{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GM4IE73XX7JXA2UPDAZQMUQUAE","short_pith_number":"pith:GM4IE73X","canonical_record":{"source":{"id":"1709.09574","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-09-27T15:15:14Z","cross_cats_sorted":[],"title_canon_sha256":"977b93acc96d489614edccf14a61b2dced9b2f3b0f156f5e2daf42298a5afe28","abstract_canon_sha256":"6e5a1d314f1a8fef7e3b8259d60ce75a9eaea561ebd6e67d0bc6c6bd698e2f33"},"schema_version":"1.0"},"canonical_sha256":"3338827f77bfd3706a8f1833065214013ae0f2a742898e49515ee8696375d513","source":{"kind":"arxiv","id":"1709.09574","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.09574","created_at":"2026-05-18T00:34:11Z"},{"alias_kind":"arxiv_version","alias_value":"1709.09574v1","created_at":"2026-05-18T00:34:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09574","created_at":"2026-05-18T00:34:11Z"},{"alias_kind":"pith_short_12","alias_value":"GM4IE73XX7JX","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GM4IE73XX7JXA2UP","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GM4IE73X","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GM4IE73XX7JXA2UPDAZQMUQUAE","target":"record","payload":{"canonical_record":{"source":{"id":"1709.09574","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-09-27T15:15:14Z","cross_cats_sorted":[],"title_canon_sha256":"977b93acc96d489614edccf14a61b2dced9b2f3b0f156f5e2daf42298a5afe28","abstract_canon_sha256":"6e5a1d314f1a8fef7e3b8259d60ce75a9eaea561ebd6e67d0bc6c6bd698e2f33"},"schema_version":"1.0"},"canonical_sha256":"3338827f77bfd3706a8f1833065214013ae0f2a742898e49515ee8696375d513","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:11.278085Z","signature_b64":"ZGW4kq7m2xZdrCKlkVlly29BJ+9ywXclZqNA8Dbt9VNn72tkvMvrzBNva6tiotR0Jiq5wXHc9bCylxFlBQu4AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3338827f77bfd3706a8f1833065214013ae0f2a742898e49515ee8696375d513","last_reissued_at":"2026-05-18T00:34:11.277363Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:11.277363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.09574","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CFPqMVBG1PsGh+rncziqzUZN5GUV6vS9xrdNXTq8U81Do9ZMvC7vOGoIZbZvrsc4im6dDVFvmpJV2pPmxz1qCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:39:34.165371Z"},"content_sha256":"ad9a5c6608702afbf1471783b684f408745e8ee84d464991e43c562316946ff7","schema_version":"1.0","event_id":"sha256:ad9a5c6608702afbf1471783b684f408745e8ee84d464991e43c562316946ff7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GM4IE73XX7JXA2UPDAZQMUQUAE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fillable arrays with constant time operations and a single bit of redundancy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Huacheng Yu, Jacob Teo Por Loong, Jelani Nelson","submitted_at":"2017-09-27T15:15:14Z","abstract_excerpt":"In the fillable array problem one must maintain an array A[1..n] of $w$-bit entries subject to random access reads and writes, and also a $\\texttt{fill}(\\Delta)$ operation which sets every entry of to some $\\Delta\\in\\{0,\\ldots,2^w-1\\}$. We show that with just one bit of redundancy, i.e. a data structure using $nw+1$ bits of memory, $\\texttt{read}/\\texttt{fill}$ can be implemented in worst case constant time, and $\\texttt{write}$ can be implemented in either amortized constant time (deterministically) or worst case expected constant (randomized). In the latter case, we need to store an addition"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09574","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uu1UpCGlnuXhQh2ZIwEKJrf/JTxgMLGOUBChqy9Yv1LDafvQx7VBTsK+xztN3xriv3liyUE9IdgsqZA19jd8Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:39:34.165732Z"},"content_sha256":"da07ea5febd4a74f1f158061626348b207203e083ca3684fee28ed194661a152","schema_version":"1.0","event_id":"sha256:da07ea5febd4a74f1f158061626348b207203e083ca3684fee28ed194661a152"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GM4IE73XX7JXA2UPDAZQMUQUAE/bundle.json","state_url":"https://pith.science/pith/GM4IE73XX7JXA2UPDAZQMUQUAE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