{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:DFDH3HQYQWCKGLNS3QKXUEFHQ6","short_pith_number":"pith:DFDH3HQY","canonical_record":{"source":{"id":"2603.23193","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-03-24T13:41:12Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"b3b77f6c3fcb69c7a27b2be5ca96099fa47725fdbdfc8356995ebcb1bbe416fc","abstract_canon_sha256":"ab5c1e2e6bc99cb4381e893c438d9c0f7bb7acb297a1d45bf250987bfa93566d"},"schema_version":"1.0"},"canonical_sha256":"19467d9e188584a32db2dc157a10a787b5f545f37a1b389a94848e3932e88aa2","source":{"kind":"arxiv","id":"2603.23193","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.23193","created_at":"2026-05-18T02:44:30Z"},{"alias_kind":"arxiv_version","alias_value":"2603.23193v3","created_at":"2026-05-18T02:44:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.23193","created_at":"2026-05-18T02:44:30Z"},{"alias_kind":"pith_short_12","alias_value":"DFDH3HQYQWCK","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"DFDH3HQYQWCKGLNS","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"DFDH3HQY","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:DFDH3HQYQWCKGLNS3QKXUEFHQ6","target":"record","payload":{"canonical_record":{"source":{"id":"2603.23193","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-03-24T13:41:12Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"b3b77f6c3fcb69c7a27b2be5ca96099fa47725fdbdfc8356995ebcb1bbe416fc","abstract_canon_sha256":"ab5c1e2e6bc99cb4381e893c438d9c0f7bb7acb297a1d45bf250987bfa93566d"},"schema_version":"1.0"},"canonical_sha256":"19467d9e188584a32db2dc157a10a787b5f545f37a1b389a94848e3932e88aa2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:30.748039Z","signature_b64":"Rl9zFb/I42yEcUFFNlr/BpOOwZ+eBUxdcIRcWCshR1zL74HAEh6D1AlNikVdKtXsPdXhIdVbuG/Bk2gliohqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19467d9e188584a32db2dc157a10a787b5f545f37a1b389a94848e3932e88aa2","last_reissued_at":"2026-05-18T02:44:30.747517Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:30.747517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2603.23193","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fhIc4hWylItOh3H1ZD0/q8lUZetmNyXZYopKy5iineWiz/5iUsuTmnUk6N3mvw+F/OPb2EqMmqjYvlTEWuoDAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T19:10:10.030073Z"},"content_sha256":"d3b0690eac04ec926a3b75546f9841247f03258deefefeac7f3d8c5421c240b8","schema_version":"1.0","event_id":"sha256:d3b0690eac04ec926a3b75546f9841247f03258deefefeac7f3d8c5421c240b8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:DFDH3HQYQWCKGLNS3QKXUEFHQ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algorithms and Hardness for Geodetic Set on Tree-like Digraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Geodetic Set can be solved in polynomial time on ditrees.","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Florent Foucaud, Lucas Lorieau, Morteza Mohammad-Noori, Narges Ghareghani, Prafullkumar Tale, Rasa Parvini Oskuei","submitted_at":"2026-03-24T13:41:12Z","abstract_excerpt":"In the GEODETIC SET problem, an input is a (di)graph $G$ and integer $k$, and the objective is to decide whether there exists a vertex subset $S$ of size $k$ such that any vertex in $V(G)\\setminus S$ lies on a shortest (directed) path between two vertices in $S$. The problem has been studied on undirected and directed graphs from both algorithmic and graph-theoretical perspectives.\n  We focus on directed graphs and prove that GEODETIC SET admits a polynomial-time algorithm on ditrees, that is, digraphs with possible 2-cycles when the underlying undirected graph is a tree (after deleting possib"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"GEODETIC SET admits a polynomial-time algorithm on ditrees, that is, digraphs with possible 2-cycles when the underlying undirected graph is a tree (after deleting possible parallel edges).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The input digraphs satisfy the structural properties like being ditrees or having bounded feedback edge set, and the algorithms correctly compute shortest paths in these structures without hidden exponential factors.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Geodetic Set can be solved in polynomial time on ditrees and in FPT time parameterized by feedback edge set on 2-cycle-free digraphs, but is NP-hard on DAGs with constant feedback vertex set and pathwidth.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Geodetic Set can be solved in polynomial time on ditrees.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5cc06fc7d4d2da81bb5ef206267ce150d6289f7f75da696193fdb688528a28f6"},"source":{"id":"2603.23193","kind":"arxiv","version":3},"verdict":{"id":"f56fdb80-258a-456b-be7b-d1a32ec9d634","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T00:24:52.706814Z","strongest_claim":"GEODETIC SET admits a polynomial-time algorithm on ditrees, that is, digraphs with possible 2-cycles when the underlying undirected graph is a tree (after deleting possible parallel edges).","one_line_summary":"Geodetic Set can be solved in polynomial time on ditrees and in FPT time parameterized by feedback edge set on 2-cycle-free digraphs, but is NP-hard on DAGs with constant feedback vertex set and pathwidth.