{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DWPRJQBCSF5TBNXFCOII7OS53G","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":"b36079b0a7b7516114d04c200ca526f32bef381fa47f48e5acd11b0373869468","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-04-20T18:52:00Z","title_canon_sha256":"89b14fc1f456e9964b8ae54f9e96f10d8a0e0bdce465eb4412c3d100e6733370"},"schema_version":"1.0","source":{"id":"1604.06058","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06058","created_at":"2026-05-18T00:48:37Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06058v3","created_at":"2026-05-18T00:48:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06058","created_at":"2026-05-18T00:48:37Z"},{"alias_kind":"pith_short_12","alias_value":"DWPRJQBCSF5T","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DWPRJQBCSF5TBNXF","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DWPRJQBC","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:476df3217d14dde3fd1d8201db8272ec50aa7e1346f1650d90820ca4426c35b4","target":"graph","created_at":"2026-05-18T00:48:37Z","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"},"paper":{"abstract_excerpt":"The choice dictionary is introduced as a data structure that can be initialized with a parameter $n\\in\\mathbb{N}=\\{1,2,\\ldots\\}$ and subsequently maintains an initially empty subset $S$ of $\\{1,\\ldots,n\\}$ under insertion, deletion, membership queries and an operation choice that returns an arbitrary element of $S$. The choice dictionary appears to be fundamental in space-efficient computing. We show that there is a choice dictionary that can be initialized with $n$ and an additional parameter $t\\in\\mathbb{N}$ and subsequently occupies $n+O(n(t/w)^t+\\log n)$ bits of memory and executes each of","authors_text":"Frank Kammer, Torben Hagerup","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-04-20T18:52:00Z","title":"Succinct Choice Dictionaries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06058","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":"sha256:47f617d896d5abe43cedf184967aa682d469cf4206454274b0764ba63fd596cc","target":"record","created_at":"2026-05-18T00:48:37Z","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":"b36079b0a7b7516114d04c200ca526f32bef381fa47f48e5acd11b0373869468","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-04-20T18:52:00Z","title_canon_sha256":"89b14fc1f456e9964b8ae54f9e96f10d8a0e0bdce465eb4412c3d100e6733370"},"schema_version":"1.0","source":{"id":"1604.06058","kind":"arxiv","version":3}},"canonical_sha256":"1d9f14c022917b30b6e513908fba5dd99045c3d7c2fce1353d58e42d6b898a83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d9f14c022917b30b6e513908fba5dd99045c3d7c2fce1353d58e42d6b898a83","first_computed_at":"2026-05-18T00:48:37.350110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:37.350110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c2dGnFk0muBUsYoqF1hLZzjtFv/emc0YC3p4Dkj6iymOriogsye/NEpVS4wCt1/mHQR4k58svC25OIQK4bgeCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:37.350746Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06058","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47f617d896d5abe43cedf184967aa682d469cf4206454274b0764ba63fd596cc","sha256:476df3217d14dde3fd1d8201db8272ec50aa7e1346f1650d90820ca4426c35b4"],"state_sha256":"8e0fb3f02c368e30eb2df1393893b41e7f60dbd7969e14b7f9001adf8ef740e8"}