{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:XMCYDJQK7LSMULM5LJDU5YR3MT","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":"32c67e7f6155fc356286af317a68c22c9cb2689f5fe7829518f1f667bdc0e8e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-02-20T18:14:47Z","title_canon_sha256":"ec1027285121a7caebad2a41559b44dc8007196e9dbe084425b783326c9e8e25"},"schema_version":"1.0","source":{"id":"2502.14794","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.14794","created_at":"2026-07-05T11:26:48Z"},{"alias_kind":"arxiv_version","alias_value":"2502.14794v3","created_at":"2026-07-05T11:26:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.14794","created_at":"2026-07-05T11:26:48Z"},{"alias_kind":"pith_short_12","alias_value":"XMCYDJQK7LSM","created_at":"2026-07-05T11:26:48Z"},{"alias_kind":"pith_short_16","alias_value":"XMCYDJQK7LSMULM5","created_at":"2026-07-05T11:26:48Z"},{"alias_kind":"pith_short_8","alias_value":"XMCYDJQK","created_at":"2026-07-05T11:26:48Z"}],"graph_snapshots":[{"event_id":"sha256:4bafcdf9e11d8082cad4ccde8da7bd9ef2e9948ee273f2eebdfaf95ba228c889","target":"graph","created_at":"2026-07-05T11:26:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2502.14794/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that $(1+o(1))\\sqrt{e/n}$ is the sharp threshold for the appearance of the square of a Hamilton cycle in $G(n,p)$, confirming the conjecture of Kahn, Narayanan, and Park. We also find the exact asymptotics of the threshold for the emergence of a spanning subgraph isomorphic to a fixed graph $F$ for a wide family of $d$-regular graphs $F$. This family includes almost all $d$-regular graphs.","authors_text":"Maksim Zhukovskii","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-02-20T18:14:47Z","title":"Sharp thresholds for spanning regular subgraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.14794","kind":"arxiv","version":3},"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":"sha256:3607317eaec70e6f5f95a1df8091eeefc6b9eb14ddab256ff7f037bdc6f14dd2","target":"record","created_at":"2026-07-05T11:26:48Z","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":"32c67e7f6155fc356286af317a68c22c9cb2689f5fe7829518f1f667bdc0e8e1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-02-20T18:14:47Z","title_canon_sha256":"ec1027285121a7caebad2a41559b44dc8007196e9dbe084425b783326c9e8e25"},"schema_version":"1.0","source":{"id":"2502.14794","kind":"arxiv","version":3}},"canonical_sha256":"bb0581a60afae4ca2d9d5a474ee23b64f540bbd8822970bd30042e82d5a31fcd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb0581a60afae4ca2d9d5a474ee23b64f540bbd8822970bd30042e82d5a31fcd","first_computed_at":"2026-07-05T11:26:48.035698Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:26:48.035698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b0AvTAW/sNHBemX27BgDGM83FtpEesmuHWJUvvDZBPBqgQ01VKHrKFPghdtNjxHo8jSdqYQOTUcs5vw62KZ4AA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:26:48.036115Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.14794","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3607317eaec70e6f5f95a1df8091eeefc6b9eb14ddab256ff7f037bdc6f14dd2","sha256:4bafcdf9e11d8082cad4ccde8da7bd9ef2e9948ee273f2eebdfaf95ba228c889"],"state_sha256":"89538d7c30ae87fa5f70302ef436325fec36ca87b241845f72ee06c9af4467f1"}