{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FSB4QBMRSDAIQTG7NVHVHMAPAG","short_pith_number":"pith:FSB4QBMR","canonical_record":{"source":{"id":"1610.05897","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-10-19T07:44:46Z","cross_cats_sorted":[],"title_canon_sha256":"5d028e7f1874b77577e01bd3fd4cd0197c6c2c627de95f4b64d9a9e783584ef8","abstract_canon_sha256":"a536f83110f9984573730d5f5df39017581d203f755de5e53a311b495da03615"},"schema_version":"1.0"},"canonical_sha256":"2c83c8059190c0884cdf6d4f53b00f01849d1ff6924b35c2bb5b52eac11df472","source":{"kind":"arxiv","id":"1610.05897","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05897","created_at":"2026-05-18T00:36:33Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05897v2","created_at":"2026-05-18T00:36:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05897","created_at":"2026-05-18T00:36:33Z"},{"alias_kind":"pith_short_12","alias_value":"FSB4QBMRSDAI","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FSB4QBMRSDAIQTG7","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FSB4QBMR","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FSB4QBMRSDAIQTG7NVHVHMAPAG","target":"record","payload":{"canonical_record":{"source":{"id":"1610.05897","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-10-19T07:44:46Z","cross_cats_sorted":[],"title_canon_sha256":"5d028e7f1874b77577e01bd3fd4cd0197c6c2c627de95f4b64d9a9e783584ef8","abstract_canon_sha256":"a536f83110f9984573730d5f5df39017581d203f755de5e53a311b495da03615"},"schema_version":"1.0"},"canonical_sha256":"2c83c8059190c0884cdf6d4f53b00f01849d1ff6924b35c2bb5b52eac11df472","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:33.072754Z","signature_b64":"+4rh/DV0XuxcizuAo9jxBAE+Kl9BqQKhWp6eVjLmQW5vPf6ExLyV2WXYZDE7AW7vrG3dpIfEHf95617yn+glCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c83c8059190c0884cdf6d4f53b00f01849d1ff6924b35c2bb5b52eac11df472","last_reissued_at":"2026-05-18T00:36:33.072280Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:33.072280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.05897","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":"2026-05-18T00:36:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D9pg7ZEPRi4Vx6qlWvc+I19AQofySoXR4GLz3mO1DwZa3jfvYmzy7Hlx+gQt7ELOfXyfVNObauWMwoDETXYZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:38:22.487394Z"},"content_sha256":"5759d2b87fb3e978e12d1eb08248220faf49bba1cd4da7a4060a6631054f51e4","schema_version":"1.0","event_id":"sha256:5759d2b87fb3e978e12d1eb08248220faf49bba1cd4da7a4060a6631054f51e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FSB4QBMRSDAIQTG7NVHVHMAPAG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fully Dynamic Algorithm for Top-$k$ Densest Subgraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Aristides Gionis, Gianmarco De Francisci Morales, Muhammad Anis Uddin Nasir, Sarunas Girdzijauskas","submitted_at":"2016-10-19T07:44:46Z","abstract_excerpt":"Given a large graph, the densest-subgraph problem asks to find a subgraph with maximum average degree. When considering the top-$k$ version of this problem, a na\\\"ive solution is to iteratively find the densest subgraph and remove it in each iteration. However, such a solution is impractical due to high processing cost. The problem is further complicated when dealing with dynamic graphs, since adding or removing an edge requires re-running the algorithm. In this paper, we study the top-$k$ densest-subgraph problem in the sliding-window model and propose an efficient fully-dynamic algorithm. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05897","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":"2026-05-18T00:36:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/E4Xb6dTxSJL2vUV2tnroNtf8FIDJAHIPGCP0j9qkwaXyqprSCJcKTms01/d4FUlYUsmVr6xPpl42ZPYi9X2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:38:22.487751Z"},"content_sha256":"405f9a2500f3f401d86a6dbad047efb5bf1b90372980510f494b4ba2ef30bb82","schema_version":"1.0","event_id":"sha256:405f9a2500f3f401d86a6dbad047efb5bf1b90372980510f494b4ba2ef30bb82"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FSB4QBMRSDAIQTG7NVHVHMAPAG/bundle.json","state_url":"https://pith.science/pith/FSB4QBMRSDAIQTG7NVHVHMAPAG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FSB4QBMRSDAIQTG7NVHVHMAPAG/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":"2026-06-11T12:38:22Z","links":{"resolver":"https://pith.science/pith/FSB4QBMRSDAIQTG7NVHVHMAPAG","bundle":"https://pith.science/pith/FSB4QBMRSDAIQTG7NVHVHMAPAG/bundle.json","state":"https://pith.science/pith/FSB4QBMRSDAIQTG7NVHVHMAPAG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FSB4QBMRSDAIQTG7NVHVHMAPAG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FSB4QBMRSDAIQTG7NVHVHMAPAG","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":"a536f83110f9984573730d5f5df39017581d203f755de5e53a311b495da03615","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-10-19T07:44:46Z","title_canon_sha256":"5d028e7f1874b77577e01bd3fd4cd0197c6c2c627de95f4b64d9a9e783584ef8"},"schema_version":"1.0","source":{"id":"1610.05897","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05897","created_at":"2026-05-18T00:36:33Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05897v2","created_at":"2026-05-18T00:36:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05897","created_at":"2026-05-18T00:36:33Z"},{"alias_kind":"pith_short_12","alias_value":"FSB4QBMRSDAI","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FSB4QBMRSDAIQTG7","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FSB4QBMR","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:405f9a2500f3f401d86a6dbad047efb5bf1b90372980510f494b4ba2ef30bb82","target":"graph","created_at":"2026-05-18T00:36:33Z","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":"Given a large graph, the densest-subgraph problem asks to find a subgraph with maximum average degree. When considering the top-$k$ version of this problem, a na\\\"ive solution is to iteratively find the densest subgraph and remove it in each iteration. However, such a solution is impractical due to high processing cost. The problem is further complicated when dealing with dynamic graphs, since adding or removing an edge requires re-running the algorithm. In this paper, we study the top-$k$ densest-subgraph problem in the sliding-window model and propose an efficient fully-dynamic algorithm. Th","authors_text":"Aristides Gionis, Gianmarco De Francisci Morales, Muhammad Anis Uddin Nasir, Sarunas Girdzijauskas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-10-19T07:44:46Z","title":"Fully Dynamic Algorithm for Top-$k$ Densest Subgraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05897","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":"sha256:5759d2b87fb3e978e12d1eb08248220faf49bba1cd4da7a4060a6631054f51e4","target":"record","created_at":"2026-05-18T00:36:33Z","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":"a536f83110f9984573730d5f5df39017581d203f755de5e53a311b495da03615","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-10-19T07:44:46Z","title_canon_sha256":"5d028e7f1874b77577e01bd3fd4cd0197c6c2c627de95f4b64d9a9e783584ef8"},"schema_version":"1.0","source":{"id":"1610.05897","kind":"arxiv","version":2}},"canonical_sha256":"2c83c8059190c0884cdf6d4f53b00f01849d1ff6924b35c2bb5b52eac11df472","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c83c8059190c0884cdf6d4f53b00f01849d1ff6924b35c2bb5b52eac11df472","first_computed_at":"2026-05-18T00:36:33.072280Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:33.072280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+4rh/DV0XuxcizuAo9jxBAE+Kl9BqQKhWp6eVjLmQW5vPf6ExLyV2WXYZDE7AW7vrG3dpIfEHf95617yn+glCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:33.072754Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.05897","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5759d2b87fb3e978e12d1eb08248220faf49bba1cd4da7a4060a6631054f51e4","sha256:405f9a2500f3f401d86a6dbad047efb5bf1b90372980510f494b4ba2ef30bb82"],"state_sha256":"e6fa0305a38312895970c84a3e18a5a93a23cd657ad5f97ee86f5f682ec342d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NLiwVzoucPJEYQyCbV69gkPD6e4+bpqxao49/be1w/1LGQlvK5xT7uInFKpa0trUcvRUsRWZ2vW99gvkyV5kDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T12:38:22.489998Z","bundle_sha256":"54702caebc8f771be58a3cb4ad0c2a27d677cd43c3f0d4e0c87aa78bf6b00529"}}