{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7QGAQ7GX2XUOU3L6KFPOJ6EOHH","short_pith_number":"pith:7QGAQ7GX","canonical_record":{"source":{"id":"1806.10051","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-06-26T15:07:47Z","cross_cats_sorted":[],"title_canon_sha256":"d3d2bc192d71a8edc419e039a315c7c0adf2fd3694e5be4da725f95915d3dfc9","abstract_canon_sha256":"d2c5688e2e232e4651c851bed24f3640eb16aaa050e29b2807c2f467c6bff5f9"},"schema_version":"1.0"},"canonical_sha256":"fc0c087cd7d5e8ea6d7e515ee4f88e39f7b201fc87e3b1fa533172acff7cb22d","source":{"kind":"arxiv","id":"1806.10051","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10051","created_at":"2026-05-18T00:12:20Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10051v1","created_at":"2026-05-18T00:12:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10051","created_at":"2026-05-18T00:12:20Z"},{"alias_kind":"pith_short_12","alias_value":"7QGAQ7GX2XUO","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7QGAQ7GX2XUOU3L6","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7QGAQ7GX","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7QGAQ7GX2XUOU3L6KFPOJ6EOHH","target":"record","payload":{"canonical_record":{"source":{"id":"1806.10051","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-06-26T15:07:47Z","cross_cats_sorted":[],"title_canon_sha256":"d3d2bc192d71a8edc419e039a315c7c0adf2fd3694e5be4da725f95915d3dfc9","abstract_canon_sha256":"d2c5688e2e232e4651c851bed24f3640eb16aaa050e29b2807c2f467c6bff5f9"},"schema_version":"1.0"},"canonical_sha256":"fc0c087cd7d5e8ea6d7e515ee4f88e39f7b201fc87e3b1fa533172acff7cb22d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:20.098951Z","signature_b64":"oWyCCbCM9eOBkMMwjrjq7yxyY7jZAR7JVPP/ZFB7+3YbeMW6nmrl5m54Ffkg/xgo93xc7038E1KFrOL7/FQoAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc0c087cd7d5e8ea6d7e515ee4f88e39f7b201fc87e3b1fa533172acff7cb22d","last_reissued_at":"2026-05-18T00:12:20.098291Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:20.098291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.10051","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":"2026-05-18T00:12:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o91HH5nUzbLBgXeWNnIZ1pKxG3a/X+VkY2Bk/cLMphCFL6TCEHpWTP1XJFnGAUZ+rcZ4HL+dRwxxXuLB/lBABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:52:48.886743Z"},"content_sha256":"40482484c8fb8c6354a2165597ad03d4ed525efbff49dd13e40cc1258201fe95","schema_version":"1.0","event_id":"sha256:40482484c8fb8c6354a2165597ad03d4ed525efbff49dd13e40cc1258201fe95"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7QGAQ7GX2XUOU3L6KFPOJ6EOHH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fully Dynamic Maximal Independent Set with Sublinear in n Update Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Baruch Schieber, Krzysztof Onak, Sepehr Assadi, Shay Solomon","submitted_at":"2018-06-26T15:07:47Z","abstract_excerpt":"The first fully dynamic algorithm for maintaining a maximal independent set (MIS) with update time that is sublinear in the number of edges was presented recently by the authors of this paper [Assadi et.al. STOC'18]. The algorithm is deterministic and its update time is $O(m^{3/4})$, where $m$ is the (dynamically changing) number of edges. Subsequently, Gupta and Khan and independently Du and Zhang [arXiv, April 2018] presented deterministic algorithms for dynamic MIS with update times of $O(m^{2/3})$ and $O(m^{2/3} \\sqrt{\\log m})$, respectively. Du and Zhang also gave a randomized algorithm w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10051","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":"2026-05-18T00:12:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"17AzU1SwYPs0CMNWRWrfyXdjAagcFnY+3Sq8uHd9XLB9GpozClMLmypdQMso0q1TkjvJDVAtNaDEIOfizeMSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:52:48.887229Z"},"content_sha256":"fcc632b5e99aacd6e32993bcdf1a8bf434b48d474e871639033504fae1c06346","schema_version":"1.0","event_id":"sha256:fcc632b5e99aacd6e32993bcdf1a8bf434b48d474e871639033504fae1c06346"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7QGAQ7GX2XUOU3L6KFPOJ6EOHH/bundle.json","state_url":"https://pith.science