{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:2WNGNWIV6JZ7JTOTBGU2MHXMJP","short_pith_number":"pith:2WNGNWIV","canonical_record":{"source":{"id":"1410.2198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-08T17:49:57Z","cross_cats_sorted":[],"title_canon_sha256":"d163d0d12565f4766830d7ce4e00a1f9fbd75be0d1cb8f5111e3639cc14839c8","abstract_canon_sha256":"c48768e59b58baf2324ead326dcc06673543827145fff16d0db19d8e43805b0a"},"schema_version":"1.0"},"canonical_sha256":"d59a66d915f273f4cdd309a9a61eec4bfcac76ba9595e4386b50fc6743f675be","source":{"kind":"arxiv","id":"1410.2198","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2198","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2198v1","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2198","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"pith_short_12","alias_value":"2WNGNWIV6JZ7","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2WNGNWIV6JZ7JTOT","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2WNGNWIV","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:2WNGNWIV6JZ7JTOTBGU2MHXMJP","target":"record","payload":{"canonical_record":{"source":{"id":"1410.2198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-08T17:49:57Z","cross_cats_sorted":[],"title_canon_sha256":"d163d0d12565f4766830d7ce4e00a1f9fbd75be0d1cb8f5111e3639cc14839c8","abstract_canon_sha256":"c48768e59b58baf2324ead326dcc06673543827145fff16d0db19d8e43805b0a"},"schema_version":"1.0"},"canonical_sha256":"d59a66d915f273f4cdd309a9a61eec4bfcac76ba9595e4386b50fc6743f675be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:47.992827Z","signature_b64":"utBPozxHba60llJZRRoKTKCZYNl3BCRwkfu5CegEHyAZ5z6BGusjrIwnwWUDGOaNNacwkJZ9BWzjRpHhxh16Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d59a66d915f273f4cdd309a9a61eec4bfcac76ba9595e4386b50fc6743f675be","last_reissued_at":"2026-05-18T02:40:47.992247Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:47.992247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.2198","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":"2026-05-18T02:40:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IktlyTYRAiB02e6mWI+PdDc9HBSm2ICzS/RAc5i4yisUaZOEJEaulFLSWvEbbobq4+7dpHe7kVExiL+nGOxADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:11:06.432364Z"},"content_sha256":"ca600ae9b50deddbd7b572565bc9adca21fc911d06d66a34bb20a7c7bafbfd82","schema_version":"1.0","event_id":"sha256:ca600ae9b50deddbd7b572565bc9adca21fc911d06d66a34bb20a7c7bafbfd82"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:2WNGNWIV6JZ7JTOTBGU2MHXMJP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Robust hamiltonicity of random directed graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andreas Noever, Asaf Ferber, Nemanja \\v{S}kori\\'c, Rajko Nenadov, Ueli Peter","submitted_at":"2014-10-08T17:49:57Z","abstract_excerpt":"In his seminal paper from 1952 Dirac showed that the complete graph on $n\\geq 3$ vertices remains Hamiltonian even if we allow an adversary to remove $\\lfloor n/2\\rfloor$ edges touching each vertex. In 1960 Ghouila-Houri obtained an analogue statement for digraphs by showing that every directed graph on $n\\geq 3$ vertices with minimum in- and out-degree at least $n/2$ contains a directed Hamilton cycle. Both statements quantify the robustness of complete graphs (digraphs) with respect to the property of containing a Hamilton cycle.\n  A natural way to generalize such results to arbitrary graphs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2198","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":"2026-05-18T02:40:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kmn2ACOowTSqQW23QTw1ZjXyjxbRWAhcTFWlBViny/xEN7svrZ2TSVLLEMqUHm/bfyABuJJpbXxBuvV6ZB6PCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:11:06.433064Z"},"content_sha256":"4b7485773454199348102977768e99cab5518f62d6c028ec98a761e6fe92d3ba","schema_version":"1.0","event_id":"sha256:4b7485773454199348102977768e99cab5518f62d6c028ec98a761e6fe92d3ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2WNGNWIV6JZ7JTOTBGU2MHXMJP/bundle.json","state_url":"https://pith.science