{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:X3W6LJCAYYIQF4UJJHMTR6S4RK","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":"e30d2b0eec083f7140799a7bfecbabaa229619ef2d82c0d0056d62137796a1b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-06-09T15:58:59Z","title_canon_sha256":"b4129c601a49e6ba97ea6dfb338a015ebc0061681c9eb3a856e19ffe8ab257d0"},"schema_version":"1.0","source":{"id":"1506.02973","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.02973","created_at":"2026-05-18T01:55:40Z"},{"alias_kind":"arxiv_version","alias_value":"1506.02973v1","created_at":"2026-05-18T01:55:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.02973","created_at":"2026-05-18T01:55:40Z"},{"alias_kind":"pith_short_12","alias_value":"X3W6LJCAYYIQ","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"X3W6LJCAYYIQF4UJ","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"X3W6LJCA","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:99b6b2790383cfa6e6c1eb828c57f6b0e74e2625b4ceb9a137cf29e362e1cdc6","target":"graph","created_at":"2026-05-18T01:55:40Z","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 this paper we study the problem of answering connectivity queries about a \\emph{graph timeline}. A graph timeline is a sequence of undirected graphs $G_1,\\ldots,G_t$ on a common set of vertices of size $n$ such that each graph is obtained from the previous one by an addition or a deletion of a single edge. We present data structures, which preprocess the timeline and can answer the following queries:\n  - forall$(u,v,a,b)$ -- does the path $u\\to v$ exist in each of $G_a,\\ldots,G_b$?\n  - exists$(u,v,a,b)$ -- does the path $u\\to v$ exist in any of $G_a,\\ldots,G_b$?\n  - forall2$(u,v,a,b)$ -- do","authors_text":"Adam Karczmarz, Jakub {\\L}\\k{a}cki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-06-09T15:58:59Z","title":"Fast and simple connectivity in graph timelines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.02973","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":"sha256:5e36d1286f8e5daa38c7d71be425bc9fd0f5885799679d33e1fed91c2c6b6881","target":"record","created_at":"2026-05-18T01:55:40Z","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":"e30d2b0eec083f7140799a7bfecbabaa229619ef2d82c0d0056d62137796a1b6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-06-09T15:58:59Z","title_canon_sha256":"b4129c601a49e6ba97ea6dfb338a015ebc0061681c9eb3a856e19ffe8ab257d0"},"schema_version":"1.0","source":{"id":"1506.02973","kind":"arxiv","version":1}},"canonical_sha256":"beede5a440c61102f28949d938fa5c8aad9c894633d41efbad5955ef8e6e94cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"beede5a440c61102f28949d938fa5c8aad9c894633d41efbad5955ef8e6e94cd","first_computed_at":"2026-05-18T01:55:40.374192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:40.374192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y6FMFrc+rdSiMouz5dkwq4P8hswATuSx2Ca8DA6QqoA+tgrgka+EvQGUZn2XME9Q8Zw5nJIvfzZBIyf3zlWsDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:40.374893Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.02973","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e36d1286f8e5daa38c7d71be425bc9fd0f5885799679d33e1fed91c2c6b6881","sha256:99b6b2790383cfa6e6c1eb828c57f6b0e74e2625b4ceb9a137cf29e362e1cdc6"],"state_sha256":"96a2e34714b237048db439ec31e7d5b59850133b622e418d8a79d81b1834014d"}