{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:TNDKNIEP27EWLLYUG6AYGFIE3B","short_pith_number":"pith:TNDKNIEP","schema_version":"1.0","canonical_sha256":"9b46a6a08fd7c965af143781831504d8538615588451ee3d7ec62c417a84c0ef","source":{"kind":"arxiv","id":"1708.09167","version":1},"attestation_state":"computed","paper":{"title":"Colored Point-set Embeddings of Acyclic Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CG","authors_text":"Alfredo Navarra, Emilio Di Giacomo, Giuseppe Liotta, Leszek Gasieniec","submitted_at":"2017-08-30T08:39:49Z","abstract_excerpt":"We show that any planar drawing of a forest of three stars whose vertices are constrained to be at fixed vertex locations may require $\\Omega(n^\\frac{2}{3})$ edges each having $\\Omega(n^\\frac{1}{3})$ bends in the worst case. The lower bound holds even when the function that maps vertices to points is not a bijection but it is defined by a 3-coloring. In contrast, a constant number of bends per edge can be obtained for 3-colored paths and for 3-colored caterpillars whose leaves all have the same color. Such results answer to a long standing open problem."},"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":"1708.09167","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-08-30T08:39:49Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"637c4551ce549c83587f022162a0d6c71e6baa307c933d4c2c75dac67a728ffa","abstract_canon_sha256":"6c90005ef5314b54f67917a44c8e15eb1d0e8269708ea0d7e51137c343222d1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:20.755170Z","signature_b64":"pp27W3pkbOPVP+vVLWEEfsog+TUyXTCiFO+5ZdWRh27ALFN1fEWnL+Yp2YxBoIm/x17rt25pfRGI0Tmd/KC0AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b46a6a08fd7c965af143781831504d8538615588451ee3d7ec62c417a84c0ef","last_reissued_at":"2026-05-18T00:36:20.754530Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:20.754530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Colored Point-set Embeddings of Acyclic Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CG","authors_text":"Alfredo Navarra, Emilio Di Giacomo, Giuseppe Liotta, Leszek Gasieniec","submitted_at":"2017-08-30T08:39:49Z","abstract_excerpt":"We show that any planar drawing of a forest of three stars whose vertices are constrained to be at fixed vertex locations may require $\\Omega(n^\\frac{2}{3})$ edges each having $\\Omega(n^\\frac{1}{3})$ bends in the worst case. The lower bound holds even when the function that maps vertices to points is not a bijection but it is defined by a 3-coloring. In contrast, a constant number of bends per edge can be obtained for 3-colored paths and for 3-colored caterpillars whose leaves all have the same color. Such results answer to a long standing open problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09167","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":"1708.09167","created_at":"2026-05-18T00:36:20.754605+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.09167v1","created_at":"2026-05-18T00:36:20.754605+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09167","created_at":"2026-05-18T00:36:20.754605+00:00"},{"alias_kind":"pith_short_12","alias_value":"TNDKNIEP27EW","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"TNDKNIEP27EWLLYU","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"TNDKNIEP","created_at":"2026-05-18T12:31:46.661854+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/TNDKNIEP27EWLLYUG6AYGFIE3B","json":"https://pith.science/pith/TNDKNIEP27EWLLYUG6AYGFIE3B.json","graph_json":"https://pith.science/api/pith-number/TNDKNIEP27EWLLYUG6AYGFIE3B/graph.json","events_json":"https://pith.science/api/pith-number/TNDKNIEP27EWLLYUG6AYGFIE3B/events.json","paper":"https://pith.science/paper/TNDKNIEP"},"agent_actions":{"view_html":"https://pith.science/pith/TNDKNIEP27EWLLYUG6AYGFIE3B","download_json":"https://pith.science/pith/TNDKNIEP27EWLLYUG6AYGFIE3B.json","view_paper":"https://pith.science/paper/TNDKNIEP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.09167&json=true","fetch_graph":"https://pith.science/api/pith-number/TNDKNIEP27EWLLYUG6AYGFIE3B/graph.json","fetch_events":"https://pith.science/api/pith-number/TNDKNIEP27EWLLYUG6AYGFIE3B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TNDKNIEP27EWLLYUG6AYGFIE3B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TNDKNIEP27EWLLYUG6AYGFIE3B/action/storage_attestation","attest_author":"https://pith.science/pith/TNDKNIEP27EWLLYUG6AYGFIE3B/action/author_attestation","sign_citation":"https://pith.science/pith/TNDKNIEP27EWLLYUG6AYGFIE3B/action/citation_signature","submit_replication":"https://pith.science/pith/TNDKNIEP27EWLLYUG6AYGFIE3B/action/replication_record"}},"created_at":"2026-05-18T00:36:20.754605+00:00","updated_at":"2026-05-18T00:36:20.754605+00:00"}