{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6YRDGAES5YCDGAI36VEO4R7YRA","short_pith_number":"pith:6YRDGAES","canonical_record":{"source":{"id":"1207.6549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-27T14:04:50Z","cross_cats_sorted":["cs.DM","cs.DS","math.CO"],"title_canon_sha256":"a2fa089846f1e1d6d8573d59c266dcd0aeeb14688056a3448de7b034232e335d","abstract_canon_sha256":"2e4ef0f0aa902873129d806e58292b5bd94b29dfc4baea8632be7f73b1460d71"},"schema_version":"1.0"},"canonical_sha256":"f622330092ee0433011bf548ee47f88828d4e6aad5d0ddaf4c56dabb2a393ba1","source":{"kind":"arxiv","id":"1207.6549","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6549","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6549v1","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6549","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"pith_short_12","alias_value":"6YRDGAES5YCD","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6YRDGAES5YCDGAI3","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6YRDGAES","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6YRDGAES5YCDGAI36VEO4R7YRA","target":"record","payload":{"canonical_record":{"source":{"id":"1207.6549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-27T14:04:50Z","cross_cats_sorted":["cs.DM","cs.DS","math.CO"],"title_canon_sha256":"a2fa089846f1e1d6d8573d59c266dcd0aeeb14688056a3448de7b034232e335d","abstract_canon_sha256":"2e4ef0f0aa902873129d806e58292b5bd94b29dfc4baea8632be7f73b1460d71"},"schema_version":"1.0"},"canonical_sha256":"f622330092ee0433011bf548ee47f88828d4e6aad5d0ddaf4c56dabb2a393ba1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:09.007064Z","signature_b64":"0XB5mNnB03EnjpozIQ97FyAlhRoQE6iwaCpwu0AV8V7rBX7m/o/I+uLAQbHf+qWN2thoqHD42v1BkIJQfOgoDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f622330092ee0433011bf548ee47f88828d4e6aad5d0ddaf4c56dabb2a393ba1","last_reissued_at":"2026-05-18T01:25:09.006515Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:09.006515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.6549","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":"2026-05-18T01:25:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qSkKOMRVTocrxKtQmTudEMAKJd62kACzCW7to3h0Yb+LrNZrYmlS+4/tNPsXaVtkLcJ4AVo5pAcY58SfDSmSAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T06:08:07.045834Z"},"content_sha256":"4df74ce93f4b71c46f20f21e572f5694d869dcbfcfc762fe5dd653deae3f55ab","schema_version":"1.0","event_id":"sha256:4df74ce93f4b71c46f20f21e572f5694d869dcbfcfc762fe5dd653deae3f55ab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6YRDGAES5YCDGAI36VEO4R7YRA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of an exhaustive search algorithm in random graphs and the n^{c\\log n} -asymptotics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.DS","math.CO"],"primary_cat":"math.PR","authors_text":"Cyril Banderier, Hsien-Kuei Hwang, Vlady Ravelomanana, Vytas Zacharovas","submitted_at":"2012-07-27T14:04:50Z","abstract_excerpt":"We analyze the cost used by a naive exhaustive search algorithm for finding a maximum independent set in random graphs under the usual G_{n,p} -model where each possible edge appears independently with the same probability p. The expected cost turns out to be of the less common asymptotic order n^{c\\log n}, which we explore from several different perspectives. Also we collect many instances where such an order appears, from algorithmics to analysis, from probability to algebra. The limiting distribution of the cost required by the algorithm under a purely idealized random model is proved to be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6549","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":"2026-05-18T01:25:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zriQBKw+69nMPSI0KzxK4jNByEW4Gn3Le6Bsxdu63Yzgt293TW/y5EEwWptPMQN+YV2b+XicaHwnqSRjMwQUDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T06:08:07.046184Z"},"content_sha256":"b5a4e8bc21c394521f31a9bc9b5c97edb95815d1c3296fd0c9d8a204c08956ff","schema_version":"1.0","event_id":"sha256:b5a4e8bc21c394521f31a9bc9b5c97edb95815d1c3296fd0c9d8a204c08956ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6YRDGAES5YCDGAI36VEO4R7YRA/bundle.json","state_url":"https://pith.science