{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:MC3ZMGEHO4527J6LJ2UCHQU3NX","short_pith_number":"pith:MC3ZMGEH","schema_version":"1.0","canonical_sha256":"60b7961887773bafa7cb4ea823c29b6dc08c578426945681667e3699fe803d6d","source":{"kind":"arxiv","id":"1111.2109","version":1},"attestation_state":"computed","paper":{"title":"A Flow-dependent Quadratic Steiner Tree Problem in the Euclidean Plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.OC"],"primary_cat":"math.MG","authors_text":"Charl Ras, Doreen Thomas, Marcus Brazil","submitted_at":"2011-11-09T06:00:16Z","abstract_excerpt":"We introduce a flow-dependent version of the quadratic Steiner tree problem in the plane. An instance of the problem on a set of embedded sources and a sink asks for a directed tree $T$ spanning these nodes and a bounded number of Steiner points, such that $\\displaystyle\\sum_{e \\in E(T)}f(e)|e|^2$ is a minimum, where $f(e)$ is the flow on edge $e$. The edges are uncapacitated and the flows are determined additively, i.e., the flow on an edge leaving a node $u$ will be the sum of the flows on all edges entering $u$. Our motivation for studying this problem is its utility as a model for relay au"},"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":"1111.2109","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-11-09T06:00:16Z","cross_cats_sorted":["cs.DS","math.OC"],"title_canon_sha256":"158f56d0c0d57b99f167794406836c059b52e2ea07bc9ff4e9a012f91b59827c","abstract_canon_sha256":"8083c6e3f7551744b20fa2bb4fa1c48003b217d7e4fc6fde0906b3ca99fb887c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:44.095014Z","signature_b64":"D4nHP9Q5lDTY7EghcIw8/71/uH737npXeYlUlVT+j65fIsRv7iimjiUBVvHXX5DfVRoAn6/aJMAMX9983//EDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60b7961887773bafa7cb4ea823c29b6dc08c578426945681667e3699fe803d6d","last_reissued_at":"2026-05-18T04:08:44.094534Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:44.094534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Flow-dependent Quadratic Steiner Tree Problem in the Euclidean Plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.OC"],"primary_cat":"math.MG","authors_text":"Charl Ras, Doreen Thomas, Marcus Brazil","submitted_at":"2011-11-09T06:00:16Z","abstract_excerpt":"We introduce a flow-dependent version of the quadratic Steiner tree problem in the plane. An instance of the problem on a set of embedded sources and a sink asks for a directed tree $T$ spanning these nodes and a bounded number of Steiner points, such that $\\displaystyle\\sum_{e \\in E(T)}f(e)|e|^2$ is a minimum, where $f(e)$ is the flow on edge $e$. The edges are uncapacitated and the flows are determined additively, i.e., the flow on an edge leaving a node $u$ will be the sum of the flows on all edges entering $u$. Our motivation for studying this problem is its utility as a model for relay au"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2109","kind":"arxiv","version":1},"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":"1111.2109","created_at":"2026-05-18T04:08:44.094613+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.2109v1","created_at":"2026-05-18T04:08:44.094613+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2109","created_at":"2026-05-18T04:08:44.094613+00:00"},{"alias_kind":"pith_short_12","alias_value":"MC3ZMGEHO452","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"MC3ZMGEHO4527J6L","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"MC3ZMGEH","created_at":"2026-05-18T12:26:34.985390+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/MC3ZMGEHO4527J6LJ2UCHQU3NX","json":"https://pith.science/pith/MC3ZMGEHO4527J6LJ2UCHQU3NX.json","graph_json":"https://pith.science/api/pith-number/MC3ZMGEHO4527J6LJ2UCHQU3NX/graph.json","events_json":"https://pith.science/api/pith-number/MC3ZMGEHO4527J6LJ2UCHQU3NX/events.json","paper":"https://pith.science/paper/MC3ZMGEH"},"agent_actions":{"view_html":"https://pith.science/pith/MC3ZMGEHO4527J6LJ2UCHQU3NX","download_json":"https://pith.science/pith/MC3ZMGEHO4527J6LJ2UCHQU3NX.json","view_paper":"https://pith.science/paper/MC3ZMGEH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.2109&json=true","fetch_graph":"https://pith.science/api/pith-number/MC3ZMGEHO4527J6LJ2UCHQU3NX/graph.json","fetch_events":"https://pith.science/api/pith-number/MC3ZMGEHO4527J6LJ2UCHQU3NX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MC3ZMGEHO4527J6LJ2UCHQU3NX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MC3ZMGEHO4527J6LJ2UCHQU3NX/action/storage_attestation","attest_author":"https://pith.science/pith/MC3ZMGEHO4527J6LJ2UCHQU3NX/action/author_attestation","sign_citation":"https://pith.science/pith/MC3ZMGEHO4527J6LJ2UCHQU3NX/action/citation_signature","submit_replication":"https://pith.science/pith/MC3ZMGEHO4527J6LJ2UCHQU3NX/action/replication_record"}},"created_at":"2026-05-18T04:08:44.094613+00:00","updated_at":"2026-05-18T04:08:44.094613+00:00"}