{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:52N7KQ47WCFHEGWWWUQJCDEWNH","short_pith_number":"pith:52N7KQ47","canonical_record":{"source":{"id":"1602.06705","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-02-22T10:07:27Z","cross_cats_sorted":[],"title_canon_sha256":"23a6813e28e1cdc0c733d03f089fc50faa20c954209010622e8f9570ce620666","abstract_canon_sha256":"720e1fc7d2db23ede46991f22d1a98d22f82c81aa9ed0cd765d64f34efb68be6"},"schema_version":"1.0"},"canonical_sha256":"ee9bf5439fb08a721ad6b520910c9669f76e7fcaaa7d747dd24d77d949d558a7","source":{"kind":"arxiv","id":"1602.06705","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.06705","created_at":"2026-05-18T01:15:49Z"},{"alias_kind":"arxiv_version","alias_value":"1602.06705v2","created_at":"2026-05-18T01:15:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06705","created_at":"2026-05-18T01:15:49Z"},{"alias_kind":"pith_short_12","alias_value":"52N7KQ47WCFH","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"52N7KQ47WCFHEGWW","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"52N7KQ47","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:52N7KQ47WCFHEGWWWUQJCDEWNH","target":"record","payload":{"canonical_record":{"source":{"id":"1602.06705","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-02-22T10:07:27Z","cross_cats_sorted":[],"title_canon_sha256":"23a6813e28e1cdc0c733d03f089fc50faa20c954209010622e8f9570ce620666","abstract_canon_sha256":"720e1fc7d2db23ede46991f22d1a98d22f82c81aa9ed0cd765d64f34efb68be6"},"schema_version":"1.0"},"canonical_sha256":"ee9bf5439fb08a721ad6b520910c9669f76e7fcaaa7d747dd24d77d949d558a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:49.483909Z","signature_b64":"WT6af3dXuTuoFzJUUDMkeIhrwN61gHzVSXypeoHtCGpUHQouDE2RV7cNLUC+5sThgW/pQtUG9XqHx0DNfzVpBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee9bf5439fb08a721ad6b520910c9669f76e7fcaaa7d747dd24d77d949d558a7","last_reissued_at":"2026-05-18T01:15:49.483106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:49.483106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.06705","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:15:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NBQqQmVXJPSA3qnQTzY65e04l3M+uG8vIs5LuA9yRW3L+9McdlhoJWQT8Sk30kRCeQY1LZTpt9Yh6wM50Q2JAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:53:11.173125Z"},"content_sha256":"5bd9377addb1831ab60c3a5bc640e5164f551f8c04c34bda1aaf5d23b5530d74","schema_version":"1.0","event_id":"sha256:5bd9377addb1831ab60c3a5bc640e5164f551f8c04c34bda1aaf5d23b5530d74"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:52N7KQ47WCFHEGWWWUQJCDEWNH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Hardness of Partially Dynamic Graph Problems and Connections to Diameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"S{\\o}ren Dahlgaard","submitted_at":"2016-02-22T10:07:27Z","abstract_excerpt":"Conditional lower bounds for dynamic graph problems has received a great deal of attention in recent years. While many results are now known for the fully-dynamic case and such bounds often imply worst-case bounds for the partially dynamic setting, it seems much more difficult to prove amortized bounds for incremental and decremental algorithms. In this paper we consider partially dynamic versions of three classic problems in graph theory. Based on popular conjectures we show that:\n  -- No algorithm with amortized update time $O(n^{1-\\varepsilon})$ exists for incremental or decremental maximum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06705","kind":"arxiv","version":2},"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":"2026-05-18T01:15:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jexXMoLk4WBE7BRlvh9YXPxbkRBFod9p9evQ8rqPsZ5VrCHq0K00CpJLjhv5z4wKhKePBtAjVfHBtFvCX0WLBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:53:11.173480Z"},"content_sha256":"5fa97ee02cf710c869bbda31fdf2f94f48d9712cf10c594bbe156ef0a9ba9b7d","schema_version":"1.0","event_id":"sha256:5fa97ee02cf710c869bbda31fdf2f94f48d9712cf10c594bbe156ef0a9ba9b7d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/52N7KQ47WCFHEGWWWUQJCDEWNH/bundle.json","state_url":"https://pith.science/pith/52N7KQ47WCFHEGWWWUQJCDEWNH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/52N7KQ47WCFHEGWWWUQJCDEWNH/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":"2026-06-27T12:53:11Z","links":{"resolver":"https://pith.science/pith/52N7KQ47WCFHEGWWWUQJCDEWNH","bundle":"https://pith.science/pith/52N7KQ47WCFHEGWWWUQJCDEWNH/bundle.json","state":"https://pith.science/pith/52N7KQ47WCFHEGWWWUQJCDEWNH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/52N7KQ47WCFHEGWWWUQJCDEWNH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:52N7KQ47WCFHEGWWWUQJCDEWNH","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":"720e1fc7d2db23ede46991f22d1a98d22f82c81aa9ed0cd765d64f34efb68be6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-02-22T10:07:27Z","title_canon_sha256":"23a6813e28e1cdc0c733d03f089fc50faa20c954209010622e8f9570ce620666"},"schema_version":"1.0","source":{"id":"1602.06705","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.06705","created_at":"2026-05-18T01:15:49Z"},{"alias_kind":"arxiv_version","alias_value":"1602.06705v2","created_at":"2026-05-18T01:15:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.06705","created_at":"2026-05-18T01:15:49Z"},{"alias_kind":"pith_short_12","alias_value":"52N7KQ47WCFH","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"52N7KQ47WCFHEGWW","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"52N7KQ47","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:5fa97ee02cf710c869bbda31fdf2f94f48d9712cf10c594bbe156ef0a9ba9b7d","target":"graph","created_at":"2026-05-18T01:15:49Z","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":"Conditional lower bounds for dynamic graph problems has received a great deal of attention in recent years. While many results are now known for the fully-dynamic case and such bounds often imply worst-case bounds for the partially dynamic setting, it seems much more difficult to prove amortized bounds for incremental and decremental algorithms. In this paper we consider partially dynamic versions of three classic problems in graph theory. Based on popular conjectures we show that:\n  -- No algorithm with amortized update time $O(n^{1-\\varepsilon})$ exists for incremental or decremental maximum","authors_text":"S{\\o}ren Dahlgaard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-02-22T10:07:27Z","title":"On the Hardness of Partially Dynamic Graph Problems and Connections to Diameter"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.06705","kind":"arxiv","version":2},"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":"sha256:5bd9377addb1831ab60c3a5bc640e5164f551f8c04c34bda1aaf5d23b5530d74","target":"record","created_at":"2026-05-18T01:15:49Z","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":"720e1fc7d2db23ede46991f22d1a98d22f82c81aa9ed0cd765d64f34efb68be6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-02-22T10:07:27Z","title_canon_sha256":"23a6813e28e1cdc0c733d03f089fc50faa20c954209010622e8f9570ce620666"},"schema_version":"1.0","source":{"id":"1602.06705","kind":"arxiv","version":2}},"canonical_sha256":"ee9bf5439fb08a721ad6b520910c9669f76e7fcaaa7d747dd24d77d949d558a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee9bf5439fb08a721ad6b520910c9669f76e7fcaaa7d747dd24d77d949d558a7","first_computed_at":"2026-05-18T01:15:49.483106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:49.483106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WT6af3dXuTuoFzJUUDMkeIhrwN61gHzVSXypeoHtCGpUHQouDE2RV7cNLUC+5sThgW/pQtUG9XqHx0DNfzVpBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:49.483909Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.06705","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bd9377addb1831ab60c3a5bc640e5164f551f8c04c34bda1aaf5d23b5530d74","sha256:5fa97ee02cf710c869bbda31fdf2f94f48d9712cf10c594bbe156ef0a9ba9b7d"],"state_sha256":"e5c4b8a404be7068141b992258a497acbfdf2f6c05eb1128bee8574c7b710824"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x3He1uqBs6QP4OxKCdkPkP9MhXFqu3ZA4LXzh5ZU8E9gyqlHhI0Eunfi82fu2OzPwn0eNIn3tLkvEF7YQLe0CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T12:53:11.175338Z","bundle_sha256":"59ef7cbe919880e155bba87a675e35c81662382e63ff0b663cd500d4e67446f1"}}