{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:PFKQPUAYRGVYYM5RIHF5SFUWEQ","short_pith_number":"pith:PFKQPUAY","canonical_record":{"source":{"id":"2402.01447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-02-02T14:38:22Z","cross_cats_sorted":[],"title_canon_sha256":"bf8a7e4b931c316ff1698271faa8197707d41998d3bc9f323f995ce117a6cff6","abstract_canon_sha256":"d07e149a7868c7ebfaeaf0b01062a2ca661bd85fc6df68f01d15a9ee8f275116"},"schema_version":"1.0"},"canonical_sha256":"795507d01889ab8c33b141cbd91696242f6b70f369f093e94b537f7d5ae603d5","source":{"kind":"arxiv","id":"2402.01447","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.01447","created_at":"2026-07-05T07:40:44Z"},{"alias_kind":"arxiv_version","alias_value":"2402.01447v1","created_at":"2026-07-05T07:40:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.01447","created_at":"2026-07-05T07:40:44Z"},{"alias_kind":"pith_short_12","alias_value":"PFKQPUAYRGVY","created_at":"2026-07-05T07:40:44Z"},{"alias_kind":"pith_short_16","alias_value":"PFKQPUAYRGVYYM5R","created_at":"2026-07-05T07:40:44Z"},{"alias_kind":"pith_short_8","alias_value":"PFKQPUAY","created_at":"2026-07-05T07:40:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:PFKQPUAYRGVYYM5RIHF5SFUWEQ","target":"record","payload":{"canonical_record":{"source":{"id":"2402.01447","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-02-02T14:38:22Z","cross_cats_sorted":[],"title_canon_sha256":"bf8a7e4b931c316ff1698271faa8197707d41998d3bc9f323f995ce117a6cff6","abstract_canon_sha256":"d07e149a7868c7ebfaeaf0b01062a2ca661bd85fc6df68f01d15a9ee8f275116"},"schema_version":"1.0"},"canonical_sha256":"795507d01889ab8c33b141cbd91696242f6b70f369f093e94b537f7d5ae603d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:40:44.393305Z","signature_b64":"infCClqnutTFw9M0rVzGbN0eGrbWeqbXwmVh9doBGnTHuic1jyjyzJ6HmsyuakWTKdM8WdzjVLbi8nd9d6n5BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"795507d01889ab8c33b141cbd91696242f6b70f369f093e94b537f7d5ae603d5","last_reissued_at":"2026-07-05T07:40:44.392702Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:40:44.392702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.01447","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":"2026-07-05T07:40:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qL930clW4o2GSmbmsV9HvUtfMol2nR9BQ4d6QI7TfEZMTLNef7EkKTfi324XWNIUtlqeNaOfejR2zEsOW3wRDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T18:42:54.633836Z"},"content_sha256":"e4a8e9d21440675377e699f5103cc2f7b6ad4f2dcd2af2c0c04dd3486131425b","schema_version":"1.0","event_id":"sha256:e4a8e9d21440675377e699f5103cc2f7b6ad4f2dcd2af2c0c04dd3486131425b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:PFKQPUAYRGVYYM5RIHF5SFUWEQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Hamilton space of pseudorandom graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kalina Petrova, Micha Christoph, Rajko Nenadov","submitted_at":"2024-02-02T14:38:22Z","abstract_excerpt":"We show that if $n$ is odd and $p \\ge C \\log n / n$, then with high probability Hamilton cycles in $G(n,p)$ span its cycle space. More generally, we show this holds for a class of graphs satisfying certain natural pseudorandom properties. The proof is based on a novel idea of parity-switchers, which can be thought of as analogues of absorbers in the context of cycle spaces. As another application of our method, we show that Hamilton cycles in a near-Dirac graph $G$, that is, a graph $G$ with odd $n$ vertices and minimum degree $n/2 + C$ for sufficiently large constant $C$, span its cycle space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.01447","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.01447/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:40:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"igpS9/LNvVYOmLfRBd0MA4m+4RxHBnOZAx3dRsBSBiN9Fg9po3SwLaOhUY0lsjHlgtQwPJr+KfRuW7qk4RLKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T18:42:54.634399Z"},"content_sha256":"47e3d063a2cd5dddbfde437f8e228a4b1e5ca7fe1ce306899bcd8a9fb83b3a61","schema_version":"1.0","event_id":"sha256:47e3d063a2cd5dddbfde437f8e228a4b1e5ca7fe1ce306899bcd8a9fb83b3a61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PFKQPUAYRGVYYM5RIHF5SFUWEQ/bundle.json","state_url":"https://pith.science/pith/PFKQPUAYRGVYYM5RIHF5SFUWEQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PFKQPUAYRGVYYM5RIHF5SFUWEQ/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":"2026-08-08T18:42:54Z","links":{"resolver":"https://pith.science/pith/PFKQPUAYRGVYYM5RIHF5SFUWEQ","bundle":"https://pith.science/pith/PFKQPUAYRGVYYM5RIHF5SFUWEQ/bundle.json","state":"https://pith.science/pith/PFKQPUAYRGVYYM5RIHF5SFUWEQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PFKQPUAYRGVYYM5RIHF5SFUWEQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:PFKQPUAYRGVYYM5RIHF5SFUWEQ","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":"d07e149a7868c7ebfaeaf0b01062a2ca661bd85fc6df68f01d15a9ee8f275116","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-02-02T14:38:22Z","title_canon_sha256":"bf8a7e4b931c316ff1698271faa8197707d41998d3bc9f323f995ce117a6cff6"},"schema_version":"1.0","source":{"id":"2402.01447","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.01447","created_at":"2026-07-05T07:40:44Z"},{"alias_kind":"arxiv_version","alias_value":"2402.01447v1","created_at":"2026-07-05T07:40:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.01447","created_at":"2026-07-05T07:40:44Z"},{"alias_kind":"pith_short_12","alias_value":"PFKQPUAYRGVY","created_at":"2026-07-05T07:40:44Z"},{"alias_kind":"pith_short_16","alias_value":"PFKQPUAYRGVYYM5R","created_at":"2026-07-05T07:40:44Z"},{"alias_kind":"pith_short_8","alias_value":"PFKQPUAY","created_at":"2026-07-05T07:40:44Z"}],"graph_snapshots":[{"event_id":"sha256:47e3d063a2cd5dddbfde437f8e228a4b1e5ca7fe1ce306899bcd8a9fb83b3a61","target":"graph","created_at":"2026-07-05T07:40:44Z","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/2402.01447/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that if $n$ is odd and $p \\ge C \\log n / n$, then with high probability Hamilton cycles in $G(n,p)$ span its cycle space. More generally, we show this holds for a class of graphs satisfying certain natural pseudorandom properties. The proof is based on a novel idea of parity-switchers, which can be thought of as analogues of absorbers in the context of cycle spaces. As another application of our method, we show that Hamilton cycles in a near-Dirac graph $G$, that is, a graph $G$ with odd $n$ vertices and minimum degree $n/2 + C$ for sufficiently large constant $C$, span its cycle space","authors_text":"Kalina Petrova, Micha Christoph, Rajko Nenadov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-02-02T14:38:22Z","title":"The Hamilton space of pseudorandom graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.01447","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:e4a8e9d21440675377e699f5103cc2f7b6ad4f2dcd2af2c0c04dd3486131425b","target":"record","created_at":"2026-07-05T07:40:44Z","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":"d07e149a7868c7ebfaeaf0b01062a2ca661bd85fc6df68f01d15a9ee8f275116","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-02-02T14:38:22Z","title_canon_sha256":"bf8a7e4b931c316ff1698271faa8197707d41998d3bc9f323f995ce117a6cff6"},"schema_version":"1.0","source":{"id":"2402.01447","kind":"arxiv","version":1}},"canonical_sha256":"795507d01889ab8c33b141cbd91696242f6b70f369f093e94b537f7d5ae603d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"795507d01889ab8c33b141cbd91696242f6b70f369f093e94b537f7d5ae603d5","first_computed_at":"2026-07-05T07:40:44.392702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:40:44.392702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"infCClqnutTFw9M0rVzGbN0eGrbWeqbXwmVh9doBGnTHuic1jyjyzJ6HmsyuakWTKdM8WdzjVLbi8nd9d6n5BA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:40:44.393305Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.01447","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4a8e9d21440675377e699f5103cc2f7b6ad4f2dcd2af2c0c04dd3486131425b","sha256:47e3d063a2cd5dddbfde437f8e228a4b1e5ca7fe1ce306899bcd8a9fb83b3a61"],"state_sha256":"d130a3dd300a4da1266611cd0abbcff56175d0c854517123f123777b02a77a5e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/q0UDgMiF5bgwBeOzNWQzRjjDJbpbWsU63CBt5P22U0iINMpWmw2QF5zOLAhMEITkUPnXqfXd3RT/xvfdjCkCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T18:42:54.641364Z","bundle_sha256":"2b133eba70523cfd77bb8446c403a815f5cdbc69c4172769bb35b4efaa27532b"}}