{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:JSDWYNJ4GBG57FVMSPIZBF7FUU","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":"2c6ec10ab6e5c514ad87c77f70143b5f5973485cc756c1796d4b70d021c22fa4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-17T17:58:13Z","title_canon_sha256":"dd72762110468f6d88683ee5bd43cf3bb51842f46342242fc18bfda8e95bb7ec"},"schema_version":"1.0","source":{"id":"2607.16390","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16390","created_at":"2026-07-21T00:20:15Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16390v1","created_at":"2026-07-21T00:20:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16390","created_at":"2026-07-21T00:20:15Z"},{"alias_kind":"pith_short_12","alias_value":"JSDWYNJ4GBG5","created_at":"2026-07-21T00:20:15Z"},{"alias_kind":"pith_short_16","alias_value":"JSDWYNJ4GBG57FVM","created_at":"2026-07-21T00:20:15Z"},{"alias_kind":"pith_short_8","alias_value":"JSDWYNJ4","created_at":"2026-07-21T00:20:15Z"}],"graph_snapshots":[{"event_id":"sha256:9f74e26bfc52e32d47e093593c1ead75049c1090df764b12133f4e9b7f2de6f0","target":"graph","created_at":"2026-07-21T00:20:15Z","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/2607.16390/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Open-addressed hash tables without reordering, such as linear probing and uniform probing, are among the simplest and most widely used data structures. Their performance is traditionally measured by probe count. We study a complementary parameter: locality, defined as the geometric distance from the first probed location to the farthest cell inspected or used.\n  At load factor $1-\\varepsilon$, uniform probing achieves the optimal $\\Theta(1/\\varepsilon)$ probe count among greedy schemes, but has essentially no locality, whereas linear probing is highly local but performs $\\Theta(1/\\varepsilon^2","authors_text":"Or Zamir","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-17T17:58:13Z","title":"Locality in Open Addressing Hash Tables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16390","kind":"arxiv","version":1},"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:b413ddecaca57f5e9f3191239ee4eb3369511b8e8c22afea92e5442553cd79a8","target":"record","created_at":"2026-07-21T00:20:15Z","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":"2c6ec10ab6e5c514ad87c77f70143b5f5973485cc756c1796d4b70d021c22fa4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.DS","submitted_at":"2026-07-17T17:58:13Z","title_canon_sha256":"dd72762110468f6d88683ee5bd43cf3bb51842f46342242fc18bfda8e95bb7ec"},"schema_version":"1.0","source":{"id":"2607.16390","kind":"arxiv","version":1}},"canonical_sha256":"4c876c353c304ddf96ac93d19097e5a50b84d6ba23f93b43dde2bfac1bbcf59c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c876c353c304ddf96ac93d19097e5a50b84d6ba23f93b43dde2bfac1bbcf59c","first_computed_at":"2026-07-21T00:20:15.422756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T00:20:15.422756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DqZWH4nOETE/YZPUq/Fb2Ncxj27vO+NdRoe5kYTruQkpCooUux4/v2RPncNzQGS3kRgSs+bP9VgD6rkwYLWoAQ==","signature_status":"signed_v1","signed_at":"2026-07-21T00:20:15.423574Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.16390","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b413ddecaca57f5e9f3191239ee4eb3369511b8e8c22afea92e5442553cd79a8","sha256:9f74e26bfc52e32d47e093593c1ead75049c1090df764b12133f4e9b7f2de6f0"],"state_sha256":"e917fba11f59f668cd428e595ce81b253ed5fa06f1e5adf9a894954db619b159"}