{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3AUVPN3AZSMQI37CLSUDGKOM2T","short_pith_number":"pith:3AUVPN3A","canonical_record":{"source":{"id":"1306.3480","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-06-14T18:42:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b672f1b968f4ba617951b1f984c5ec6c7482d6d2f91f0d92f8522ac9714a1734","abstract_canon_sha256":"c7d820d45ec401f4e91f4a2f0e1919dacfa48ae57fa3fd223c513c8eb4bd6509"},"schema_version":"1.0"},"canonical_sha256":"d82957b760cc99046fe25ca83329ccd4d98112093e96166e378b2a1ce8921c07","source":{"kind":"arxiv","id":"1306.3480","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3480","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3480v2","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3480","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"pith_short_12","alias_value":"3AUVPN3AZSMQ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3AUVPN3AZSMQI37C","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3AUVPN3A","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3AUVPN3AZSMQI37CLSUDGKOM2T","target":"record","payload":{"canonical_record":{"source":{"id":"1306.3480","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-06-14T18:42:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b672f1b968f4ba617951b1f984c5ec6c7482d6d2f91f0d92f8522ac9714a1734","abstract_canon_sha256":"c7d820d45ec401f4e91f4a2f0e1919dacfa48ae57fa3fd223c513c8eb4bd6509"},"schema_version":"1.0"},"canonical_sha256":"d82957b760cc99046fe25ca83329ccd4d98112093e96166e378b2a1ce8921c07","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:44.089148Z","signature_b64":"FXGXS7bAj2JbVQ/8fsjciMz95tPZrdI4pMfYzvNth7G7fJlHksNKcW9LdQSuSnia6xoYKfTg79NlQOL4M71NCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d82957b760cc99046fe25ca83329ccd4d98112093e96166e378b2a1ce8921c07","last_reissued_at":"2026-05-18T03:17:44.088473Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:44.088473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.3480","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:17:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JfXWGBsGT8AcXShtfYXfaGTGE5HS+N8+7a71479Jbjrona0EgS3IKr6PbfmjJnZRnvyTK2vIOi0P0r3410NfDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T11:54:06.866980Z"},"content_sha256":"8ec8f52f98b8fdfdc86b70c18b81a68fe581dbc85efbdf2f7827fcc6bc28a055","schema_version":"1.0","event_id":"sha256:8ec8f52f98b8fdfdc86b70c18b81a68fe581dbc85efbdf2f7827fcc6bc28a055"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3AUVPN3AZSMQI37CLSUDGKOM2T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Faster Algorithm for Packing Branchings in Digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Mario Leston Rey, Orlando Lee","submitted_at":"2013-06-14T18:42:35Z","abstract_excerpt":"We consider the problem of finding an integral packing of branchings in a capacitated digraph with root-set demands. Schrijver described an algorithm that returns a packing with at most m+n^3+r branchings that makes at most m(m+n^3+r) calls to an oracle that basically computes a minimum cut, where n is the number of vertices, m is the number of arcs and r is the number of root-sets of the input digraph. In this work we provide an algorithm, inspired on ideas of Schrijver and on an paper of Gabow and Manu, that returns a packing with at most m+r-1 branchings and makes at most 2n+m+r-1 oracle ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3480","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:17:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1rl30Pjd9dkwRQ5maxV3ek+deFa6Kiq75CIriAIshUQ649V9fO+8alt0g4BjN9RK+8hqvwR7we6YhmJT1By8CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T11:54:06.867634Z"},"content_sha256":"d8fb987f367e7c6a1869be640a961042a6073f1718178c6b843d1c9a6b3dd604","schema_version":"1.0","event_id":"sha256:d8fb987f367e7c6a1869be640a961042a6073f1718178c6b843d1c9a6b3dd604"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3AUVPN3AZSMQI37CLSUDGKOM2T/bundle.json","state_url":"https://pith.science/pith/3