{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UQJ674APG4IVMKLJI5C6JTVCN5","short_pith_number":"pith:UQJ674AP","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"},"canonical_sha256":"a413eff00f37115629694745e4cea26f65ecca9e70784d05d75df5ab9bc0a5a4","source":{"kind":"arxiv","id":"1710.00799","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00799","created_at":"2026-05-18T00:06:51Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00799v3","created_at":"2026-05-18T00:06:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00799","created_at":"2026-05-18T00:06:51Z"},{"alias_kind":"pith_short_12","alias_value":"UQJ674APG4IV","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UQJ674APG4IVMKLJ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UQJ674AP","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UQJ674APG4IVMKLJI5C6JTVCN5","target":"record","payload":{"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"},"canonical_sha256":"a413eff00f37115629694745e4cea26f65ecca9e70784d05d75df5ab9bc0a5a4","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"},"source_kind":"arxiv","source_id":"1710.00799","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cbKBxcPBh/1lUNjU8UYjSvDy1jiUJ5aELjeN/Ajdc6pG1C7r387Q+loTUJHVXzt+tGjj+8S1AR72DKs+mecLBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:04:31.090878Z"},"content_sha256":"57079922f90359e2418057e0c7630b9d1febf186cb32890aa8fa3de0a9526069","schema_version":"1.0","event_id":"sha256:57079922f90359e2418057e0c7630b9d1febf186cb32890aa8fa3de0a9526069"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UQJ674APG4IVMKLJI5C6JTVCN5","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"md1ZYvqr4WNXMOU5cBGoqAViCrk83+0wDpl4h20x25/7RZdANDhGVTBEDeg2rAV5nIWF5fptHAbgqqasU6k2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:04:31.091724Z"},"content_sha256":"abe83921f0ed40af474534f0d714302d96e9431d07a37f13b005bd2404724c7d","schema_version":"1.0","event_id":"sha256:abe83921f0ed40af474534f0d714302d96e9431d07a37f13b005bd2404724c7d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UQJ674APG4IVMKLJI5C6JTVCN5/bundle.json","state_url":"https://pith.science/pith/UQJ674APG4IVMKLJI5C6JTVCN5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UQJ674APG4IVMKLJI5C6JTVCN5/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":"2026-06-10T23:04:31Z","links":{"resolver":"https://pith.science/pith/UQJ674APG4IVMKLJI5C6JTVCN5","bundle":"https://pith.science/pith/UQJ674APG4IVMKLJI5C6JTVCN5/bundle.json","state":"https://pith.science/pith/UQJ674APG4IVMKLJI5C6JTVCN5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UQJ674APG4IVMKLJI5C6JTVCN5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UQJ674APG4IVMKLJI5C6JTVCN5","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":"314c47f93b0f75c9ba2763d59133d845da3b6d6e29cb0c1cece2daba320ea057","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-02T17:12:02Z","title_canon_sha256":"9574907257d53c476480351ce6aa8ac0bc59c6fc2405e76ddaa3e16c20b3746e"},"schema_version":"1.0","source":{"id":"1710.00799","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00799","created_at":"2026-05-18T00:06:51Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00799v3","created_at":"2026-05-18T00:06:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00799","created_at":"2026-05-18T00:06:51Z"},{"alias_kind":"pith_short_12","alias_value":"UQJ674APG4IV","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UQJ674APG4IVMKLJ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UQJ674AP","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:abe83921f0ed40af474534f0d714302d96e9431d07a37f13b005bd2404724c7d","target":"graph","created_at":"2026-05-18T00:06:51Z","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":"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","authors_text":"Angelika Steger, Milo\\v{s} Truji\\'c, Rajko Nenadov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-02T17:12:02Z","title":"Resilience of Perfect Matchings and Hamiltonicity in Random Graph Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00799","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":"sha256:57079922f90359e2418057e0c7630b9d1febf186cb32890aa8fa3de0a9526069","target":"record","created_at":"2026-05-18T00:06:51Z","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":"314c47f93b0f75c9ba2763d59133d845da3b6d6e29cb0c1cece2daba320ea057","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-02T17:12:02Z","title_canon_sha256":"9574907257d53c476480351ce6aa8ac0bc59c6fc2405e76ddaa3e16c20b3746e"},"schema_version":"1.0","source":{"id":"1710.00799","kind":"arxiv","version":3}},"canonical_sha256":"a413eff00f37115629694745e4cea26f65ecca9e70784d05d75df5ab9bc0a5a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a413eff00f37115629694745e4cea26f65ecca9e70784d05d75df5ab9bc0a5a4","first_computed_at":"2026-05-18T00:06:51.082584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:51.082584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ieC+rau4iuIA5tcVtS1/uyNho4Aw39iYmMEo76qyloHenhlNQkCPAXeV17tCtFNh1OFcwa1mxmgbx6qIs89sAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:51.083271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00799","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57079922f90359e2418057e0c7630b9d1febf186cb32890aa8fa3de0a9526069","sha256:abe83921f0ed40af474534f0d714302d96e9431d07a37f13b005bd2404724c7d"],"state_sha256":"817fa66a25393752be08f2b8f736ff9346c1f8fb471aa8164c7bb34abf29a74a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JCs4linVOM/lt5VxdOkP8sSfpQ68UmeAEZ2sMDemJR3QRQ/Ygs8xEWbQ3XoyRqY1Yq1hyg8C+whpzsoCUQxyCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T23:04:31.095135Z","bundle_sha256":"0d507208eb9cac2d2cdd355b85549896953819fffb1d569ccd11fc2bfc77a027"}}