/pith/7QGAQ7GX2XUOU3L6KFPOJ6EOHH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7QGAQ7GX2XUOU3L6KFPOJ6EOHH/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":"2026-05-27T03:52:48Z","links":{"resolver":"https://pith.science/pith/7QGAQ7GX2XUOU3L6KFPOJ6EOHH","bundle":"https://pith.science/pith/7QGAQ7GX2XUOU3L6KFPOJ6EOHH/bundle.json","state":"https://pith.science/pith/7QGAQ7GX2XUOU3L6KFPOJ6EOHH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7QGAQ7GX2XUOU3L6KFPOJ6EOHH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7QGAQ7GX2XUOU3L6KFPOJ6EOHH","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":"d2c5688e2e232e4651c851bed24f3640eb16aaa050e29b2807c2f467c6bff5f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-06-26T15:07:47Z","title_canon_sha256":"d3d2bc192d71a8edc419e039a315c7c0adf2fd3694e5be4da725f95915d3dfc9"},"schema_version":"1.0","source":{"id":"1806.10051","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10051","created_at":"2026-05-18T00:12:20Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10051v1","created_at":"2026-05-18T00:12:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10051","created_at":"2026-05-18T00:12:20Z"},{"alias_kind":"pith_short_12","alias_value":"7QGAQ7GX2XUO","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7QGAQ7GX2XUOU3L6","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7QGAQ7GX","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:fcc632b5e99aacd6e32993bcdf1a8bf434b48d474e871639033504fae1c06346","target":"graph","created_at":"2026-05-18T00:12:20Z","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 first fully dynamic algorithm for maintaining a maximal independent set (MIS) with update time that is sublinear in the number of edges was presented recently by the authors of this paper [Assadi et.al. STOC'18]. The algorithm is deterministic and its update time is $O(m^{3/4})$, where $m$ is the (dynamically changing) number of edges. Subsequently, Gupta and Khan and independently Du and Zhang [arXiv, April 2018] presented deterministic algorithms for dynamic MIS with update times of $O(m^{2/3})$ and $O(m^{2/3} \\sqrt{\\log m})$, respectively. Du and Zhang also gave a randomized algorithm w","authors_text":"Baruch Schieber, Krzysztof Onak, Sepehr Assadi, Shay Solomon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-06-26T15:07:47Z","title":"Fully Dynamic Maximal Independent Set with Sublinear in n Update Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10051","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":"sha256:40482484c8fb8c6354a2165597ad03d4ed525efbff49dd13e40cc1258201fe95","target":"record","created_at":"2026-05-18T00:12:20Z","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":"d2c5688e2e232e4651c851bed24f3640eb16aaa050e29b2807c2f467c6bff5f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-06-26T15:07:47Z","title_canon_sha256":"d3d2bc192d71a8edc419e039a315c7c0adf2fd3694e5be4da725f95915d3dfc9"},"schema_version":"1.0","source":{"id":"1806.10051","kind":"arxiv","version":1}},"canonical_sha256":"fc0c087cd7d5e8ea6d7e515ee4f88e39f7b201fc87e3b1fa533172acff7cb22d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc0c087cd7d5e8ea6d7e515ee4f88e39f7b201fc87e3b1fa533172acff7cb22d","first_computed_at":"2026-05-18T00:12:20.098291Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:20.098291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oWyCCbCM9eOBkMMwjrjq7yxyY7jZAR7JVPP/ZFB7+3YbeMW6nmrl5m54Ffkg/xgo93xc7038E1KFrOL7/FQoAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:20.098951Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.10051","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40482484c8fb8c6354a2165597ad03d4ed525efbff49dd13e40cc1258201fe95","sha256:fcc632b5e99aacd6e32993bcdf1a8bf434b48d474e871639033504fae1c06346"],"state_sha256":"c88e8a82271de8c6afb79f851bd4fdba49536dec015eb91c1d03e08f9c19b9cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NBOXil1Gtlrnt7KoM36D/3AS8iJXKo2Gt0d4n7ONvuv3en7IcI6GQSbj5F5EeVRJLHs/o+ww9r8jZhfsLMYrAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T03:52:48.890049Z","bundle_sha256":"62afb0aca1c979c3f0e6d4f99d0cf7103d8c8d0a1c6bd66a852d97dddd5756f2"}}