{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MC3ZMGEHO4527J6LJ2UCHQU3NX","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":"8083c6e3f7551744b20fa2bb4fa1c48003b217d7e4fc6fde0906b3ca99fb887c","cross_cats_sorted":["cs.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-11-09T06:00:16Z","title_canon_sha256":"158f56d0c0d57b99f167794406836c059b52e2ea07bc9ff4e9a012f91b59827c"},"schema_version":"1.0","source":{"id":"1111.2109","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2109","created_at":"2026-05-18T04:08:44Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2109v1","created_at":"2026-05-18T04:08:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2109","created_at":"2026-05-18T04:08:44Z"},{"alias_kind":"pith_short_12","alias_value":"MC3ZMGEHO452","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MC3ZMGEHO4527J6L","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MC3ZMGEH","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:a3454466b8d66d1e3ef9950e98adc4e8b5bc8506bbd5ae277b245b3a9e2ef7ba","target":"graph","created_at":"2026-05-18T04:08:44Z","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 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","authors_text":"Charl Ras, Doreen Thomas, Marcus Brazil","cross_cats":["cs.DS","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-11-09T06:00:16Z","title":"A Flow-dependent Quadratic Steiner Tree Problem in the Euclidean Plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2109","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":"sha256:0938802d486e823cb6c2c328aa3cdd6b7aa4541478c8669d8fdf064134c896b4","target":"record","created_at":"2026-05-18T04:08:44Z","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":"8083c6e3f7551744b20fa2bb4fa1c48003b217d7e4fc6fde0906b3ca99fb887c","cross_cats_sorted":["cs.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-11-09T06:00:16Z","title_canon_sha256":"158f56d0c0d57b99f167794406836c059b52e2ea07bc9ff4e9a012f91b59827c"},"schema_version":"1.0","source":{"id":"1111.2109","kind":"arxiv","version":1}},"canonical_sha256":"60b7961887773bafa7cb4ea823c29b6dc08c578426945681667e3699fe803d6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60b7961887773bafa7cb4ea823c29b6dc08c578426945681667e3699fe803d6d","first_computed_at":"2026-05-18T04:08:44.094534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:44.094534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D4nHP9Q5lDTY7EghcIw8/71/uH737npXeYlUlVT+j65fIsRv7iimjiUBVvHXX5DfVRoAn6/aJMAMX9983//EDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:44.095014Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.2109","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0938802d486e823cb6c2c328aa3cdd6b7aa4541478c8669d8fdf064134c896b4","sha256:a3454466b8d66d1e3ef9950e98adc4e8b5bc8506bbd5ae277b245b3a9e2ef7ba"],"state_sha256":"0528a9e732481643d60a01261462b06c1dcc74b7a49bbdd33d8932e223a52e7f"}