{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:WQTG7USVGDPYDAI4KFHGZNT455","short_pith_number":"pith:WQTG7USV","canonical_record":{"source":{"id":"2607.25396","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-28T07:56:19Z","cross_cats_sorted":[],"title_canon_sha256":"af189817be5428e08c248eaf494dd815f7fe84bb924c8460f1fd40fcd95dd1e3","abstract_canon_sha256":"314e76ba0434c03c07a8c52915afdd6558fd5b333173fba5e0bb32792fe349b9"},"schema_version":"1.0"},"canonical_sha256":"b4266fd25530df81811c514e6cb67cef4fde1dcc6df2fa85ff24a38d2172667c","source":{"kind":"arxiv","id":"2607.25396","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.25396","created_at":"2026-07-29T01:25:13Z"},{"alias_kind":"arxiv_version","alias_value":"2607.25396v1","created_at":"2026-07-29T01:25:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.25396","created_at":"2026-07-29T01:25:13Z"},{"alias_kind":"pith_short_12","alias_value":"WQTG7USVGDPY","created_at":"2026-07-29T01:25:13Z"},{"alias_kind":"pith_short_16","alias_value":"WQTG7USVGDPYDAI4","created_at":"2026-07-29T01:25:13Z"},{"alias_kind":"pith_short_8","alias_value":"WQTG7USV","created_at":"2026-07-29T01:25:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:WQTG7USVGDPYDAI4KFHGZNT455","target":"record","payload":{"canonical_record":{"source":{"id":"2607.25396","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-28T07:56:19Z","cross_cats_sorted":[],"title_canon_sha256":"af189817be5428e08c248eaf494dd815f7fe84bb924c8460f1fd40fcd95dd1e3","abstract_canon_sha256":"314e76ba0434c03c07a8c52915afdd6558fd5b333173fba5e0bb32792fe349b9"},"schema_version":"1.0"},"canonical_sha256":"b4266fd25530df81811c514e6cb67cef4fde1dcc6df2fa85ff24a38d2172667c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-29T01:25:13.474859Z","signature_b64":"GZJYzRFoi93hVPOvYGw6bYC4IMpqrbui/N4kRQao3iLDQK90IVHmxHddqCwYb3ImgwSWHghtdIdMPrGiEmphBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4266fd25530df81811c514e6cb67cef4fde1dcc6df2fa85ff24a38d2172667c","last_reissued_at":"2026-07-29T01:25:13.474020Z","signature_status":"signed_v1","first_computed_at":"2026-07-29T01:25:13.474020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.25396","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":"2026-07-29T01:25:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lCX9U0pyqqGxTO8Vxqz7bX95d8Cn68t6MA4bHlu+38gqtc/hN3RGKY+j0q8XzUVkTvgcXuZCsz7q5WoetmMQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T02:38:18.572996Z"},"content_sha256":"3fb44ac9bed6560f56614f452bc8d208181949779f276ac786c64a26d133fd65","schema_version":"1.0","event_id":"sha256:3fb44ac9bed6560f56614f452bc8d208181949779f276ac786c64a26d133fd65"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:WQTG7USVGDPYDAI4KFHGZNT455","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal coloring of $\\{\\mathrm{cap},\\mathrm{even\\ hole}\\}$-free graphs with no short odd holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Feng Liu, Shuang Sun, Yan Wang","submitted_at":"2026-07-28T07:56:19Z","abstract_excerpt":"A \\emph{hole} is an induced cycle of length at least four, and an \\emph{even hole} is a hole of even length. A \\emph{cap} is obtained from a hole by adding a vertex adjacent to exactly two consecutive vertices of the hole. Chen, Xu, and Xu proved that every $\\{\\mathrm{cap},\\mathrm{even\\ hole}\\}$-free graph $G$ satisfies $\\chi(G)\\leq \\left\\lceil\\frac{5}{4}\\omega(G)\\right\\rceil$, and improved this bound to $\\chi(G)\\leq \\left\\lceil\\frac{7}{6}\\omega(G)\\right\\rceil$ when $5$-holes are also excluded. They asked whether, for every integer $q\\geq3$, every $\\{\\mathrm{cap},\\mathrm{even\\ hole}\\}$-free gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25396","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/2607.25396/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":"2026-07-29T01:25:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZOsJaArSf3jUuuzcLpYgGxKj6X7d66HaZa1UplaeDTVkDmS3hssDKAM2wfcuFHzqwiNJ2pteEXzpUo85F7wHDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T02:38:18.573657Z"},"content_sha256":"d316485e1d655efa4ea1b1de0b3ca5387fa109b52376aff54d03dd2965f1d951","schema_version":"1.0","event_id":"sha256:d316485e1d655efa4ea1b1de0b3ca5387fa109b52376aff54d03dd2965f1d951"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WQTG7USVGDPYDAI4KFHGZNT455/bundle.json","state_url":"https://pith.science/pith/WQTG7USVGDPYDAI4KFHGZNT455/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WQTG7USVGDPYDAI4KFHGZNT455/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":"2026-08-06T02:38:18Z","links":{"resolver":"https://pith.science/pith/WQTG7USVGDPYDAI4KFHGZNT455","bundle":"https://pith.science/pith/WQTG7USVGDPYDAI4KFHGZNT455/bundle.json","state":"https://pith.science/pith/WQTG7USVGDPYDAI4KFHGZNT455/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WQTG7USVGDPYDAI4KFHGZNT455/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WQTG7USVGDPYDAI4KFHGZNT455","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":"314e76ba0434c03c07a8c52915afdd6558fd5b333173fba5e0bb32792fe349b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-28T07:56:19Z","title_canon_sha256":"af189817be5428e08c248eaf494dd815f7fe84bb924c8460f1fd40fcd95dd1e3"},"schema_version":"1.0","source":{"id":"2607.25396","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.25396","created_at":"2026-07-29T01:25:13Z"},{"alias_kind":"arxiv_version","alias_value":"2607.25396v1","created_at":"2026-07-29T01:25:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.25396","created_at":"2026-07-29T01:25:13Z"},{"alias_kind":"pith_short_12","alias_value":"WQTG7USVGDPY","created_at":"2026-07-29T01:25:13Z"},{"alias_kind":"pith_short_16","alias_value":"WQTG7USVGDPYDAI4","created_at":"2026-07-29T01:25:13Z"},{"alias_kind":"pith_short_8","alias_value":"WQTG7USV","created_at":"2026-07-29T01:25:13Z"}],"graph_snapshots":[{"event_id":"sha256:d316485e1d655efa4ea1b1de0b3ca5387fa109b52376aff54d03dd2965f1d951","target":"graph","created_at":"2026-07-29T01:25:13Z","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/2607.25396/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A \\emph{hole} is an induced cycle of length at least four, and an \\emph{even hole} is a hole of even length. A \\emph{cap} is obtained from a hole by adding a vertex adjacent to exactly two consecutive vertices of the hole. Chen, Xu, and Xu proved that every $\\{\\mathrm{cap},\\mathrm{even\\ hole}\\}$-free graph $G$ satisfies $\\chi(G)\\leq \\left\\lceil\\frac{5}{4}\\omega(G)\\right\\rceil$, and improved this bound to $\\chi(G)\\leq \\left\\lceil\\frac{7}{6}\\omega(G)\\right\\rceil$ when $5$-holes are also excluded. They asked whether, for every integer $q\\geq3$, every $\\{\\mathrm{cap},\\mathrm{even\\ hole}\\}$-free gr","authors_text":"Feng Liu, Shuang Sun, Yan Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-28T07:56:19Z","title":"Optimal coloring of $\\{\\mathrm{cap},\\mathrm{even\\ hole}\\}$-free graphs with no short odd holes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25396","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":"sha256:3fb44ac9bed6560f56614f452bc8d208181949779f276ac786c64a26d133fd65","target":"record","created_at":"2026-07-29T01:25:13Z","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":"314e76ba0434c03c07a8c52915afdd6558fd5b333173fba5e0bb32792fe349b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-07-28T07:56:19Z","title_canon_sha256":"af189817be5428e08c248eaf494dd815f7fe84bb924c8460f1fd40fcd95dd1e3"},"schema_version":"1.0","source":{"id":"2607.25396","kind":"arxiv","version":1}},"canonical_sha256":"b4266fd25530df81811c514e6cb67cef4fde1dcc6df2fa85ff24a38d2172667c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4266fd25530df81811c514e6cb67cef4fde1dcc6df2fa85ff24a38d2172667c","first_computed_at":"2026-07-29T01:25:13.474020Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-29T01:25:13.474020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GZJYzRFoi93hVPOvYGw6bYC4IMpqrbui/N4kRQao3iLDQK90IVHmxHddqCwYb3ImgwSWHghtdIdMPrGiEmphBg==","signature_status":"signed_v1","signed_at":"2026-07-29T01:25:13.474859Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.25396","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fb44ac9bed6560f56614f452bc8d208181949779f276ac786c64a26d133fd65","sha256:d316485e1d655efa4ea1b1de0b3ca5387fa109b52376aff54d03dd2965f1d951"],"state_sha256":"aef30f3dee61e492ef927fe63559d44e6331a92724f17b6c5a4b96f55048a660"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DaiVw4CRfN1G8tf8zVAqBSx5AARoWGjX1Dqyl3U69nXMQRxU+NyuwSzALd4CVbLHeJkjO/LpUiR77u3UlmHsAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T02:38:18.580378Z","bundle_sha256":"ba2a389d973be2fdaaa3035dfbb610d5a11f13dc03dbeff715674bfea7c54ffe"}}