{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ROE7T7P24STDK4JLRYFB3WJMKU","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":"f2c275b7342488e26ed3274ff4c29c92b9cd2d64d9a927292f8cadf40ddbcaf2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-08-08T08:50:44Z","title_canon_sha256":"013bdc1578d8bb33f46d155c45dd10e2cfb341c85bcae09043ebac69ad9825b2"},"schema_version":"1.0","source":{"id":"2608.08013","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.08013","created_at":"2026-08-11T01:21:23Z"},{"alias_kind":"arxiv_version","alias_value":"2608.08013v1","created_at":"2026-08-11T01:21:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.08013","created_at":"2026-08-11T01:21:23Z"},{"alias_kind":"pith_short_12","alias_value":"ROE7T7P24STD","created_at":"2026-08-11T01:21:23Z"},{"alias_kind":"pith_short_16","alias_value":"ROE7T7P24STDK4JL","created_at":"2026-08-11T01:21:23Z"},{"alias_kind":"pith_short_8","alias_value":"ROE7T7P2","created_at":"2026-08-11T01:21:23Z"}],"graph_snapshots":[{"event_id":"sha256:a859236ab6114b7947e6219d58eebf244d570e0273c6b41d27baf6dc8c1557d9","target":"graph","created_at":"2026-08-11T01:21:23Z","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/2608.08013/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In open addressed hashing, quadratic probing is attractive for striking a nice balance between having a high locality of reference and a low number of probes per search. However, these are empirical observations, not theoretical guarantees. Indeed, until recently, it was not known whether quadratic probing had constant expected insertion cost under any positive load factor $\\alpha > 0$, even with uniformly random hash functions.\n  In a recent breakthrough---albeit a numerically understated breakthrough---Kuszmaul and Xi (2024) proved that any fixed offset sequence (including quadratic probing)","authors_text":"Chengzhang Wan, Seth Pettie, Yuhao Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-08-08T08:50:44Z","title":"A Simple Analysis of Quadratic Probing and Other Open Addressing Schemes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08013","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":"sha256:4e26ffc6b15cbf11b167b2210066d20633d53b3cb9e80ee063e552dc7d3d419f","target":"record","created_at":"2026-08-11T01:21:23Z","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":"f2c275b7342488e26ed3274ff4c29c92b9cd2d64d9a927292f8cadf40ddbcaf2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-08-08T08:50:44Z","title_canon_sha256":"013bdc1578d8bb33f46d155c45dd10e2cfb341c85bcae09043ebac69ad9825b2"},"schema_version":"1.0","source":{"id":"2608.08013","kind":"arxiv","version":1}},"canonical_sha256":"8b89f9fdfae4a635712b8e0a1dd92c5515ca82d96f0d306d48b4442f04350b20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b89f9fdfae4a635712b8e0a1dd92c5515ca82d96f0d306d48b4442f04350b20","first_computed_at":"2026-08-11T01:21:23.134178Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-11T01:21:23.134178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ysmli/P8X/muqBobbifeAYy5S++1qVLalcAxiuF/koqtwEGEl7pPs1IY2xHod0VDb+998azfPRCb+zWdw13NDQ==","signature_status":"signed_v1","signed_at":"2026-08-11T01:21:23.136676Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.08013","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e26ffc6b15cbf11b167b2210066d20633d53b3cb9e80ee063e552dc7d3d419f","sha256:a859236ab6114b7947e6219d58eebf244d570e0273c6b41d27baf6dc8c1557d9"],"state_sha256":"0174ed994147601f2a83a087d24dade11739f5310fcb0f29483fc659b5c9ff4b"}