{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:UQJ674APG4IVMKLJI5C6JTVCN5","short_pith_number":"pith:UQJ674AP","schema_version":"1.0","canonical_sha256":"a413eff00f37115629694745e4cea26f65ecca9e70784d05d75df5ab9bc0a5a4","source":{"kind":"arxiv","id":"1710.00799","version":3},"attestation_state":"computed","paper":{"title":"Resilience of Perfect Matchings and Hamiltonicity in Random Graph Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Angelika Steger, Milo\\v{s} Truji\\'c, Rajko Nenadov","submitted_at":"2017-10-02T17:12:02Z","abstract_excerpt":"Let $\\{G_i\\}$ be the random graph process: starting with an empty graph $G_0$ with $n$ vertices, in every step $i \\geq 1$ the graph $G_i$ is formed by taking an edge chosen uniformly at random among the non-existing ones and adding it to the graph $G_{i - 1}$. The classical `hitting-time' result of Ajtai, Koml\\'{o}s, and Szemer\\'{e}di, and independently Bollob\\'{a}s, states that asymptotically almost surely the graph becomes Hamiltonian as soon as the minimum degree reaches $2$, that is if $\\delta(G_i) \\ge 2$ then $G_i$ is Hamiltonian. We establish a resilience version of this result. In parti"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1710.00799","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-02T17:12:02Z","cross_cats_sorted":[],"title_canon_sha256":"9574907257d53c476480351ce6aa8ac0bc59c6fc2405e76ddaa3e16c20b3746e","abstract_canon_sha256":"314c47f93b0f75c9ba2763d59133d845da3b6d6e29cb0c1cece2daba320ea057"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:51.083271Z","signature_b64":"ieC+rau4iuIA5tcVtS1/uyNho4Aw39iYmMEo76qyloHenhlNQkCPAXeV17tCtFNh1OFcwa1mxmgbx6qIs89sAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a413eff00f37115629694745e4cea26f65ecca9e70784d05d75df5ab9bc0a5a4","last_reissued_at":"2026-05-18T00:06:51.082584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:51.082584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Resilience of Perfect Matchings and Hamiltonicity in Random Graph Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Angelika Steger, Milo\\v{s} Truji\\'c, Rajko Nenadov","submitted_at":"2017-10-02T17:12:02Z","abstract_excerpt":"Let $\\{G_i\\}$ be the random graph process: starting with an empty graph $G_0$ with $n$ vertices, in every step $i \\geq 1$ the graph $G_i$ is formed by taking an edge chosen uniformly at random among the non-existing ones and adding it to the graph $G_{i - 1}$. The classical `hitting-time' result of Ajtai, Koml\\'{o}s, and Szemer\\'{e}di, and independently Bollob\\'{a}s, states that asymptotically almost surely the graph becomes Hamiltonian as soon as the minimum degree reaches $2$, that is if $\\delta(G_i) \\ge 2$ then $G_i$ is Hamiltonian. We establish a resilience version of this result. In parti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00799","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1710.00799","created_at":"2026-05-18T00:06:51.082697+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.00799v3","created_at":"2026-05-18T00:06:51.082697+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00799","created_at":"2026-05-18T00:06:51.082697+00:00"},{"alias_kind":"pith_short_12","alias_value":"UQJ674APG4IV","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"UQJ674APG4IVMKLJ","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"UQJ674AP","created_at":"2026-05-18T12:31:49.984773+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UQJ674APG4IVMKLJI5C6JTVCN5","json":"https://pith.science/pith/UQJ674APG4IVMKLJI5C6JTVCN5.json","graph_json":"https://pith.science/api/pith-number/UQJ674APG4IVMKLJI5C6JTVCN5/graph.json","events_json":"https://pith.science/api/pith-number/UQJ674APG4IVMKLJI5C6JTVCN5/events.json","paper":"https://pith.science/paper/UQJ674AP"},"agent_actions":{"view_html":"https://pith.science/pith/UQJ674APG4IVMKLJI5C6JTVCN5","download_json":"https://pith.science/pith/UQJ674APG4IVMKLJI5C6JTVCN5.json","view_paper":"https://pith.science/paper/UQJ674AP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.00799&json=true","fetch_graph":"https://pith.science/api/pith-number/UQJ674APG4IVMKLJI5C6JTVCN5/graph.json","fetch_events":"https://pith.science/api/pith-number/UQJ674APG4IVMKLJI5C6JTVCN5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UQJ674APG4IVMKLJI5C6JTVCN5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UQJ674APG4IVMKLJI5C6JTVCN5/action/storage_attestation","attest_author":"https://pith.science/pith/UQJ674APG4IVMKLJI5C6JTVCN5/action/author_attestation","sign_citation":"https://pith.science/pith/UQJ674APG4IVMKLJI5C6JTVCN5/action/citation_signature","submit_replication":"https://pith.science/pith/UQJ674APG4IVMKLJI5C6JTVCN5/action/replication_record"}},"created_at":"2026-05-18T00:06:51.082697+00:00","updated_at":"2026-05-18T00:06:51.082697+00:00"}