{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LL2H242GVAMNQ4JCPF7LDHBBIZ","short_pith_number":"pith:LL2H242G","canonical_record":{"source":{"id":"1507.06866","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-24T14:57:18Z","cross_cats_sorted":[],"title_canon_sha256":"4f6ff1100b6868c85ecc275d3e576a5319bc75fb294e71ddfdc28074605418c5","abstract_canon_sha256":"45386821885c22a799b4e1e7243c15169b334a523b9bf9a128767779523b7a9c"},"schema_version":"1.0"},"canonical_sha256":"5af47d7346a818d87122797eb19c21466f3c36c242a03325c07f30ca045b6fca","source":{"kind":"arxiv","id":"1507.06866","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.06866","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"arxiv_version","alias_value":"1507.06866v1","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06866","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"pith_short_12","alias_value":"LL2H242GVAMN","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LL2H242GVAMNQ4JC","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LL2H242G","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LL2H242GVAMNQ4JCPF7LDHBBIZ","target":"record","payload":{"canonical_record":{"source":{"id":"1507.06866","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-24T14:57:18Z","cross_cats_sorted":[],"title_canon_sha256":"4f6ff1100b6868c85ecc275d3e576a5319bc75fb294e71ddfdc28074605418c5","abstract_canon_sha256":"45386821885c22a799b4e1e7243c15169b334a523b9bf9a128767779523b7a9c"},"schema_version":"1.0"},"canonical_sha256":"5af47d7346a818d87122797eb19c21466f3c36c242a03325c07f30ca045b6fca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:21.833149Z","signature_b64":"1AL4TvulEb0G1q+EwbUx9+FaNFzZrq3UNeizRemGuFglE6tJ1sP+GA8CWWx7iYzNicFVHpPN0PpN+ZzPkVQwDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5af47d7346a818d87122797eb19c21466f3c36c242a03325c07f30ca045b6fca","last_reissued_at":"2026-05-18T01:36:21.832485Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:21.832485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.06866","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":"2026-05-18T01:36:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cGuFFh1jfyPUZoRUWpDRGjwhh/Ki+s5Ark8WrPi36WdmNRDIgtIvyfstZvwKJXMbdBdRlBHWbMSQCtkKmBxeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:47:23.236670Z"},"content_sha256":"467851dc18a9460f447704f2b1e8aa8faed75e9053b27ebb64722e8198ce63b5","schema_version":"1.0","event_id":"sha256:467851dc18a9460f447704f2b1e8aa8faed75e9053b27ebb64722e8198ce63b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LL2H242GVAMNQ4JCPF7LDHBBIZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compressed Data Structures for Dynamic Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"J. Ian Munro, Yakov Nekrich","submitted_at":"2015-07-24T14:57:18Z","abstract_excerpt":"We consider the problem of storing a dynamic string $S$ over an alphabet $\\Sigma=\\{\\,1,\\ldots,\\sigma\\,\\}$ in compressed form. Our representation supports insertions and deletions of symbols and answers three fundamental queries: $\\mathrm{access}(i,S)$ returns the $i$-th symbol in $S$, $\\mathrm{rank}_a(i,S)$ counts how many times a symbol $a$ occurs among the first $i$ positions in $S$, and $\\mathrm{select}_a(i,S)$ finds the position where a symbol $a$ occurs for the $i$-th time. We present the first fully-dynamic data structure for arbitrarily large alphabets that achieves optimal query times "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06866","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":"2026-05-18T01:36:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WirWDA67soxcmLcLVjrREkDaM3JivcC43YDsqUpOU5IHz1RMUFnQ+rrVREjW/qHo5ZxTh1gbJYz1Dpn8caq3CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:47:23.237407Z"},"content_sha256":"f19f290fe9600b5fe0c1801cee48dddca308e5449fa06578617080a2e208595c","schema_version":"1.0","event_id":"sha256:f19f290fe9600b5fe0c1801cee48dddca308e5449fa06578617080a2e208595c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LL2H242GVAMNQ4JCPF7LDHBBIZ/bundle.json","state_url":"https://pith.science/pith/LL2H242GVAMNQ4JCPF7LDHBBIZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LL2H242GVAMNQ4JCPF7LDHBBIZ/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":"2026-05-27T15:47:23Z","links":{"resolver":"https://pith.science/pith/LL2H242GVAMNQ4JCPF7LDHBBIZ","bundle":"https://pith.science/pith/LL2H242GVAMNQ4JCPF7LDHBBIZ/bundle.json","state":"https://pith.science/pith/LL2H242GVAMNQ4JCPF7LDHBBIZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LL2H242GVAMNQ4JCPF7LDHBBIZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LL2H242GVAMNQ4JCPF7LDHBBIZ","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":"45386821885c22a799b4e1e7243c15169b334a523b9bf9a128767779523b7a9c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-24T14:57:18Z","title_canon_sha256":"4f6ff1100b6868c85ecc275d3e576a5319bc75fb294e71ddfdc28074605418c5"},"schema_version":"1.0","source":{"id":"1507.06866","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.06866","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"arxiv_version","alias_value":"1507.06866v1","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06866","created_at":"2026-05-18T01:36:21Z"},{"alias_kind":"pith_short_12","alias_value":"LL2H242GVAMN","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LL2H242GVAMNQ4JC","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LL2H242G","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:f19f290fe9600b5fe0c1801cee48dddca308e5449fa06578617080a2e208595c","target":"graph","created_at":"2026-05-18T01:36:21Z","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":"We consider the problem of storing a dynamic string $S$ over an alphabet $\\Sigma=\\{\\,1,\\ldots,\\sigma\\,\\}$ in compressed form. Our representation supports insertions and deletions of symbols and answers three fundamental queries: $\\mathrm{access}(i,S)$ returns the $i$-th symbol in $S$, $\\mathrm{rank}_a(i,S)$ counts how many times a symbol $a$ occurs among the first $i$ positions in $S$, and $\\mathrm{select}_a(i,S)$ finds the position where a symbol $a$ occurs for the $i$-th time. We present the first fully-dynamic data structure for arbitrarily large alphabets that achieves optimal query times ","authors_text":"J. Ian Munro, Yakov Nekrich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-24T14:57:18Z","title":"Compressed Data Structures for Dynamic Sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06866","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":"sha256:467851dc18a9460f447704f2b1e8aa8faed75e9053b27ebb64722e8198ce63b5","target":"record","created_at":"2026-05-18T01:36:21Z","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":"45386821885c22a799b4e1e7243c15169b334a523b9bf9a128767779523b7a9c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-07-24T14:57:18Z","title_canon_sha256":"4f6ff1100b6868c85ecc275d3e576a5319bc75fb294e71ddfdc28074605418c5"},"schema_version":"1.0","source":{"id":"1507.06866","kind":"arxiv","version":1}},"canonical_sha256":"5af47d7346a818d87122797eb19c21466f3c36c242a03325c07f30ca045b6fca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5af47d7346a818d87122797eb19c21466f3c36c242a03325c07f30ca045b6fca","first_computed_at":"2026-05-18T01:36:21.832485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:21.832485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1AL4TvulEb0G1q+EwbUx9+FaNFzZrq3UNeizRemGuFglE6tJ1sP+GA8CWWx7iYzNicFVHpPN0PpN+ZzPkVQwDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:21.833149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.06866","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:467851dc18a9460f447704f2b1e8aa8faed75e9053b27ebb64722e8198ce63b5","sha256:f19f290fe9600b5fe0c1801cee48dddca308e5449fa06578617080a2e208595c"],"state_sha256":"5304d3c80ae7327659cdc497ae03ea50c2c1ec75df78c299738f560600d2697e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Y03PY3H/VzX6ogYr5DFuXh71ppUyjVbobSy36+Lfy6iXGHL88+i0tEI4XY4MNNfg8yd28SGBw1ZTHIIqV4pBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T15:47:23.241307Z","bundle_sha256":"0de0396eaeb3aaeeb8d5aa0d0d27af9126b067ef197a6a4430524b1678ff32b1"}}