{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:LGCCRLI276T5EBIKCGGGHDF7N4","short_pith_number":"pith:LGCCRLI2","schema_version":"1.0","canonical_sha256":"598428ad1affa7d2050a118c638cbf6f03409a607b054a80093af72f7f176c39","source":{"kind":"arxiv","id":"2506.11704","version":2},"attestation_state":"computed","paper":{"title":"Isometric-Universal Graphs for Trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Cyril Gavoille, Edgar Baucher, Fran\\c{c}ois Dross","submitted_at":"2025-06-13T12:19:18Z","abstract_excerpt":"We consider the problem of finding the smallest graph that contains two input trees each with at most $n$ vertices preserving their distances. In other words, we look for an isometric-universal graph with the minimum number of vertices for two given trees. We prove that this problem can be solved in time $O(n^{5/2}\\log{n})$. We extend this result to forests instead of trees, and propose an algorithm with running time $O(n^{7/2}\\log{n})$. As a key ingredient, we show that a smallest isometric-universal graph of two trees essentially is a tree. Furthermore, we prove that these results cannot be "},"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":"2506.11704","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-06-13T12:19:18Z","cross_cats_sorted":[],"title_canon_sha256":"af5790437b2b9762e3e3d8e638382702e0660a22ebbeacce79b9152e9b54afda","abstract_canon_sha256":"ba10166f0eaf523bca9683a311880c77bd4e5b8c05c6dc6f3a7337886f972952"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:22:19.124638Z","signature_b64":"MEA/71rdS3ggCc5x5YdCOqY8f/aihDMMkdr0rbs6vr4ZT2PJHWPeh+iLjowPaX/oktKVrdcFCNSQfwzj8Y0hCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"598428ad1affa7d2050a118c638cbf6f03409a607b054a80093af72f7f176c39","last_reissued_at":"2026-07-05T11:22:19.124144Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:22:19.124144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isometric-Universal Graphs for Trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Cyril Gavoille, Edgar Baucher, Fran\\c{c}ois Dross","submitted_at":"2025-06-13T12:19:18Z","abstract_excerpt":"We consider the problem of finding the smallest graph that contains two input trees each with at most $n$ vertices preserving their distances. In other words, we look for an isometric-universal graph with the minimum number of vertices for two given trees. We prove that this problem can be solved in time $O(n^{5/2}\\log{n})$. We extend this result to forests instead of trees, and propose an algorithm with running time $O(n^{7/2}\\log{n})$. As a key ingredient, we show that a smallest isometric-universal graph of two trees essentially is a tree. Furthermore, we prove that these results cannot be "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11704","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.11704/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.11704","created_at":"2026-07-05T11:22:19.124201+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.11704v2","created_at":"2026-07-05T11:22:19.124201+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.11704","created_at":"2026-07-05T11:22:19.124201+00:00"},{"alias_kind":"pith_short_12","alias_value":"LGCCRLI276T5","created_at":"2026-07-05T11:22:19.124201+00:00"},{"alias_kind":"pith_short_16","alias_value":"LGCCRLI276T5EBIK","created_at":"2026-07-05T11:22:19.124201+00:00"},{"alias_kind":"pith_short_8","alias_value":"LGCCRLI2","created_at":"2026-07-05T11:22:19.124201+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/LGCCRLI276T5EBIKCGGGHDF7N4","json":"https://pith.science/pith/LGCCRLI276T5EBIKCGGGHDF7N4.json","graph_json":"https://pith.science/api/pith-number/LGCCRLI276T5EBIKCGGGHDF7N4/graph.json","events_json":"https://pith.science/api/pith-number/LGCCRLI276T5EBIKCGGGHDF7N4/events.json","paper":"https://pith.science/paper/LGCCRLI2"},"agent_actions":{"view_html":"https://pith.science/pith/LGCCRLI276T5EBIKCGGGHDF7N4","download_json":"https://pith.science/pith/LGCCRLI276T5EBIKCGGGHDF7N4.json","view_paper":"https://pith.science/paper/LGCCRLI2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.11704&json=true","fetch_graph":"https://pith.science/api/pith-number/LGCCRLI276T5EBIKCGGGHDF7N4/graph.json","fetch_events":"https://pith.science/api/pith-number/LGCCRLI276T5EBIKCGGGHDF7N4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LGCCRLI276T5EBIKCGGGHDF7N4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LGCCRLI276T5EBIKCGGGHDF7N4/action/storage_attestation","attest_author":"https://pith.science/pith/LGCCRLI276T5EBIKCGGGHDF7N4/action/author_attestation","sign_citation":"https://pith.science/pith/LGCCRLI276T5EBIKCGGGHDF7N4/action/citation_signature","submit_replication":"https://pith.science/pith/LGCCRLI276T5EBIKCGGGHDF7N4/action/replication_record"}},"created_at":"2026-07-05T11:22:19.124201+00:00","updated_at":"2026-07-05T11:22:19.124201+00:00"}