{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YZEWMHW5Y3SOPV4NY3OG2ZH62G","short_pith_number":"pith:YZEWMHW5","canonical_record":{"source":{"id":"1509.00764","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-02T16:04:59Z","cross_cats_sorted":["cs.NE","cs.SI"],"title_canon_sha256":"6535de453ef91ea6da43edf73d36d02e4ce9b014f8a3d3a66948261fded82602","abstract_canon_sha256":"28307f590cf224864ab5ae9d4ef8a0c452d8fecea8f65717cac9353f5dce8de9"},"schema_version":"1.0"},"canonical_sha256":"c649661eddc6e4e7d78dc6dc6d64fed1ac3f48cd908c70dca38100d18f3769e9","source":{"kind":"arxiv","id":"1509.00764","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00764","created_at":"2026-05-18T01:34:06Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00764v1","created_at":"2026-05-18T01:34:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00764","created_at":"2026-05-18T01:34:06Z"},{"alias_kind":"pith_short_12","alias_value":"YZEWMHW5Y3SO","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YZEWMHW5Y3SOPV4N","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YZEWMHW5","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YZEWMHW5Y3SOPV4NY3OG2ZH62G","target":"record","payload":{"canonical_record":{"source":{"id":"1509.00764","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-02T16:04:59Z","cross_cats_sorted":["cs.NE","cs.SI"],"title_canon_sha256":"6535de453ef91ea6da43edf73d36d02e4ce9b014f8a3d3a66948261fded82602","abstract_canon_sha256":"28307f590cf224864ab5ae9d4ef8a0c452d8fecea8f65717cac9353f5dce8de9"},"schema_version":"1.0"},"canonical_sha256":"c649661eddc6e4e7d78dc6dc6d64fed1ac3f48cd908c70dca38100d18f3769e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:06.096884Z","signature_b64":"43UUPGOlJMAykFjqBtRxcWD6TSOqlMJ42vKYVm1R+8c/5BZd0Ip6DEmAvo3jv5Tjj/mhhhlCPV+eAWeDC12KAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c649661eddc6e4e7d78dc6dc6d64fed1ac3f48cd908c70dca38100d18f3769e9","last_reissued_at":"2026-05-18T01:34:06.096389Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:06.096389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.00764","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":"2026-05-18T01:34:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cW8hT3a04FVH/w8qoqS1ICQxTBdE+OQJ+ytME3N3Ggch27+MOSqADxytSTcz4FrfRpMTnoHmElGpJSpXMSk9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:22:12.274279Z"},"content_sha256":"775a3f9285f4b4c72cbdb109a47a6127506d61524ec6a65ca91f42c435209e89","schema_version":"1.0","event_id":"sha256:775a3f9285f4b4c72cbdb109a47a6127506d61524ec6a65ca91f42c435209e89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YZEWMHW5Y3SOPV4NY3OG2ZH62G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finding Near-Optimal Independent Sets at Scale","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NE","cs.SI"],"primary_cat":"cs.DS","authors_text":"Christian Schulz, Darren Strash, Peter Sanders, Renato F. Werneck, Sebastian Lamm","submitted_at":"2015-09-02T16:04:59Z","abstract_excerpt":"The independent set problem is NP-hard and particularly difficult to solve in large sparse graphs. In this work, we develop an advanced evolutionary algorithm, which incorporates kernelization techniques to compute large independent sets in huge sparse networks. A recent exact algorithm has shown that large networks can be solved exactly by employing a branch-and-reduce technique that recursively kernelizes the graph and performs branching. However, one major drawback of their algorithm is that, for huge graphs, branching still can take exponential time. To avoid this problem, we recursively c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00764","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":"2026-05-18T01:34:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GKNjoBP6W5OzUeDcYM6vmxSCryrF+sB3CGmC1H8iZ0DN4ORA8PhIXoRh/aIPIeycHC1yRr4a37v7yG7Mj2GcDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:22:12.274683Z"},"content_sha256":"9f662860955a92ea26305cf797891b3c0d395e9c781c62409b351bb95ed87ea6","schema_version":"1.0","event_id":"sha256:9f662860955a92ea26305cf797891b3c0d395e9c781c62409b351bb95ed87ea6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YZEWMHW5Y3SOPV4NY3OG2ZH62G/bundle.json","state_url":"https://pith.science