{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ZAISBNE6LJFAOIQ2RU36YP2NEZ","short_pith_number":"pith:ZAISBNE6","canonical_record":{"source":{"id":"2605.22553","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-21T14:35:30Z","cross_cats_sorted":[],"title_canon_sha256":"e02f402d5539b53fd27cd481e65efecdc42bfdcaef03d11d65def6b9031390be","abstract_canon_sha256":"e49cfad64a33aa77e5a06580843dcbe4777dd2ecbacf173a515060ff03cf3d69"},"schema_version":"1.0"},"canonical_sha256":"c81120b49e5a4a07221a8d37ec3f4d264a588d2d502cf7e206805246ff985a41","source":{"kind":"arxiv","id":"2605.22553","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22553","created_at":"2026-05-22T01:04:57Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22553v1","created_at":"2026-05-22T01:04:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22553","created_at":"2026-05-22T01:04:57Z"},{"alias_kind":"pith_short_12","alias_value":"ZAISBNE6LJFA","created_at":"2026-05-22T01:04:57Z"},{"alias_kind":"pith_short_16","alias_value":"ZAISBNE6LJFAOIQ2","created_at":"2026-05-22T01:04:57Z"},{"alias_kind":"pith_short_8","alias_value":"ZAISBNE6","created_at":"2026-05-22T01:04:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ZAISBNE6LJFAOIQ2RU36YP2NEZ","target":"record","payload":{"canonical_record":{"source":{"id":"2605.22553","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-21T14:35:30Z","cross_cats_sorted":[],"title_canon_sha256":"e02f402d5539b53fd27cd481e65efecdc42bfdcaef03d11d65def6b9031390be","abstract_canon_sha256":"e49cfad64a33aa77e5a06580843dcbe4777dd2ecbacf173a515060ff03cf3d69"},"schema_version":"1.0"},"canonical_sha256":"c81120b49e5a4a07221a8d37ec3f4d264a588d2d502cf7e206805246ff985a41","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:04:57.097874Z","signature_b64":"/IoztH6GBGKHYnh/J3ZhOJ5GuwI8sfoxdqV3vy45mk4agvN5yiexjmVCy1PkuvoO8Vk0iVGLDviv5lpIBFlDBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c81120b49e5a4a07221a8d37ec3f4d264a588d2d502cf7e206805246ff985a41","last_reissued_at":"2026-05-22T01:04:57.097128Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:04:57.097128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.22553","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":"2026-05-22T01:04:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o4bjvLFu/OFWYgPV93hwgBjTKZpoT7g39Bzwy6EaDATb91ALo7tn+5IPi/HIIgasU5wP8ExunctyRRGGjoFECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:05:55.421329Z"},"content_sha256":"812c0c89c0ed82aa084b8cfe5b32d0aa288056c16790ff8f0e4838d17a1f4754","schema_version":"1.0","event_id":"sha256:812c0c89c0ed82aa084b8cfe5b32d0aa288056c16790ff8f0e4838d17a1f4754"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ZAISBNE6LJFAOIQ2RU36YP2NEZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Ore-type Alon-Yuster Theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guanghui Wang, Lin-Peng Zhang, Yilin Guo, Yuping Gao","submitted_at":"2026-05-21T14:35:30Z","abstract_excerpt":"A graph $G$ admits an $H$-tiling if it contains a collection of vertex-disjoint copies of $H$. In this paper, we confirm a conjecture proposed by K\\\"{u}hn, Osthus, and Treglown by showing that for any given graph $H$, there exists a constant $C(H)$ such that the following holds. If $G$ is a sufficiently large $n$-vertex graph satisfying $d(x) + d(y) \\geq 2\\left(1 - 1/\\chi_{\\text{cr}}(H)\\right)n$ for all nonadjacent vertices $x, y \\in V(G)$, then $G$ contains an $H$-tiling covering all but at most $C(H)$ vertices. Here $\\chi_{\\text{cr}}(H)$ denotes the critical chromatic number of $H$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22553","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/2605.22553/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":"2026-05-22T01:04:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zAiDAABQPvpzmDO9gFUb+1oA4MmcQ94KRv9eFS+agYZr6xx2qMbGSFsNtqIKvF4HD3h4QOLhauKUTn/gMYR4CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:05:55.421710Z"},"content_sha256":"3b8b4a5774b5c757b0005e3f7f93a0e46aba904e1f5d5cc6bf5113d87c6d9c66","schema_version":"1.0","event_id":"sha256:3b8b4a5774b5c757b0005e3f7f93a0e46aba904e1f5d5cc6bf5113d87c6d9c66"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZAISBNE6LJFAOIQ2RU36YP2NEZ/bundle.json","state_url":"https://pith.science