{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:2DZ5A62ITFRMGQE3OWJCSXUBPO","short_pith_number":"pith:2DZ5A62I","canonical_record":{"source":{"id":"2310.04138","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-10-06T10:22:47Z","cross_cats_sorted":[],"title_canon_sha256":"91b1c7e2ca1cbd0e6d6672108d17ca24fc8739d00fc4c34a67d7d75668667956","abstract_canon_sha256":"5555714a2f7d2e86a6cb324c03a0e31b47f3ca442dbdf1e40ec25aab934b4b31"},"schema_version":"1.0"},"canonical_sha256":"d0f3d07b489962c3409b7592295e817ba79f9861bec2432aa0ba30c2c8313a5c","source":{"kind":"arxiv","id":"2310.04138","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.04138","created_at":"2026-06-24T01:14:55Z"},{"alias_kind":"arxiv_version","alias_value":"2310.04138v2","created_at":"2026-06-24T01:14:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.04138","created_at":"2026-06-24T01:14:55Z"},{"alias_kind":"pith_short_12","alias_value":"2DZ5A62ITFRM","created_at":"2026-06-24T01:14:55Z"},{"alias_kind":"pith_short_16","alias_value":"2DZ5A62ITFRMGQE3","created_at":"2026-06-24T01:14:55Z"},{"alias_kind":"pith_short_8","alias_value":"2DZ5A62I","created_at":"2026-06-24T01:14:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:2DZ5A62ITFRMGQE3OWJCSXUBPO","target":"record","payload":{"canonical_record":{"source":{"id":"2310.04138","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-10-06T10:22:47Z","cross_cats_sorted":[],"title_canon_sha256":"91b1c7e2ca1cbd0e6d6672108d17ca24fc8739d00fc4c34a67d7d75668667956","abstract_canon_sha256":"5555714a2f7d2e86a6cb324c03a0e31b47f3ca442dbdf1e40ec25aab934b4b31"},"schema_version":"1.0"},"canonical_sha256":"d0f3d07b489962c3409b7592295e817ba79f9861bec2432aa0ba30c2c8313a5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T01:14:55.068042Z","signature_b64":"u2jxv0AYCu36EqbEn41n6KF7KgnENSBkDLdi7gRWbQL4MV9WVax68PaWtbtUrSZcpETHzSacsC188NK6ufrWDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0f3d07b489962c3409b7592295e817ba79f9861bec2432aa0ba30c2c8313a5c","last_reissued_at":"2026-06-24T01:14:55.067641Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T01:14:55.067641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2310.04138","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-24T01:14:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ORGzkqRxMYS/CXsbRKjOtlGbiXuPq4eph2+ZmSJ3If5jDtQDHtxzRiZuDbgZle6PSuk+hn5SBODd1H7E29pbCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:30:29.301956Z"},"content_sha256":"6b6c0a303983cb08ca2c62b483ab724a177c568df9b6cfc1df72521c0105a3bd","schema_version":"1.0","event_id":"sha256:6b6c0a303983cb08ca2c62b483ab724a177c568df9b6cfc1df72521c0105a3bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:2DZ5A62ITFRMGQE3OWJCSXUBPO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universality for transversal Hamilton cycles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Candida Bowtell, Katherine Staden, Patrick Morris, Yanitsa Pehova","submitted_at":"2023-10-06T10:22:47Z","abstract_excerpt":"Let $\\mathbf{G}=\\{G_1, \\ldots, G_m\\}$ be a graph collection on a common vertex set $V$ of size $n$ such that $\\delta(G_i) \\geq (1+o(1))n/2$ for every $i \\in [m]$. We show that $\\mathbf{G}$ contains every Hamilton cycle pattern. That is, for every map $\\chi: [n] \\to [m]$ there is a Hamilton cycle whose $i$-th edge lies in $G_{\\chi(i)}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.04138","kind":"arxiv","version":2},"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/2310.04138/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":"2026-06-24T01:14:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N5eLAIqHpoqkzBcy/w3cI9SIwKEwGVJSz36af1k0WakMu17M07508wtaCAVIoZBByTRCkUWoHEYamAIl6TZ8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:30:29.302335Z"},"content_sha256":"14b91d10c5a72ba588161275bc6bcb50036b758a96fcc35cc321ee69bd5f402b","schema_version":"1.0","event_id":"sha256:14b91d10c5a72ba588161275bc6bcb50036b758a96fcc35cc321ee69bd5f402b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2DZ5A62ITFRMGQE3OWJCSXUBPO/bundle.json","state_url":"https://pith.science/pith/2DZ5A62ITFRMGQE3OWJCSXUBPO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2DZ5A62ITFRMGQE3OWJCSXUBPO/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":"2026-06-25T10:30:29Z","links":{"resolver":"https://pith.science/pith/2DZ5A62ITFRMGQE3OWJCSXUBPO","bundle":"https://pith.science/pith/2DZ5A62ITFRMGQE3OWJCSXUBPO/bundle.json","state":"https://pith.science/pith/2DZ5A62ITFRMGQE3OWJCSXUBPO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2DZ5A62ITFRMGQE3OWJCSXUBPO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:2DZ5A62ITFRMGQE3OWJCSXUBPO","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":"5555714a2f7d2e86a6cb324c03a0e31b47f3ca442dbdf1e40ec25aab934b4b31","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-10-06T10:22:47Z","title_canon_sha256":"91b1c7e2ca1cbd0e6d6672108d17ca24fc8739d00fc4c34a67d7d75668667956"},"schema_version":"1.0","source":{"id":"2310.04138","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.04138","created_at":"2026-06-24T01:14:55Z"},{"alias_kind":"arxiv_version","alias_value":"2310.04138v2","created_at":"2026-06-24T01:14:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.04138","created_at":"2026-06-24T01:14:55Z"},{"alias_kind":"pith_short_12","alias_value":"2DZ5A62ITFRM","created_at":"2026-06-24T01:14:55Z"},{"alias_kind":"pith_short_16","alias_value":"2DZ5A62ITFRMGQE3","created_at":"2026-06-24T01:14:55Z"},{"alias_kind":"pith_short_8","alias_value":"2DZ5A62I","created_at":"2026-06-24T01:14:55Z"}],"graph_snapshots":[{"event_id":"sha256:14b91d10c5a72ba588161275bc6bcb50036b758a96fcc35cc321ee69bd5f402b","target":"graph","created_at":"2026-06-24T01:14:55Z","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/2310.04138/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathbf{G}=\\{G_1, \\ldots, G_m\\}$ be a graph collection on a common vertex set $V$ of size $n$ such that $\\delta(G_i) \\geq (1+o(1))n/2$ for every $i \\in [m]$. We show that $\\mathbf{G}$ contains every Hamilton cycle pattern. That is, for every map $\\chi: [n] \\to [m]$ there is a Hamilton cycle whose $i$-th edge lies in $G_{\\chi(i)}$.","authors_text":"Candida Bowtell, Katherine Staden, Patrick Morris, Yanitsa Pehova","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-10-06T10:22:47Z","title":"Universality for transversal Hamilton cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.04138","kind":"arxiv","version":2},"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":"sha256:6b6c0a303983cb08ca2c62b483ab724a177c568df9b6cfc1df72521c0105a3bd","target":"record","created_at":"2026-06-24T01:14:55Z","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":"5555714a2f7d2e86a6cb324c03a0e31b47f3ca442dbdf1e40ec25aab934b4b31","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-10-06T10:22:47Z","title_canon_sha256":"91b1c7e2ca1cbd0e6d6672108d17ca24fc8739d00fc4c34a67d7d75668667956"},"schema_version":"1.0","source":{"id":"2310.04138","kind":"arxiv","version":2}},"canonical_sha256":"d0f3d07b489962c3409b7592295e817ba79f9861bec2432aa0ba30c2c8313a5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0f3d07b489962c3409b7592295e817ba79f9861bec2432aa0ba30c2c8313a5c","first_computed_at":"2026-06-24T01:14:55.067641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T01:14:55.067641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u2jxv0AYCu36EqbEn41n6KF7KgnENSBkDLdi7gRWbQL4MV9WVax68PaWtbtUrSZcpETHzSacsC188NK6ufrWDQ==","signature_status":"signed_v1","signed_at":"2026-06-24T01:14:55.068042Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.04138","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b6c0a303983cb08ca2c62b483ab724a177c568df9b6cfc1df72521c0105a3bd","sha256:14b91d10c5a72ba588161275bc6bcb50036b758a96fcc35cc321ee69bd5f402b"],"state_sha256":"4aad433af3c8752f96f7797f51e722268527621b21d8f98ce8bc1a2a70a1e8b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pDmnV/s9UUgqJbSHimBV+p5iEb6yAb63hf/f+Zo3f6ldAFES2QP+bIFph+7CiaqBdIp9u/vdd7LOXR9RlcRKAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T10:30:29.304300Z","bundle_sha256":"6e98aed4c1cc576fe68d8b2479d57d809d22adfdcda10c690e12668afae016ff"}}