51:26Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1985v1","created_at":"2026-05-18T03:51:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1985","created_at":"2026-05-18T03:51:26Z"},{"alias_kind":"pith_short_12","alias_value":"P2X6TK5DAZD5","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"P2X6TK5DAZD5AK3C","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"P2X6TK5D","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:4c330a69e2884955327cc59579c95d73afc19c98ad902d3193a674475ab583cb","target":"graph","created_at":"2026-05-18T03:51:26Z","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 provide the directed counterpart of a slight extension of Katoh and Tanigawa's result on rooted-tree decompositions with matroid constraints. Our result characterises digraphs having a packing of arborescences with matroid constraints. It is a proper extension of Edmonds' result on packing of spanning arborescences and implies - using a general orientation result of Frank - the above result of Katoh and Tanigawa. We also give a complete description of the convex hull of the incidence vectors of the basic packings of arborescences and prove that the mimimum cost version of the problem can be","authors_text":"Olivier Durand de Gevigney, Viet-Hang Nguyen, Zolt\\'an Szigeti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-07-09T08:37:15Z","title":"Basic Packing of Arborescences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1985","kind":"arxiv","version":1},"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":"sha256:02ee47e718cc02cd63e6cd775a592caac51329b4db7394129a0d18a86d3817e4","target":"record","created_at":"2026-05-18T03:51:26Z","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":"b3fc716d1d383e32f32ef5ce3194c9b19839a9d0778b6749f269fbaf87abdb16","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-07-09T08:37:15Z","title_canon_sha256":"6a58da6d191fc4cc0a3efce6a475399a4a1c3fb9023b23396feed0b2df85e04e"},"schema_version":"1.0","source":{"id":"1207.1985","kind":"arxiv","version":1}},"canonical_sha256":"7eafe9aba30647d02b62862b576e5bb00b5f31a834e0576718e8e9682010ab69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7eafe9aba30647d02b62862b576e5bb00b5f31a834e0576718e8e9682010ab69","first_computed_at":"2026-05-18T03:51:26.393196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:26.393196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wkT+LU/6NO01Ye+sAqO982qwzVF3yTN++gfZ9agJyB02AnTZjdc/BZARy7SEFF/LvnqM0Xx0WPAvBUoiNt1OBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:26.394143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1985","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02ee47e718cc02cd63e6cd775a592caac51329b4db7394129a0d18a86d3817e4","sha256:4c330a69e2884955327cc59579c95d73afc19c98ad902d3193a674475ab583cb"],"state_sha256":"73d3058b8d7eb7ea91098e75e95e1304916f942c251fb05c8f146e30196fb447"}