/pith/2WNGNWIV6JZ7JTOTBGU2MHXMJP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2WNGNWIV6JZ7JTOTBGU2MHXMJP/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":"2026-05-25T16:11:06Z","links":{"resolver":"https://pith.science/pith/2WNGNWIV6JZ7JTOTBGU2MHXMJP","bundle":"https://pith.science/pith/2WNGNWIV6JZ7JTOTBGU2MHXMJP/bundle.json","state":"https://pith.science/pith/2WNGNWIV6JZ7JTOTBGU2MHXMJP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2WNGNWIV6JZ7JTOTBGU2MHXMJP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2WNGNWIV6JZ7JTOTBGU2MHXMJP","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":"c48768e59b58baf2324ead326dcc06673543827145fff16d0db19d8e43805b0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-08T17:49:57Z","title_canon_sha256":"d163d0d12565f4766830d7ce4e00a1f9fbd75be0d1cb8f5111e3639cc14839c8"},"schema_version":"1.0","source":{"id":"1410.2198","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2198","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2198v1","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2198","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"pith_short_12","alias_value":"2WNGNWIV6JZ7","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2WNGNWIV6JZ7JTOT","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2WNGNWIV","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:4b7485773454199348102977768e99cab5518f62d6c028ec98a761e6fe92d3ba","target":"graph","created_at":"2026-05-18T02:40:47Z","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":"In his seminal paper from 1952 Dirac showed that the complete graph on $n\\geq 3$ vertices remains Hamiltonian even if we allow an adversary to remove $\\lfloor n/2\\rfloor$ edges touching each vertex. In 1960 Ghouila-Houri obtained an analogue statement for digraphs by showing that every directed graph on $n\\geq 3$ vertices with minimum in- and out-degree at least $n/2$ contains a directed Hamilton cycle. Both statements quantify the robustness of complete graphs (digraphs) with respect to the property of containing a Hamilton cycle.\n  A natural way to generalize such results to arbitrary graphs","authors_text":"Andreas Noever, Asaf Ferber, Nemanja \\v{S}kori\\'c, Rajko Nenadov, Ueli Peter","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-08T17:49:57Z","title":"Robust hamiltonicity of random directed graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2198","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:ca600ae9b50deddbd7b572565bc9adca21fc911d06d66a34bb20a7c7bafbfd82","target":"record","created_at":"2026-05-18T02:40:47Z","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":"c48768e59b58baf2324ead326dcc06673543827145fff16d0db19d8e43805b0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-08T17:49:57Z","title_canon_sha256":"d163d0d12565f4766830d7ce4e00a1f9fbd75be0d1cb8f5111e3639cc14839c8"},"schema_version":"1.0","source":{"id":"1410.2198","kind":"arxiv","version":1}},"canonical_sha256":"d59a66d915f273f4cdd309a9a61eec4bfcac76ba9595e4386b50fc6743f675be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d59a66d915f273f4cdd309a9a61eec4bfcac76ba9595e4386b50fc6743f675be","first_computed_at":"2026-05-18T02:40:47.992247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:47.992247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"utBPozxHba60llJZRRoKTKCZYNl3BCRwkfu5CegEHyAZ5z6BGusjrIwnwWUDGOaNNacwkJZ9BWzjRpHhxh16Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:47.992827Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.2198","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca600ae9b50deddbd7b572565bc9adca21fc911d06d66a34bb20a7c7bafbfd82","sha256:4b7485773454199348102977768e99cab5518f62d6c028ec98a761e6fe92d3ba"],"state_sha256":"0d996a1d4c968f3e3ab0ff4023a5be8128581ee18b7d55949a6b485124a905bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lYLimCdz27POfr7xA61ZnNlEF10EchhEcw8Stff3gk3TMXeqTCJR3seCLCXN1wVrst1WSL3F6bcEvaOKJCnNAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:11:06.436988Z","bundle_sha256":"dac1c36aee855f68294015ef171c9578ed5cfe50c191d536a17ec90dedd52e68"}}