{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:C6HSIT4JLZZS4BIPDP4AN2IDPQ","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":"bee51284169be9d664345066340954f5a6ce6dbc9f1f8499c7e85f879711067c","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.PL","submitted_at":"2023-09-20T04:29:05Z","title_canon_sha256":"f7181e84fa60130ccba923c4c9b97816c367b7de44407a53bb2aa4f7ac2e61b3"},"schema_version":"1.0","source":{"id":"2309.11056","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.11056","created_at":"2026-07-05T06:53:45Z"},{"alias_kind":"arxiv_version","alias_value":"2309.11056v2","created_at":"2026-07-05T06:53:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.11056","created_at":"2026-07-05T06:53:45Z"},{"alias_kind":"pith_short_12","alias_value":"C6HSIT4JLZZS","created_at":"2026-07-05T06:53:45Z"},{"alias_kind":"pith_short_16","alias_value":"C6HSIT4JLZZS4BIP","created_at":"2026-07-05T06:53:45Z"},{"alias_kind":"pith_short_8","alias_value":"C6HSIT4J","created_at":"2026-07-05T06:53:45Z"}],"graph_snapshots":[{"event_id":"sha256:557cad5669f85366eee8c4cc22809dc58654059813e7603c168819e446584227","target":"graph","created_at":"2026-07-05T06:53:45Z","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/2309.11056/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Ordered sequences of data, specified with a join operation to combine sequences, serve as a foundation for the implementation of parallel functional algorithms. This abstract data type can be elegantly and efficiently implemented using balanced binary trees, where a join operation is provided to combine two trees and rebalance as necessary. In this work, we present a verified implementation and cost analysis of joinable red-black trees in $\\textbf{calf}$, a dependent type theory for cost analysis. We implement red-black trees and auxiliary intermediate data structures in such a way that all co","authors_text":"Harrison Grodin (1), Robert Harper (1) ((1) Carnegie Mellon University), Runming Li (1)","cross_cats":["cs.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.PL","submitted_at":"2023-09-20T04:29:05Z","title":"A Verified Cost Analysis of Joinable Red-Black Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.11056","kind":"arxiv","version":2},"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":"sha256:6bdfd3f59a2f169aacbba1e2baff0dd0ee77597731186ad7d20c0ebb8908081f","target":"record","created_at":"2026-07-05T06:53:45Z","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":"bee51284169be9d664345066340954f5a6ce6dbc9f1f8499c7e85f879711067c","cross_cats_sorted":["cs.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.PL","submitted_at":"2023-09-20T04:29:05Z","title_canon_sha256":"f7181e84fa60130ccba923c4c9b97816c367b7de44407a53bb2aa4f7ac2e61b3"},"schema_version":"1.0","source":{"id":"2309.11056","kind":"arxiv","version":2}},"canonical_sha256":"178f244f895e732e050f1bf806e9037c215f9252a0c0d67722bb6432352bfb2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"178f244f895e732e050f1bf806e9037c215f9252a0c0d67722bb6432352bfb2f","first_computed_at":"2026-07-05T06:53:45.236749Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:53:45.236749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"37K/9IVTu2t3d7p6FAbP6qDWDGtwwZE5jxsfJafOIGnCN5rmU64b7OyHWvIdiNfaFTEx6AdP9xOrD/N1n98gAA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:53:45.237160Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.11056","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6bdfd3f59a2f169aacbba1e2baff0dd0ee77597731186ad7d20c0ebb8908081f","sha256:557cad5669f85366eee8c4cc22809dc58654059813e7603c168819e446584227"],"state_sha256":"85e5eb66f22980a5c2788092270dca217db8e7d381eed4c54397d4db03d109a4"}