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The input digraphs satisfy the structural properties like being ditrees or having bounded feedback edge set, and the algorithms correctly compute shortest paths in these structures without hidden exponential factors.","pith_extraction_headline":"Geodetic Set can be solved in polynomial time on ditrees."},"references":{"count":30,"sample":[{"doi":"","year":2022,"title":"Discrete Mathematics345(10), 112985 (2022)","work_id":"a9367b3e-a2e0-468f-bd1c-68f613ddfb87","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"Discrete Applied Mathematics323, 14–27 (2022)","work_id":"187e2e69-3f7d-4ec3-b488-bf1769e5d305","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Bergougnoux, B., Defrain, O., Mc Inerney, F.: Enumerating minimal solution sets for metric graph problems. In: Proc. of the 50th Inter- national Workshop on Graph-Theoretic Concepts in Computer Scienc","work_id":"5c54454e-9823-4a4d-a11b-683b381411b7","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"In: 31st International Symposium on Algorithms and Compu- tation (ISAAC 2020)","work_id":"6d663b8a-da07-4700-9b8d-4964158c0890","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2020,"title":"In: Proceedings of the 6th International Conference on Algo- rithms and Discrete Applied Mathematics (CALDAM 2020)","work_id":"be4b2222-2b52-4958-89d9-24d68ab6d767","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":30,"snapshot_sha256":"6ae957cbb80e737bba18a0b09e12ebe53beb2dfaf284d2b1ba2c689ebe5bf957","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"},"verdict_id":"f56fdb80-258a-456b-be7b-d1a32ec9d634"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u+C/VTbJu6TFNzlF61O8HPohfze00KecMFAQVAn2+Ux/C4NASVHYEevytDTZ49WxhIVThiQWp1x+9SuOa9RNBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T19:10:10.031207Z"},"content_sha256":"6e7c8ecc9a2316df0b59c1d7715f22470d9cab12c728945595012acd851a3bf6","schema_version":"1.0","event_id":"sha256:6e7c8ecc9a2316df0b59c1d7715f22470d9cab12c728945595012acd851a3bf6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DFDH3HQYQWCKGLNS3QKXUEFHQ6/bundle.json","state_url":"https://pith.science/pith/DFDH3HQYQWCKGLNS3QKXUEFHQ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DFDH3HQYQWCKGLNS3QKXUEFHQ6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T19:10:10Z","links":{"resolver":"https://pith.science/pith/DFDH3HQYQWCKGLNS3QKXUEFHQ6","bundle":"https://pith.science/pith/DFDH3HQYQWCKGLNS3QKXUEFHQ6/bundle.json","state":"https://pith.science/pith/DFDH3HQYQWCKGLNS3QKXUEFHQ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DFDH3HQYQWCKGLNS3QKXUEFHQ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DFDH3HQYQWCKGLNS3QKXUEFHQ6","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":"ab5c1e2e6bc99cb4381e893c438d9c0f7bb7acb297a1d45bf250987bfa93566d","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-03-24T13:41:12Z","title_canon_sha256":"b3b77f6c3fcb69c7a27b2be5ca96099fa47725fdbdfc8356995ebcb1bbe416fc"},"schema_version":"1.0","source":{"id":"2603.23193","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.23193","created_at":"2026-05-18T02:44:30Z"},{"alias_kind":"arxiv_version","alias_value":"2603.23193v3","created_at":"2026-05-18T02:44:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.23193","created_at":"2026-05-18T02:44:30Z"},{"alias_kind":"pith_short_12","alias_value":"DFDH3HQYQWCK","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"DFDH3HQYQWCKGLNS","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"DFDH3HQY","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:6e7c8ecc9a2316df0b59c1d7715f22470d9cab12c728945595012acd851a3bf6","target":"graph","created_at":"2026-05-18T02:44:30Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"GEODETIC SET admits a polynomial-time algorithm on ditrees, that is, digraphs with possible 2-cycles when the underlying undirected graph is a tree (after deleting possible parallel edges)."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The input digraphs satisfy the structural properties like being ditrees or having bounded feedback edge set, and the algorithms correctly compute shortest paths in these structures without hidden exponential factors."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Geodetic Set can be solved in polynomial time on ditrees and in FPT time parameterized by feedback edge set on 2-cycle-free digraphs, but is NP-hard on DAGs with constant feedback vertex set and pathwidth."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Geodetic Set can be solved in polynomial time on ditrees."