{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:UNA7PRDYP3QY5JDUGYLPYCYAVF","short_pith_number":"pith:UNA7PRDY","canonical_record":{"source":{"id":"2605.27943","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-27T04:30:32Z","cross_cats_sorted":[],"title_canon_sha256":"cc28ebeb230ba0e329a3552446f04ed022d2e6cf231a155466735295a71a1c07","abstract_canon_sha256":"4f564e7130cbf6b3e113bbb334d58c0359758bb293896ccf44ed7933c62a94de"},"schema_version":"1.0"},"canonical_sha256":"a341f7c4787ee18ea4743616fc0b00a95b2592fc003dde5e2ac495616890fd0b","source":{"kind":"arxiv","id":"2605.27943","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27943","created_at":"2026-05-28T01:04:53Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27943v1","created_at":"2026-05-28T01:04:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27943","created_at":"2026-05-28T01:04:53Z"},{"alias_kind":"pith_short_12","alias_value":"UNA7PRDYP3QY","created_at":"2026-05-28T01:04:53Z"},{"alias_kind":"pith_short_16","alias_value":"UNA7PRDYP3QY5JDU","created_at":"2026-05-28T01:04:53Z"},{"alias_kind":"pith_short_8","alias_value":"UNA7PRDY","created_at":"2026-05-28T01:04:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:UNA7PRDYP3QY5JDUGYLPYCYAVF","target":"record","payload":{"canonical_record":{"source":{"id":"2605.27943","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-27T04:30:32Z","cross_cats_sorted":[],"title_canon_sha256":"cc28ebeb230ba0e329a3552446f04ed022d2e6cf231a155466735295a71a1c07","abstract_canon_sha256":"4f564e7130cbf6b3e113bbb334d58c0359758bb293896ccf44ed7933c62a94de"},"schema_version":"1.0"},"canonical_sha256":"a341f7c4787ee18ea4743616fc0b00a95b2592fc003dde5e2ac495616890fd0b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T01:04:53.451916Z","signature_b64":"NApvr8rhZCKX/4vyRKuTPiloKlBwD9cuusRSq8NvN2hwZOFLbCqXd1vy7XtZuCGYCAh6fvarPKL5Ew6gtENHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a341f7c4787ee18ea4743616fc0b00a95b2592fc003dde5e2ac495616890fd0b","last_reissued_at":"2026-05-28T01:04:53.451432Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T01:04:53.451432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.27943","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":"2026-05-28T01:04:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Znn3Z9dnAZY+dC/AQtFhKyckd5D+fSYPR+SWkJipuhwnLZiInC+N0QNHeCLadf1mnVcMGObCPlafyDen+jMsAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:16:09.004228Z"},"content_sha256":"5a46e2ef1a2a83c52c20e39fb009a3414dcb59f825a655f6484ab34d54fba86c","schema_version":"1.0","event_id":"sha256:5a46e2ef1a2a83c52c20e39fb009a3414dcb59f825a655f6484ab34d54fba86c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:UNA7PRDYP3QY5JDUGYLPYCYAVF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graphs with girth 8 and without longer even holes are 3-colorable","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Rong Wu, Yan Wang","submitted_at":"2026-05-27T04:30:32Z","abstract_excerpt":"For an integer $\\ell\\geq 2$, let ${\\cal{H}}_{\\ell}$ denote the family of graphs which have girth $2\\ell$ and have no even hole of length greater than $2\\ell$. Wu, Xu and Xu conjectured that every graph in $\\bigcup_{\\ell\\geq 2} {\\cal{H}}_{\\ell}$ is $3$-colorable. Chen showed that every graph in $\\bigcup_{\\ell\\geq 5} {\\cal{H}}_{\\ell}$ is $3$-colorable. In this paper, we prove that every graph in ${\\cal{H}}_4$ is $3$-colorable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27943","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/2605.27943/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":"2026-05-28T01:04:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yKpslqdGXLCqEyo6nQZCGItRGbB8oycnsG8sCXQLFnbmCkhF8gQhLP/VQ4aoawu3KdXfhDz3E/is5t3RRpOeAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:16:09.005019Z"},"content_sha256":"c2352477c70cd0b2716d5dae568ae3b8c668aab6d83e87a2f70cc9a03d637573","schema_version":"1.0","event_id":"sha256:c2352477c70cd0b2716d5dae568ae3b8c668aab6d83e87a2f70cc9a03d637573"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UNA7PRDYP3QY5JDUGYLPYCYAVF/bundle.json","state_url":"https://pith.science