{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:6RIAK3XJQVY2XPPNC7ZRNJXLJA","short_pith_number":"pith:6RIAK3XJ","canonical_record":{"source":{"id":"1109.1504","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2011-09-07T16:08:28Z","cross_cats_sorted":[],"title_canon_sha256":"323b5473ab93f0f349386c8ec615c0d47e224a3f01cce99e333c13c37fb2e7be","abstract_canon_sha256":"4e58f2e678a3eff62cd5a586446a51c715463f6d6a10cec839b122c845f158ff"},"schema_version":"1.0"},"canonical_sha256":"f450056ee98571abbded17f316a6eb482d8bb8074efd481d2ff7d488aee50a7b","source":{"kind":"arxiv","id":"1109.1504","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1504","created_at":"2026-05-18T02:21:36Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1504v2","created_at":"2026-05-18T02:21:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1504","created_at":"2026-05-18T02:21:36Z"},{"alias_kind":"pith_short_12","alias_value":"6RIAK3XJQVY2","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6RIAK3XJQVY2XPPN","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6RIAK3XJ","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:6RIAK3XJQVY2XPPNC7ZRNJXLJA","target":"record","payload":{"canonical_record":{"source":{"id":"1109.1504","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2011-09-07T16:08:28Z","cross_cats_sorted":[],"title_canon_sha256":"323b5473ab93f0f349386c8ec615c0d47e224a3f01cce99e333c13c37fb2e7be","abstract_canon_sha256":"4e58f2e678a3eff62cd5a586446a51c715463f6d6a10cec839b122c845f158ff"},"schema_version":"1.0"},"canonical_sha256":"f450056ee98571abbded17f316a6eb482d8bb8074efd481d2ff7d488aee50a7b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:36.876696Z","signature_b64":"YyKP8oerPDQIlMULeEt1ZLPig7EW+/n2KQpSbW2d47C7TiwSY+YSdoOdChNZVK3F/OoXzkhvXO51hge4ybStBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f450056ee98571abbded17f316a6eb482d8bb8074efd481d2ff7d488aee50a7b","last_reissued_at":"2026-05-18T02:21:36.876251Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:36.876251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.1504","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":"2026-05-18T02:21:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fro5dkZtTosr2aW4a+m7E15yr8ZFsWKpSEMzKJsIPZkA/Qd5KiXN7tVBm04bSS4nRNW7LcYwXwJxmqDfqV+HAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:39:28.517304Z"},"content_sha256":"ba96850fe160494f016cd4d3a838def3b89155b57af92f36ca1fd2dd9af2cc50","schema_version":"1.0","event_id":"sha256:ba96850fe160494f016cd4d3a838def3b89155b57af92f36ca1fd2dd9af2cc50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:6RIAK3XJQVY2XPPNC7ZRNJXLJA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A New Method for Lower Bounds on the Running Time of Evolutionary Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NE","authors_text":"Dirk Sudholt","submitted_at":"2011-09-07T16:08:28Z","abstract_excerpt":"We present a new method for proving lower bounds on the expected running time of evolutionary algorithms. It is based on fitness-level partitions and an additional condition on transition probabilities between fitness levels. The method is versatile, intuitive, elegant, and very powerful. It yields exact or near-exact lower bounds for LO, OneMax, long k-paths, and all functions with a unique optimum. Most lower bounds are very general: they hold for all evolutionary algorithms that only use bit-flip mutation as variation operator---i.e. for all selection operators and population models. The lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1504","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":"2026-05-18T02:21:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KmJS1aZ6iI9bAf/dFpRMFg7A2O1Rqxzn2MlXF4mt5zIRQ16Bv0a1yjUJvHUZC0qn01Q2STclliuMpJT3jOA6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:39:28.517679Z"},"content_sha256":"24300b9e3e756279f1738ea18f68210a1b36cf5d8a1ebe138d87115231439c21","schema_version":"1.0","event_id":"sha256:24300b9e3e756279f1738ea18f68210a1b36cf5d8a1ebe138d87115231439c21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6RIAK3XJQVY2XPPNC7ZRNJXLJA/bundle.json","state_url":"https://