{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:VADU6F5FOV67NCG4P664OUOTPM","short_pith_number":"pith:VADU6F5F","schema_version":"1.0","canonical_sha256":"a8074f17a5757df688dc7fbdc751d37b2324702a78964fd1ae9f99a9fa709c1e","source":{"kind":"arxiv","id":"0909.4270","version":2},"attestation_state":"computed","paper":{"title":"The Gilbert Arborescence Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.OC","authors_text":"C. J. Ras, D. A. Thomas, K. J. Swanepoel, M. Brazil, M. G. Volz","submitted_at":"2009-09-23T18:11:32Z","abstract_excerpt":"We investigate the problem of designing a minimum cost flow network interconnecting n sources and a single sink, each with known locations in a normed space and with associated flow demands. The network may contain any finite number of additional unprescribed nodes from the space; these are known as the Steiner points. For concave increasing cost functions, a minimum cost network of this sort has a tree topology, and hence can be called a Minimum Gilbert Arborescence (MGA). We characterise the local topological structure of Steiner points in MGAs, showing, in particular, that for a wide range "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0909.4270","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2009-09-23T18:11:32Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"2febed2e2ceb8c5401a6e1e1a624a0e4866ae4daf5a58de6459b49f39937e922","abstract_canon_sha256":"5de37ac749e8a3c62e05b55620d927a647f4f660320052f92d93a069ea959414"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:21.457466Z","signature_b64":"FR8iBPJjIZj+tuyrnixgC7/nsg8y+M6QXxkUsr1lgnzFHDqxNGOnBy5ST9LRrddlsZPNRHkw4UEfI3urwQkGDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8074f17a5757df688dc7fbdc751d37b2324702a78964fd1ae9f99a9fa709c1e","last_reissued_at":"2026-05-18T02:28:21.456865Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:21.456865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Gilbert Arborescence Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.OC","authors_text":"C. J. Ras, D. A. Thomas, K. J. Swanepoel, M. Brazil, M. G. Volz","submitted_at":"2009-09-23T18:11:32Z","abstract_excerpt":"We investigate the problem of designing a minimum cost flow network interconnecting n sources and a single sink, each with known locations in a normed space and with associated flow demands. The network may contain any finite number of additional unprescribed nodes from the space; these are known as the Steiner points. For concave increasing cost functions, a minimum cost network of this sort has a tree topology, and hence can be called a Minimum Gilbert Arborescence (MGA). We characterise the local topological structure of Steiner points in MGAs, showing, in particular, that for a wide range "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.4270","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0909.4270","created_at":"2026-05-18T02:28:21.456959+00:00"},{"alias_kind":"arxiv_version","alias_value":"0909.4270v2","created_at":"2026-05-18T02:28:21.456959+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.4270","created_at":"2026-05-18T02:28:21.456959+00:00"},{"alias_kind":"pith_short_12","alias_value":"VADU6F5FOV67","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"VADU6F5FOV67NCG4","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"VADU6F5F","created_at":"2026-05-18T12:26:02.257875+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VADU6F5FOV67NCG4P664OUOTPM","json":"https://pith.science/pith/VADU6F5FOV67NCG4P664OUOTPM.json","graph_json":"https://pith.science/api/pith-number/VADU6F5FOV67NCG4P664OUOTPM/graph.json","events_json":"https://pith.science/api/pith-number/VADU6F5FOV67NCG4P664OUOTPM/events.json","paper":"https://pith.science/paper/VADU6F5F"},"agent_actions":{"view_html":"https://pith.science/pith/VADU6F5FOV67NCG4P664OUOTPM","download_json":"https://pith.science/pith/VADU6F5FOV67NCG4P664OUOTPM.json","view_paper":"https://pith.science/paper/VADU6F5F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0909.4270&json=true","fetch_graph":"https://pith.science/api/pith-number/VADU6F5FOV67NCG4P664OUOTPM/graph.json","fetch_events":"https://pith.science/api/pith-number/VADU6F5FOV67NCG4P664OUOTPM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VADU6F5FOV67NCG4P664OUOTPM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VADU6F5FOV67NCG4P664OUOTPM/action/storage_attestation","attest_author":"https://pith.science/pith/VADU6F5FOV67NCG4P664OUOTPM/action/author_attestation","sign_citation":"https://pith.science/pith/VADU6F5FOV67NCG4P664OUOTPM/action/citation_signature","submit_replication":"https://pith.science/pith/VADU6F5FOV67NCG4P664OUOTPM/action/replication_record"}},"created_at":"2026-05-18T02:28:21.456959+00:00","updated_at":"2026-05-18T02:28:21.456959+00:00"}