GM4IE73XX7JXA2UPDAZQMUQUAE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T23:39:34Z","links":{"resolver":"https://pith.science/pith/GM4IE73XX7JXA2UPDAZQMUQUAE","bundle":"https://pith.science/pith/GM4IE73XX7JXA2UPDAZQMUQUAE/bundle.json","state":"https://pith.science/pith/GM4IE73XX7JXA2UPDAZQMUQUAE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GM4IE73XX7JXA2UPDAZQMUQUAE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GM4IE73XX7JXA2UPDAZQMUQUAE","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":"6e5a1d314f1a8fef7e3b8259d60ce75a9eaea561ebd6e67d0bc6c6bd698e2f33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-09-27T15:15:14Z","title_canon_sha256":"977b93acc96d489614edccf14a61b2dced9b2f3b0f156f5e2daf42298a5afe28"},"schema_version":"1.0","source":{"id":"1709.09574","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.09574","created_at":"2026-05-18T00:34:11Z"},{"alias_kind":"arxiv_version","alias_value":"1709.09574v1","created_at":"2026-05-18T00:34:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09574","created_at":"2026-05-18T00:34:11Z"},{"alias_kind":"pith_short_12","alias_value":"GM4IE73XX7JX","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GM4IE73XX7JXA2UP","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GM4IE73X","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:da07ea5febd4a74f1f158061626348b207203e083ca3684fee28ed194661a152","target":"graph","created_at":"2026-05-18T00:34:11Z","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":"In the fillable array problem one must maintain an array A[1..n] of $w$-bit entries subject to random access reads and writes, and also a $\\texttt{fill}(\\Delta)$ operation which sets every entry of to some $\\Delta\\in\\{0,\\ldots,2^w-1\\}$. We show that with just one bit of redundancy, i.e. a data structure using $nw+1$ bits of memory, $\\texttt{read}/\\texttt{fill}$ can be implemented in worst case constant time, and $\\texttt{write}$ can be implemented in either amortized constant time (deterministically) or worst case expected constant (randomized). In the latter case, we need to store an addition","authors_text":"Huacheng Yu, Jacob Teo Por Loong, Jelani Nelson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-09-27T15:15:14Z","title":"Fillable arrays with constant time operations and a single bit of redundancy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09574","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:ad9a5c6608702afbf1471783b684f408745e8ee84d464991e43c562316946ff7","target":"record","created_at":"2026-05-18T00:34:11Z","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":"6e5a1d314f1a8fef7e3b8259d60ce75a9eaea561ebd6e67d0bc6c6bd698e2f33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-09-27T15:15:14Z","title_canon_sha256":"977b93acc96d489614edccf14a61b2dced9b2f3b0f156f5e2daf42298a5afe28"},"schema_version":"1.0","source":{"id":"1709.09574","kind":"arxiv","version":1}},"canonical_sha256":"3338827f77bfd3706a8f1833065214013ae0f2a742898e49515ee8696375d513","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3338827f77bfd3706a8f1833065214013ae0f2a742898e49515ee8696375d513","first_computed_at":"2026-05-18T00:34:11.277363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:11.277363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZGW4kq7m2xZdrCKlkVlly29BJ+9ywXclZqNA8Dbt9VNn72tkvMvrzBNva6tiotR0Jiq5wXHc9bCylxFlBQu4AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:11.278085Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.09574","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad9a5c6608702afbf1471783b684f408745e8ee84d464991e43c562316946ff7","sha256:da07ea5febd4a74f1f158061626348b207203e083ca3684fee28ed194661a152"],"state_sha256":"a9b476023a517731df59d33b1cdefd54fed61bc6b1fbbd81dbd04cd399d973d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gHJ+LuQ9QN/F3xzf81Eu9Yd+lUpxMXnl9k8xX89neZdB3KzWVfxW2pzroO2RqSY6SV3iMqXrkqHBTsYwvvs5DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:39:34.167637Z","bundle_sha256":"f49229ac0950fc5e5d7c447db36ecbdbafa0df0e0cc002de774082297767411f"}}