/pith/6YRDGAES5YCDGAI36VEO4R7YRA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6YRDGAES5YCDGAI36VEO4R7YRA/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":"2026-06-21T06:08:07Z","links":{"resolver":"https://pith.science/pith/6YRDGAES5YCDGAI36VEO4R7YRA","bundle":"https://pith.science/pith/6YRDGAES5YCDGAI36VEO4R7YRA/bundle.json","state":"https://pith.science/pith/6YRDGAES5YCDGAI36VEO4R7YRA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6YRDGAES5YCDGAI36VEO4R7YRA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6YRDGAES5YCDGAI36VEO4R7YRA","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":"2e4ef0f0aa902873129d806e58292b5bd94b29dfc4baea8632be7f73b1460d71","cross_cats_sorted":["cs.DM","cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-27T14:04:50Z","title_canon_sha256":"a2fa089846f1e1d6d8573d59c266dcd0aeeb14688056a3448de7b034232e335d"},"schema_version":"1.0","source":{"id":"1207.6549","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6549","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6549v1","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6549","created_at":"2026-05-18T01:25:09Z"},{"alias_kind":"pith_short_12","alias_value":"6YRDGAES5YCD","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6YRDGAES5YCDGAI3","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6YRDGAES","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:b5a4e8bc21c394521f31a9bc9b5c97edb95815d1c3296fd0c9d8a204c08956ff","target":"graph","created_at":"2026-05-18T01:25:09Z","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 analyze the cost used by a naive exhaustive search algorithm for finding a maximum independent set in random graphs under the usual G_{n,p} -model where each possible edge appears independently with the same probability p. The expected cost turns out to be of the less common asymptotic order n^{c\\log n}, which we explore from several different perspectives. Also we collect many instances where such an order appears, from algorithmics to analysis, from probability to algebra. The limiting distribution of the cost required by the algorithm under a purely idealized random model is proved to be","authors_text":"Cyril Banderier, Hsien-Kuei Hwang, Vlady Ravelomanana, Vytas Zacharovas","cross_cats":["cs.DM","cs.DS","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-27T14:04:50Z","title":"Analysis of an exhaustive search algorithm in random graphs and the n^{c\\log n} -asymptotics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6549","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":"sha256:4df74ce93f4b71c46f20f21e572f5694d869dcbfcfc762fe5dd653deae3f55ab","target":"record","created_at":"2026-05-18T01:25:09Z","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":"2e4ef0f0aa902873129d806e58292b5bd94b29dfc4baea8632be7f73b1460d71","cross_cats_sorted":["cs.DM","cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-27T14:04:50Z","title_canon_sha256":"a2fa089846f1e1d6d8573d59c266dcd0aeeb14688056a3448de7b034232e335d"},"schema_version":"1.0","source":{"id":"1207.6549","kind":"arxiv","version":1}},"canonical_sha256":"f622330092ee0433011bf548ee47f88828d4e6aad5d0ddaf4c56dabb2a393ba1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f622330092ee0433011bf548ee47f88828d4e6aad5d0ddaf4c56dabb2a393ba1","first_computed_at":"2026-05-18T01:25:09.006515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:09.006515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0XB5mNnB03EnjpozIQ97FyAlhRoQE6iwaCpwu0AV8V7rBX7m/o/I+uLAQbHf+qWN2thoqHD42v1BkIJQfOgoDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:09.007064Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.6549","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4df74ce93f4b71c46f20f21e572f5694d869dcbfcfc762fe5dd653deae3f55ab","sha256:b5a4e8bc21c394521f31a9bc9b5c97edb95815d1c3296fd0c9d8a204c08956ff"],"state_sha256":"dae11aba349f7c9f023c441e782e4f549258c44ba28ab9d8ea84ab7e292ef187"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CavjLpVibRO3MfzjftMQqzgMV55INY1lbkXAUEI7ys+qKKC4uJp2RkZIOzAinPi/gqpr1Z6JGRpGY0wuaedGBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T06:08:07.048152Z","bundle_sha256":"294aa08f2a8b8785efbadce300fde283bb900fd547b2dcb758f09a9f9e263b6d"}}