AUVPN3AZSMQI37CLSUDGKOM2T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3AUVPN3AZSMQI37CLSUDGKOM2T/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-22T11:54:06Z","links":{"resolver":"https://pith.science/pith/3AUVPN3AZSMQI37CLSUDGKOM2T","bundle":"https://pith.science/pith/3AUVPN3AZSMQI37CLSUDGKOM2T/bundle.json","state":"https://pith.science/pith/3AUVPN3AZSMQI37CLSUDGKOM2T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3AUVPN3AZSMQI37CLSUDGKOM2T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3AUVPN3AZSMQI37CLSUDGKOM2T","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":"c7d820d45ec401f4e91f4a2f0e1919dacfa48ae57fa3fd223c513c8eb4bd6509","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-06-14T18:42:35Z","title_canon_sha256":"b672f1b968f4ba617951b1f984c5ec6c7482d6d2f91f0d92f8522ac9714a1734"},"schema_version":"1.0","source":{"id":"1306.3480","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3480","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3480v2","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3480","created_at":"2026-05-18T03:17:44Z"},{"alias_kind":"pith_short_12","alias_value":"3AUVPN3AZSMQ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3AUVPN3AZSMQI37C","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3AUVPN3A","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:d8fb987f367e7c6a1869be640a961042a6073f1718178c6b843d1c9a6b3dd604","target":"graph","created_at":"2026-05-18T03:17:44Z","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 consider the problem of finding an integral packing of branchings in a capacitated digraph with root-set demands. Schrijver described an algorithm that returns a packing with at most m+n^3+r branchings that makes at most m(m+n^3+r) calls to an oracle that basically computes a minimum cut, where n is the number of vertices, m is the number of arcs and r is the number of root-sets of the input digraph. In this work we provide an algorithm, inspired on ideas of Schrijver and on an paper of Gabow and Manu, that returns a packing with at most m+r-1 branchings and makes at most 2n+m+r-1 oracle ca","authors_text":"Mario Leston Rey, Orlando Lee","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-06-14T18:42:35Z","title":"A Faster Algorithm for Packing Branchings in Digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3480","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":"sha256:8ec8f52f98b8fdfdc86b70c18b81a68fe581dbc85efbdf2f7827fcc6bc28a055","target":"record","created_at":"2026-05-18T03:17:44Z","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":"c7d820d45ec401f4e91f4a2f0e1919dacfa48ae57fa3fd223c513c8eb4bd6509","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-06-14T18:42:35Z","title_canon_sha256":"b672f1b968f4ba617951b1f984c5ec6c7482d6d2f91f0d92f8522ac9714a1734"},"schema_version":"1.0","source":{"id":"1306.3480","kind":"arxiv","version":2}},"canonical_sha256":"d82957b760cc99046fe25ca83329ccd4d98112093e96166e378b2a1ce8921c07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d82957b760cc99046fe25ca83329ccd4d98112093e96166e378b2a1ce8921c07","first_computed_at":"2026-05-18T03:17:44.088473Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:44.088473Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FXGXS7bAj2JbVQ/8fsjciMz95tPZrdI4pMfYzvNth7G7fJlHksNKcW9LdQSuSnia6xoYKfTg79NlQOL4M71NCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:44.089148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.3480","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ec8f52f98b8fdfdc86b70c18b81a68fe581dbc85efbdf2f7827fcc6bc28a055","sha256:d8fb987f367e7c6a1869be640a961042a6073f1718178c6b843d1c9a6b3dd604"],"state_sha256":"680ca4d2804253a02c0b609d197b8b33cca6ed39c7e24ae09f5c9b7439dab0be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xmvSYwl5rk1hZ3q9mG9AO6sdH9uoSxpDgPn3+FvH3gm6ThSnKQfAFHspZhJxPaTrFK8QcIDEgLvrkKlLHLRrCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T11:54:06.870665Z","bundle_sha256":"cf56b79fd275a4caec70c00943af89fb94754f148b388a5bb444b7563bb1b340"}}