{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LETZ5NKVTYACD6FPMD3MKRVEBM","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":"dbe800974b1e5bb24ac268d273fff52a686c9f174dd5d29f65b8fc04058fb0db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-27T17:53:27Z","title_canon_sha256":"805f4255f14d394b252bc61b5ab1c63ac408d50c6826a4f5fc5cc92bcfc1a3e6"},"schema_version":"1.0","source":{"id":"1802.10048","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.10048","created_at":"2026-07-05T02:00:40Z"},{"alias_kind":"arxiv_version","alias_value":"1802.10048v3","created_at":"2026-07-05T02:00:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.10048","created_at":"2026-07-05T02:00:40Z"},{"alias_kind":"pith_short_12","alias_value":"LETZ5NKVTYAC","created_at":"2026-07-05T02:00:40Z"},{"alias_kind":"pith_short_16","alias_value":"LETZ5NKVTYACD6FP","created_at":"2026-07-05T02:00:40Z"},{"alias_kind":"pith_short_8","alias_value":"LETZ5NKV","created_at":"2026-07-05T02:00:40Z"}],"graph_snapshots":[{"event_id":"sha256:a1004d5a019e1a3a26d8b0236c1ef2bf79171ab6030175f9aa93d9964abc8733","target":"graph","created_at":"2026-07-05T02:00:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1802.10048/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Diameter -- the task of computing the length of a longest shortest path -- is a fundamental graph problem. Assuming the Strong Exponential Time Hypothesis, there is no $O(n^{1.99})$-time algorithm even in sparse graphs [Roditty and Williams, 2013]. To circumvent this lower bound we aim for algorithms with running time $f(k)(n+m)$ where $k$ is a parameter and $f$ is a function as small as possible. We investigate which parameters allow for such running times. To this end, we systematically explore a hierarchy of structural graph parameters.","authors_text":"Andr\\'e Nichterlein, Matthias Bentert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-27T17:53:27Z","title":"Parameterized Complexity of Diameter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.10048","kind":"arxiv","version":3},"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":"sha256:5fa1c9514613ed92c45d8c017047ee2f6a881b93deb35c3c93cbbe63cdf86367","target":"record","created_at":"2026-07-05T02:00:40Z","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":"dbe800974b1e5bb24ac268d273fff52a686c9f174dd5d29f65b8fc04058fb0db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-27T17:53:27Z","title_canon_sha256":"805f4255f14d394b252bc61b5ab1c63ac408d50c6826a4f5fc5cc92bcfc1a3e6"},"schema_version":"1.0","source":{"id":"1802.10048","kind":"arxiv","version":3}},"canonical_sha256":"59279eb5559e0021f8af60f6c546a40b0a95aee322ec14e176c7dbe4993b899c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59279eb5559e0021f8af60f6c546a40b0a95aee322ec14e176c7dbe4993b899c","first_computed_at":"2026-07-05T02:00:40.717680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:00:40.717680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sFTMbZv93z/xJ2AEB+Pi8upenR8OfY465VFE7Ktivug/kdLFb6s65L9pVYenpAZKPt/SXvoQMQaNwM+GtbPEDA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:00:40.718169Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.10048","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fa1c9514613ed92c45d8c017047ee2f6a881b93deb35c3c93cbbe63cdf86367","sha256:a1004d5a019e1a3a26d8b0236c1ef2bf79171ab6030175f9aa93d9964abc8733"],"state_sha256":"d7f0426b661f7ad74f207e79f9d5206c9689209b435ecc329b4fb847df3c2a4c"}