}],"snapshot_sha256":"5cc06fc7d4d2da81bb5ef206267ce150d6289f7f75da696193fdb688528a28f6"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In the GEODETIC SET problem, an input is a (di)graph $G$ and integer $k$, and the objective is to decide whether there exists a vertex subset $S$ of size $k$ such that any vertex in $V(G)\\setminus S$ lies on a shortest (directed) path between two vertices in $S$. The problem has been studied on undirected and directed graphs from both algorithmic and graph-theoretical perspectives.\n  We focus on directed graphs and prove that GEODETIC SET admits a polynomial-time algorithm on ditrees, that is, digraphs with possible 2-cycles when the underlying undirected graph is a tree (after deleting possib","authors_text":"Florent Foucaud, Lucas Lorieau, Morteza Mohammad-Noori, Narges Ghareghani, Prafullkumar Tale, Rasa Parvini Oskuei","cross_cats":["cs.DM"],"headline":"Geodetic Set can be solved in polynomial time on ditrees.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-03-24T13:41:12Z","title":"Algorithms and Hardness for Geodetic Set on Tree-like Digraphs"},"references":{"count":30,"internal_anchors":0,"resolved_work":30,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"Discrete Mathematics345(10), 112985 (2022)","work_id":"a9367b3e-a2e0-468f-bd1c-68f613ddfb87","year":2022},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Discrete Applied Mathematics323, 14–27 (2022)","work_id":"187e2e69-3f7d-4ec3-b488-bf1769e5d305","year":2022},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Bergougnoux, B., Defrain, O., Mc Inerney, F.: Enumerating minimal solution sets for metric graph problems. In: Proc. of the 50th Inter- national Workshop on Graph-Theoretic Concepts in Computer Scienc","work_id":"5c54454e-9823-4a4d-a11b-683b381411b7","year":2024},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"In: 31st International Symposium on Algorithms and Compu- tation (ISAAC 2020)","work_id":"6d663b8a-da07-4700-9b8d-4964158c0890","year":2020},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"In: Proceedings of the 6th International Conference on Algo- rithms and Discrete Applied Mathematics (CALDAM 2020)","work_id":"be4b2222-2b52-4958-89d9-24d68ab6d767","year":2020}],"snapshot_sha256":"6ae957cbb80e737bba18a0b09e12ebe53beb2dfaf284d2b1ba2c689ebe5bf957"},"source":{"id":"2603.23193","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-15T00:24:52.706814Z","id":"f56fdb80-258a-456b-be7b-d1a32ec9d634","model_set":{"reader":"grok-4.3"},"one_line_summary":"Geodetic Set can be solved in polynomial time on ditrees and in FPT time parameterized by feedback edge set on 2-cycle-free digraphs, but is NP-hard on DAGs with constant feedback vertex set and pathwidth.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Geodetic Set can be solved in polynomial time on ditrees.","strongest_claim":"GEODETIC SET admits a polynomial-time algorithm on ditrees, that is, digraphs with possible 2-cycles when the underlying undirected graph is a tree (after deleting possible parallel edges).","weakest_assumption":"The input digraphs satisfy the structural properties like being ditrees or having bounded feedback edge set, and the algorithms correctly compute shortest paths in these structures without hidden exponential factors."}},"verdict_id":"f56fdb80-258a-456b-be7b-d1a32ec9d634"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d3b0690eac04ec926a3b75546f9841247f03258deefefeac7f3d8c5421c240b8","target":"record","created_at":"2026-05-18T02:44:30Z","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":"ab5c1e2e6bc99cb4381e893c438d9c0f7bb7acb297a1d45bf250987bfa93566d","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2026-03-24T13:41:12Z","title_canon_sha256":"b3b77f6c3fcb69c7a27b2be5ca96099fa47725fdbdfc8356995ebcb1bbe416fc"},"schema_version":"1.0","source":{"id":"2603.23193","kind":"arxiv","version":3}},"canonical_sha256":"19467d9e188584a32db2dc157a10a787b5f545f37a1b389a94848e3932e88aa2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19467d9e188584a32db2dc157a10a787b5f545f37a1b389a94848e3932e88aa2","first_computed_at":"2026-05-18T02:44:30.747517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:30.747517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rl9zFb/I42yEcUFFNlr/BpOOwZ+eBUxdcIRcWCshR1zL74HAEh6D1AlNikVdKtXsPdXhIdVbuG/Bk2gliohqCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:30.748039Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.23193","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3b0690eac04ec926a3b75546f9841247f03258deefefeac7f3d8c5421c240b8","sha256:6e7c8ecc9a2316df0b59c1d7715f22470d9cab12c728945595012acd851a3bf6"],"state_sha256":"38bf112c62357dc6d52787204d16e58d53ad913a9d6e57473270dbffccb3954e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"82i1gHJUUlGS40GcYaHq/TyZ8B1GtoK8uJ+XeWUYR9pxV5CTjLKGsHaeNtY9GDFZpn48N/Y+N99bFWQjlHZFDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T19:10:10.036093Z","bundle_sha256":"0ff4dc968f8961013bcf2a3d8e6a38d50840fefc2463c8325bcd0a291b3970cd"}}