pith.science/pith/6RIAK3XJQVY2XPPNC7ZRNJXLJA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6RIAK3XJQVY2XPPNC7ZRNJXLJA/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":"2026-06-02T23:39:28Z","links":{"resolver":"https://pith.science/pith/6RIAK3XJQVY2XPPNC7ZRNJXLJA","bundle":"https://pith.science/pith/6RIAK3XJQVY2XPPNC7ZRNJXLJA/bundle.json","state":"https://pith.science/pith/6RIAK3XJQVY2XPPNC7ZRNJXLJA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6RIAK3XJQVY2XPPNC7ZRNJXLJA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6RIAK3XJQVY2XPPNC7ZRNJXLJA","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":"4e58f2e678a3eff62cd5a586446a51c715463f6d6a10cec839b122c845f158ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2011-09-07T16:08:28Z","title_canon_sha256":"323b5473ab93f0f349386c8ec615c0d47e224a3f01cce99e333c13c37fb2e7be"},"schema_version":"1.0","source":{"id":"1109.1504","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1504","created_at":"2026-05-18T02:21:36Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1504v2","created_at":"2026-05-18T02:21:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1504","created_at":"2026-05-18T02:21:36Z"},{"alias_kind":"pith_short_12","alias_value":"6RIAK3XJQVY2","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6RIAK3XJQVY2XPPN","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6RIAK3XJ","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:24300b9e3e756279f1738ea18f68210a1b36cf5d8a1ebe138d87115231439c21","target":"graph","created_at":"2026-05-18T02:21:36Z","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":"We present a new method for proving lower bounds on the expected running time of evolutionary algorithms. It is based on fitness-level partitions and an additional condition on transition probabilities between fitness levels. The method is versatile, intuitive, elegant, and very powerful. It yields exact or near-exact lower bounds for LO, OneMax, long k-paths, and all functions with a unique optimum. Most lower bounds are very general: they hold for all evolutionary algorithms that only use bit-flip mutation as variation operator---i.e. for all selection operators and population models. The lo","authors_text":"Dirk Sudholt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2011-09-07T16:08:28Z","title":"A New Method for Lower Bounds on the Running Time of Evolutionary Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1504","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:ba96850fe160494f016cd4d3a838def3b89155b57af92f36ca1fd2dd9af2cc50","target":"record","created_at":"2026-05-18T02:21:36Z","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":"4e58f2e678a3eff62cd5a586446a51c715463f6d6a10cec839b122c845f158ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2011-09-07T16:08:28Z","title_canon_sha256":"323b5473ab93f0f349386c8ec615c0d47e224a3f01cce99e333c13c37fb2e7be"},"schema_version":"1.0","source":{"id":"1109.1504","kind":"arxiv","version":2}},"canonical_sha256":"f450056ee98571abbded17f316a6eb482d8bb8074efd481d2ff7d488aee50a7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f450056ee98571abbded17f316a6eb482d8bb8074efd481d2ff7d488aee50a7b","first_computed_at":"2026-05-18T02:21:36.876251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:36.876251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YyKP8oerPDQIlMULeEt1ZLPig7EW+/n2KQpSbW2d47C7TiwSY+YSdoOdChNZVK3F/OoXzkhvXO51hge4ybStBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:36.876696Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.1504","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba96850fe160494f016cd4d3a838def3b89155b57af92f36ca1fd2dd9af2cc50","sha256:24300b9e3e756279f1738ea18f68210a1b36cf5d8a1ebe138d87115231439c21"],"state_sha256":"2f22d21d2e2fd80064909db299aee310b4dbc8c33d41d0e372db805301f45679"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cvgPa1DfOHMXw2rtkh3BOy4joGWf/VfeOeHhgN5TRX4mmmmJ/Q66zVy/Wb1PkUVysNLewGHwD9QKCnJlC1gUAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:39:28.519935Z","bundle_sha256":"3d0f857bc8064d06c3dd67e65f56cb1220712386d6c5997412a4a13d9858b908"}}