/pith/ZAISBNE6LJFAOIQ2RU36YP2NEZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZAISBNE6LJFAOIQ2RU36YP2NEZ/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":"2026-06-02T08:05:55Z","links":{"resolver":"https://pith.science/pith/ZAISBNE6LJFAOIQ2RU36YP2NEZ","bundle":"https://pith.science/pith/ZAISBNE6LJFAOIQ2RU36YP2NEZ/bundle.json","state":"https://pith.science/pith/ZAISBNE6LJFAOIQ2RU36YP2NEZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZAISBNE6LJFAOIQ2RU36YP2NEZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZAISBNE6LJFAOIQ2RU36YP2NEZ","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":"e49cfad64a33aa77e5a06580843dcbe4777dd2ecbacf173a515060ff03cf3d69","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-21T14:35:30Z","title_canon_sha256":"e02f402d5539b53fd27cd481e65efecdc42bfdcaef03d11d65def6b9031390be"},"schema_version":"1.0","source":{"id":"2605.22553","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22553","created_at":"2026-05-22T01:04:57Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22553v1","created_at":"2026-05-22T01:04:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22553","created_at":"2026-05-22T01:04:57Z"},{"alias_kind":"pith_short_12","alias_value":"ZAISBNE6LJFA","created_at":"2026-05-22T01:04:57Z"},{"alias_kind":"pith_short_16","alias_value":"ZAISBNE6LJFAOIQ2","created_at":"2026-05-22T01:04:57Z"},{"alias_kind":"pith_short_8","alias_value":"ZAISBNE6","created_at":"2026-05-22T01:04:57Z"}],"graph_snapshots":[{"event_id":"sha256:3b8b4a5774b5c757b0005e3f7f93a0e46aba904e1f5d5cc6bf5113d87c6d9c66","target":"graph","created_at":"2026-05-22T01:04:57Z","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/2605.22553/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A graph $G$ admits an $H$-tiling if it contains a collection of vertex-disjoint copies of $H$. In this paper, we confirm a conjecture proposed by K\\\"{u}hn, Osthus, and Treglown by showing that for any given graph $H$, there exists a constant $C(H)$ such that the following holds. If $G$ is a sufficiently large $n$-vertex graph satisfying $d(x) + d(y) \\geq 2\\left(1 - 1/\\chi_{\\text{cr}}(H)\\right)n$ for all nonadjacent vertices $x, y \\in V(G)$, then $G$ contains an $H$-tiling covering all but at most $C(H)$ vertices. Here $\\chi_{\\text{cr}}(H)$ denotes the critical chromatic number of $H$.","authors_text":"Guanghui Wang, Lin-Peng Zhang, Yilin Guo, Yuping Gao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-21T14:35:30Z","title":"An Ore-type Alon-Yuster Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22553","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":"sha256:812c0c89c0ed82aa084b8cfe5b32d0aa288056c16790ff8f0e4838d17a1f4754","target":"record","created_at":"2026-05-22T01:04:57Z","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":"e49cfad64a33aa77e5a06580843dcbe4777dd2ecbacf173a515060ff03cf3d69","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-21T14:35:30Z","title_canon_sha256":"e02f402d5539b53fd27cd481e65efecdc42bfdcaef03d11d65def6b9031390be"},"schema_version":"1.0","source":{"id":"2605.22553","kind":"arxiv","version":1}},"canonical_sha256":"c81120b49e5a4a07221a8d37ec3f4d264a588d2d502cf7e206805246ff985a41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c81120b49e5a4a07221a8d37ec3f4d264a588d2d502cf7e206805246ff985a41","first_computed_at":"2026-05-22T01:04:57.097128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:04:57.097128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/IoztH6GBGKHYnh/J3ZhOJ5GuwI8sfoxdqV3vy45mk4agvN5yiexjmVCy1PkuvoO8Vk0iVGLDviv5lpIBFlDBw==","signature_status":"signed_v1","signed_at":"2026-05-22T01:04:57.097874Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.22553","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:812c0c89c0ed82aa084b8cfe5b32d0aa288056c16790ff8f0e4838d17a1f4754","sha256:3b8b4a5774b5c757b0005e3f7f93a0e46aba904e1f5d5cc6bf5113d87c6d9c66"],"state_sha256":"3d84f370e44c0f6ebdbb40e11f31f6baeb0d2481d4a1e2c629af8b9710b75a9c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PoUmsYB5WAPfqY2BOjDEHnMN49l2kqwPMqRPgHBPg04VWAQ8hZwWPaNociGQi1nYRIx7Nh8TB+HPysWIz002Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T08:05:55.423794Z","bundle_sha256":"fb31730945168c3036f3cee2e6f5f1234456291e8f4f9ea7afb4ab555b64eb67"}}