{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:AIMYIJHFE2SXXZLJAQRE4W2YWE","short_pith_number":"pith:AIMYIJHF","canonical_record":{"source":{"id":"1406.1142","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-04T18:58:38Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"adb3f7d8a755e9765f02553f453d841708b32f5ecb2ad58c3359a10bfa74501a","abstract_canon_sha256":"15ff50b5621f57b19b921fec1523d5fb2df67262274c68c62859dcd398644158"},"schema_version":"1.0"},"canonical_sha256":"02198424e526a57be56904224e5b58b13d3bf4d19aeafbe4d6084900c8d8cb40","source":{"kind":"arxiv","id":"1406.1142","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.1142","created_at":"2026-05-18T02:50:24Z"},{"alias_kind":"arxiv_version","alias_value":"1406.1142v1","created_at":"2026-05-18T02:50:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1142","created_at":"2026-05-18T02:50:24Z"},{"alias_kind":"pith_short_12","alias_value":"AIMYIJHFE2SX","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AIMYIJHFE2SXXZLJ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AIMYIJHF","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:AIMYIJHFE2SXXZLJAQRE4W2YWE","target":"record","payload":{"canonical_record":{"source":{"id":"1406.1142","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-04T18:58:38Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"adb3f7d8a755e9765f02553f453d841708b32f5ecb2ad58c3359a10bfa74501a","abstract_canon_sha256":"15ff50b5621f57b19b921fec1523d5fb2df67262274c68c62859dcd398644158"},"schema_version":"1.0"},"canonical_sha256":"02198424e526a57be56904224e5b58b13d3bf4d19aeafbe4d6084900c8d8cb40","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:24.775227Z","signature_b64":"cHeiL7JV6zO/L7olWpA/PmKcDMLcLlzzM5CwIzr4dq63tErScxTDmIYW5wqvLTkFaelY8iHXbmsDcs1fVPgdDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02198424e526a57be56904224e5b58b13d3bf4d19aeafbe4d6084900c8d8cb40","last_reissued_at":"2026-05-18T02:50:24.774766Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:24.774766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.1142","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":"2026-05-18T02:50:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5IxxY02P9Vt4Oe1JTc4lv3MVTf6JQtiijdVt0DjKDnF4UPqmBmwppCBMNMK2AKNMEB08FGfXkHZL0oJgsVIPBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:24:55.608764Z"},"content_sha256":"51a4b766ee6da657a32b2350e5f87c7fb5d35ccdea97cdc229f120182f1b1bf1","schema_version":"1.0","event_id":"sha256:51a4b766ee6da657a32b2350e5f87c7fb5d35ccdea97cdc229f120182f1b1bf1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:AIMYIJHFE2SXXZLJAQRE4W2YWE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cover time of a random graph with a degree sequence II: Allowing vertices of degree two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Alan Frieze, Colin Cooper, Eyal Lubetzky","submitted_at":"2014-06-04T18:58:38Z","abstract_excerpt":"We study the cover time of a random graph chosen uniformly at random from the set of graphs with vertex set $[n]$ and degree sequence $\\mathbf{d}=(d_i)_{i=1}^n$. In a previous work, the asymptotic cover time was obtained under a number of assumptions on $\\mathbf{d}$, the most significant being that $d_i\\geq 3$ for all $i$. Here we replace this assumption by $d_i\\geq 2$. As a corollary, we establish the asymptotic cover time for the 2-core of the emerging giant component of $\\mathcal{G}(n,p)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1142","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":"2026-05-18T02:50:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7SDa41oV8ulQ3SzxQjg5GZdz6It1lxMO2nO97DOLq6jQClgOatHGcxKJapdav1buNTU0LWzi3VMO3rMoH2Y/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:24:55.609192Z"},"content_sha256":"43e7a94d154dee3151eefb7aa5fb56efa5d7168eef88ec73a552946fb343b682","schema_version":"1.0","event_id":"sha256:43e7a94d154dee3151eefb7aa5fb56efa5d7168eef88ec73a552946fb343b682"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AIMYIJHFE2SXXZLJAQRE4W2YWE/bundle.json","state_url":"https://pith.science