/pith/YZEWMHW5Y3SOPV4NY3OG2ZH62G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YZEWMHW5Y3SOPV4NY3OG2ZH62G/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":"2026-05-31T03:22:12Z","links":{"resolver":"https://pith.science/pith/YZEWMHW5Y3SOPV4NY3OG2ZH62G","bundle":"https://pith.science/pith/YZEWMHW5Y3SOPV4NY3OG2ZH62G/bundle.json","state":"https://pith.science/pith/YZEWMHW5Y3SOPV4NY3OG2ZH62G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YZEWMHW5Y3SOPV4NY3OG2ZH62G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YZEWMHW5Y3SOPV4NY3OG2ZH62G","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":"28307f590cf224864ab5ae9d4ef8a0c452d8fecea8f65717cac9353f5dce8de9","cross_cats_sorted":["cs.NE","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-02T16:04:59Z","title_canon_sha256":"6535de453ef91ea6da43edf73d36d02e4ce9b014f8a3d3a66948261fded82602"},"schema_version":"1.0","source":{"id":"1509.00764","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00764","created_at":"2026-05-18T01:34:06Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00764v1","created_at":"2026-05-18T01:34:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00764","created_at":"2026-05-18T01:34:06Z"},{"alias_kind":"pith_short_12","alias_value":"YZEWMHW5Y3SO","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YZEWMHW5Y3SOPV4N","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YZEWMHW5","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:9f662860955a92ea26305cf797891b3c0d395e9c781c62409b351bb95ed87ea6","target":"graph","created_at":"2026-05-18T01:34:06Z","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 independent set problem is NP-hard and particularly difficult to solve in large sparse graphs. In this work, we develop an advanced evolutionary algorithm, which incorporates kernelization techniques to compute large independent sets in huge sparse networks. A recent exact algorithm has shown that large networks can be solved exactly by employing a branch-and-reduce technique that recursively kernelizes the graph and performs branching. However, one major drawback of their algorithm is that, for huge graphs, branching still can take exponential time. To avoid this problem, we recursively c","authors_text":"Christian Schulz, Darren Strash, Peter Sanders, Renato F. Werneck, Sebastian Lamm","cross_cats":["cs.NE","cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-02T16:04:59Z","title":"Finding Near-Optimal Independent Sets at Scale"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00764","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":"sha256:775a3f9285f4b4c72cbdb109a47a6127506d61524ec6a65ca91f42c435209e89","target":"record","created_at":"2026-05-18T01:34:06Z","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":"28307f590cf224864ab5ae9d4ef8a0c452d8fecea8f65717cac9353f5dce8de9","cross_cats_sorted":["cs.NE","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-02T16:04:59Z","title_canon_sha256":"6535de453ef91ea6da43edf73d36d02e4ce9b014f8a3d3a66948261fded82602"},"schema_version":"1.0","source":{"id":"1509.00764","kind":"arxiv","version":1}},"canonical_sha256":"c649661eddc6e4e7d78dc6dc6d64fed1ac3f48cd908c70dca38100d18f3769e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c649661eddc6e4e7d78dc6dc6d64fed1ac3f48cd908c70dca38100d18f3769e9","first_computed_at":"2026-05-18T01:34:06.096389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:06.096389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"43UUPGOlJMAykFjqBtRxcWD6TSOqlMJ42vKYVm1R+8c/5BZd0Ip6DEmAvo3jv5Tjj/mhhhlCPV+eAWeDC12KAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:06.096884Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.00764","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:775a3f9285f4b4c72cbdb109a47a6127506d61524ec6a65ca91f42c435209e89","sha256:9f662860955a92ea26305cf797891b3c0d395e9c781c62409b351bb95ed87ea6"],"state_sha256":"dad89139582fcc5d88d07d1a5b41af5d8d3aedd22f9294edddf59865f58329e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aTfwwpkBg+qaEWrhC+y4fndnhg2PzPEt2/plmN6j/sc5H0IwJ3rLRgBorDyUm0mKwz1pTyIogst8PtAdNND4AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:22:12.277039Z","bundle_sha256":"181338f219f5fce4d2b47dcda3d5b5e0037798028242c0b766997b6c6598f887"}}