/pith/UNA7PRDYP3QY5JDUGYLPYCYAVF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UNA7PRDYP3QY5JDUGYLPYCYAVF/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":"2026-06-01T02:16:09Z","links":{"resolver":"https://pith.science/pith/UNA7PRDYP3QY5JDUGYLPYCYAVF","bundle":"https://pith.science/pith/UNA7PRDYP3QY5JDUGYLPYCYAVF/bundle.json","state":"https://pith.science/pith/UNA7PRDYP3QY5JDUGYLPYCYAVF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UNA7PRDYP3QY5JDUGYLPYCYAVF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:UNA7PRDYP3QY5JDUGYLPYCYAVF","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":"4f564e7130cbf6b3e113bbb334d58c0359758bb293896ccf44ed7933c62a94de","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-27T04:30:32Z","title_canon_sha256":"cc28ebeb230ba0e329a3552446f04ed022d2e6cf231a155466735295a71a1c07"},"schema_version":"1.0","source":{"id":"2605.27943","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27943","created_at":"2026-05-28T01:04:53Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27943v1","created_at":"2026-05-28T01:04:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27943","created_at":"2026-05-28T01:04:53Z"},{"alias_kind":"pith_short_12","alias_value":"UNA7PRDYP3QY","created_at":"2026-05-28T01:04:53Z"},{"alias_kind":"pith_short_16","alias_value":"UNA7PRDYP3QY5JDU","created_at":"2026-05-28T01:04:53Z"},{"alias_kind":"pith_short_8","alias_value":"UNA7PRDY","created_at":"2026-05-28T01:04:53Z"}],"graph_snapshots":[{"event_id":"sha256:c2352477c70cd0b2716d5dae568ae3b8c668aab6d83e87a2f70cc9a03d637573","target":"graph","created_at":"2026-05-28T01:04:53Z","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/2605.27943/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For an integer $\\ell\\geq 2$, let ${\\cal{H}}_{\\ell}$ denote the family of graphs which have girth $2\\ell$ and have no even hole of length greater than $2\\ell$. Wu, Xu and Xu conjectured that every graph in $\\bigcup_{\\ell\\geq 2} {\\cal{H}}_{\\ell}$ is $3$-colorable. Chen showed that every graph in $\\bigcup_{\\ell\\geq 5} {\\cal{H}}_{\\ell}$ is $3$-colorable. In this paper, we prove that every graph in ${\\cal{H}}_4$ is $3$-colorable.","authors_text":"Rong Wu, Yan Wang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-27T04:30:32Z","title":"Graphs with girth 8 and without longer even holes are 3-colorable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27943","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":"sha256:5a46e2ef1a2a83c52c20e39fb009a3414dcb59f825a655f6484ab34d54fba86c","target":"record","created_at":"2026-05-28T01:04:53Z","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":"4f564e7130cbf6b3e113bbb334d58c0359758bb293896ccf44ed7933c62a94de","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-27T04:30:32Z","title_canon_sha256":"cc28ebeb230ba0e329a3552446f04ed022d2e6cf231a155466735295a71a1c07"},"schema_version":"1.0","source":{"id":"2605.27943","kind":"arxiv","version":1}},"canonical_sha256":"a341f7c4787ee18ea4743616fc0b00a95b2592fc003dde5e2ac495616890fd0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a341f7c4787ee18ea4743616fc0b00a95b2592fc003dde5e2ac495616890fd0b","first_computed_at":"2026-05-28T01:04:53.451432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T01:04:53.451432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NApvr8rhZCKX/4vyRKuTPiloKlBwD9cuusRSq8NvN2hwZOFLbCqXd1vy7XtZuCGYCAh6fvarPKL5Ew6gtENHBA==","signature_status":"signed_v1","signed_at":"2026-05-28T01:04:53.451916Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.27943","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a46e2ef1a2a83c52c20e39fb009a3414dcb59f825a655f6484ab34d54fba86c","sha256:c2352477c70cd0b2716d5dae568ae3b8c668aab6d83e87a2f70cc9a03d637573"],"state_sha256":"7f7a046475a9baa67acb46000ef3bfc763b97a1f26e5e14446506ed0d6062866"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XL4uAJ+Sh7U4Gx4DlK5wo7aR3EI3xlNPNFvKygM7l54o9zKvzyfPawjCP9NMFXdm4m43N8S0jzPoO+EcMEzLAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:16:09.009180Z","bundle_sha256":"6657f503d71575458f82c0c6c73d6d8bf74fb9c6a2285b2d060bd567ba8de5cf"}}