/pith/AIMYIJHFE2SXXZLJAQRE4W2YWE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AIMYIJHFE2SXXZLJAQRE4W2YWE/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":"2026-05-29T20:24:55Z","links":{"resolver":"https://pith.science/pith/AIMYIJHFE2SXXZLJAQRE4W2YWE","bundle":"https://pith.science/pith/AIMYIJHFE2SXXZLJAQRE4W2YWE/bundle.json","state":"https://pith.science/pith/AIMYIJHFE2SXXZLJAQRE4W2YWE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AIMYIJHFE2SXXZLJAQRE4W2YWE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AIMYIJHFE2SXXZLJAQRE4W2YWE","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":"15ff50b5621f57b19b921fec1523d5fb2df67262274c68c62859dcd398644158","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-04T18:58:38Z","title_canon_sha256":"adb3f7d8a755e9765f02553f453d841708b32f5ecb2ad58c3359a10bfa74501a"},"schema_version":"1.0","source":{"id":"1406.1142","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.1142","created_at":"2026-05-18T02:50:24Z"},{"alias_kind":"arxiv_version","alias_value":"1406.1142v1","created_at":"2026-05-18T02:50:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1142","created_at":"2026-05-18T02:50:24Z"},{"alias_kind":"pith_short_12","alias_value":"AIMYIJHFE2SX","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AIMYIJHFE2SXXZLJ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AIMYIJHF","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:43e7a94d154dee3151eefb7aa5fb56efa5d7168eef88ec73a552946fb343b682","target":"graph","created_at":"2026-05-18T02:50:24Z","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 study the cover time of a random graph chosen uniformly at random from the set of graphs with vertex set $[n]$ and degree sequence $\\mathbf{d}=(d_i)_{i=1}^n$. In a previous work, the asymptotic cover time was obtained under a number of assumptions on $\\mathbf{d}$, the most significant being that $d_i\\geq 3$ for all $i$. Here we replace this assumption by $d_i\\geq 2$. As a corollary, we establish the asymptotic cover time for the 2-core of the emerging giant component of $\\mathcal{G}(n,p)$.","authors_text":"Alan Frieze, Colin Cooper, Eyal Lubetzky","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-04T18:58:38Z","title":"Cover time of a random graph with a degree sequence II: Allowing vertices of degree two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1142","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":"sha256:51a4b766ee6da657a32b2350e5f87c7fb5d35ccdea97cdc229f120182f1b1bf1","target":"record","created_at":"2026-05-18T02:50:24Z","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":"15ff50b5621f57b19b921fec1523d5fb2df67262274c68c62859dcd398644158","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-04T18:58:38Z","title_canon_sha256":"adb3f7d8a755e9765f02553f453d841708b32f5ecb2ad58c3359a10bfa74501a"},"schema_version":"1.0","source":{"id":"1406.1142","kind":"arxiv","version":1}},"canonical_sha256":"02198424e526a57be56904224e5b58b13d3bf4d19aeafbe4d6084900c8d8cb40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02198424e526a57be56904224e5b58b13d3bf4d19aeafbe4d6084900c8d8cb40","first_computed_at":"2026-05-18T02:50:24.774766Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:24.774766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cHeiL7JV6zO/L7olWpA/PmKcDMLcLlzzM5CwIzr4dq63tErScxTDmIYW5wqvLTkFaelY8iHXbmsDcs1fVPgdDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:24.775227Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.1142","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51a4b766ee6da657a32b2350e5f87c7fb5d35ccdea97cdc229f120182f1b1bf1","sha256:43e7a94d154dee3151eefb7aa5fb56efa5d7168eef88ec73a552946fb343b682"],"state_sha256":"ca4ecb8364c6630f27f90e2904d7162923accb98f4ab49cad2f612ed1f84c6eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VB8QiNSpZt8AZUEHVmqp8pjNTQukLsP27M3k567J3kSUMliO4ut8GIa7T6dLnkIyng9FNMVwdaGLPXRNe3niAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T20:24:55.612106Z","bundle_sha256":"47ee74ac21796d1d00d8344b6ea825693486bc3ea3fff352fa60ea337121400e"}}