{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:3GYN4GYEBX7PV2HA7YXSJWZRXC","short_pith_number":"pith:3GYN4GYE","canonical_record":{"source":{"id":"2605.18783","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-06T13:07:26Z","cross_cats_sorted":[],"title_canon_sha256":"2234e0ae0d3f31e0659ef494fa162d45e0ccb8e713c021651dc94233bf521201","abstract_canon_sha256":"53d3dedba0fac299e71bf34c09c267081185508f04ee4a2ccf97ceeb01bd3080"},"schema_version":"1.0"},"canonical_sha256":"d9b0de1b040dfefae8e0fe2f24db31b8b3a20fd876dfa830449971336dcfbe2d","source":{"kind":"arxiv","id":"2605.18783","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.18783","created_at":"2026-05-20T00:06:22Z"},{"alias_kind":"arxiv_version","alias_value":"2605.18783v1","created_at":"2026-05-20T00:06:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.18783","created_at":"2026-05-20T00:06:22Z"},{"alias_kind":"pith_short_12","alias_value":"3GYN4GYEBX7P","created_at":"2026-05-20T00:06:22Z"},{"alias_kind":"pith_short_16","alias_value":"3GYN4GYEBX7PV2HA","created_at":"2026-05-20T00:06:22Z"},{"alias_kind":"pith_short_8","alias_value":"3GYN4GYE","created_at":"2026-05-20T00:06:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:3GYN4GYEBX7PV2HA7YXSJWZRXC","target":"record","payload":{"canonical_record":{"source":{"id":"2605.18783","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-06T13:07:26Z","cross_cats_sorted":[],"title_canon_sha256":"2234e0ae0d3f31e0659ef494fa162d45e0ccb8e713c021651dc94233bf521201","abstract_canon_sha256":"53d3dedba0fac299e71bf34c09c267081185508f04ee4a2ccf97ceeb01bd3080"},"schema_version":"1.0"},"canonical_sha256":"d9b0de1b040dfefae8e0fe2f24db31b8b3a20fd876dfa830449971336dcfbe2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:06:22.017818Z","signature_b64":"0qCwUmOH8yWMDh5Unxy0KMoxXjXjr8piMqs4CK/UaBzQfF/hEq2jQjGl4SSSZe3yEFZEi96T1nlgs8v0ZsXdBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9b0de1b040dfefae8e0fe2f24db31b8b3a20fd876dfa830449971336dcfbe2d","last_reissued_at":"2026-05-20T00:06:22.016619Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:06:22.016619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.18783","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":"2026-05-20T00:06:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WPiaLU3mF31OXF81MuFqnRtsitC8wRDgDJiCcuFI/gxCkqzJyrPETLpFA0xMauBK+Id2NC/bqcmqpnG50WwjCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T09:45:41.223663Z"},"content_sha256":"bb888167ab24593879e09ddba024c04852771dc5fa6747bc9894411f503e4e62","schema_version":"1.0","event_id":"sha256:bb888167ab24593879e09ddba024c04852771dc5fa6747bc9894411f503e4e62"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:3GYN4GYEBX7PV2HA7YXSJWZRXC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Hilton-Zhao vertex-splitting conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xuli Qi, Yanrui Feng","submitted_at":"2026-05-06T13:07:26Z","abstract_excerpt":"Let $G$ be a simple graph with order $n$, maximum degree $\\Delta(G)$, and chromatic index $\\chi'(G)$, respectively. A graph $G$ is edge-chromatic critical if $\\chi'(H)<\\chi'(G)$ for every proper subgraph $H$ of $G$. Assume that $G$ is an $n$-vertex connected regular Class $1$ graph, and let $G^*$ be obtained from $G$ by splitting one vertex into two vertices. Hilton and Zhao in 1997 proposed the vertex-splitting conjecture: if $\\Delta(G)>\\frac{n}{3}$, then $G^*$ is edge-chromatic critical. Recently, Cao, Chen, and Shan (Discrete Math. 2022) verified the conjecture for $\\Delta(G)\\ge\\frac{3n}{4}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18783","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/2605.18783/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":"2026-05-20T00:06:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IUyRQHtRaxGQCqaNQA37TRrTDOe7H9i7MST8sWKLdA/9mmKojDJ0hp074vyjs1ERbDbPH2mzvKvmC9mBgRU5Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T09:45:41.224041Z"},"content_sha256":"5fa80280f0eb6d965c5c826ba045b8f6a7a16584399f676efef1187103b7ea72","schema_version":"1.0","event_id":"sha256:5fa80280f0eb6d965c5c826ba045b8f6a7a16584399f676efef1187103b7ea72"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3GYN4GYEBX7PV2HA7YXSJWZRXC/bundle.json","state_url":"https://pith.science/pith/3GYN4GYEBX7PV2HA7YXSJWZRXC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3GYN4GYEBX7PV2HA7YXSJWZRXC/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":"2026-07-02T09:45:41Z","links":{"resolver":"https://pith.science/pith/3GYN4GYEBX7PV2HA7YXSJWZRXC","bundle":"https://pith.science/pith/3GYN4GYEBX7PV2HA7YXSJWZRXC/bundle.json","state":"https://pith.science/pith/3GYN4GYEBX7PV2HA7YXSJWZRXC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3GYN4GYEBX7PV2HA7YXSJWZRXC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3GYN4GYEBX7PV2HA7YXSJWZRXC","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":"53d3dedba0fac299e71bf34c09c267081185508f04ee4a2ccf97ceeb01bd3080","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-06T13:07:26Z","title_canon_sha256":"2234e0ae0d3f31e0659ef494fa162d45e0ccb8e713c021651dc94233bf521201"},"schema_version":"1.0","source":{"id":"2605.18783","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.18783","created_at":"2026-05-20T00:06:22Z"},{"alias_kind":"arxiv_version","alias_value":"2605.18783v1","created_at":"2026-05-20T00:06:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.18783","created_at":"2026-05-20T00:06:22Z"},{"alias_kind":"pith_short_12","alias_value":"3GYN4GYEBX7P","created_at":"2026-05-20T00:06:22Z"},{"alias_kind":"pith_short_16","alias_value":"3GYN4GYEBX7PV2HA","created_at":"2026-05-20T00:06:22Z"},{"alias_kind":"pith_short_8","alias_value":"3GYN4GYE","created_at":"2026-05-20T00:06:22Z"}],"graph_snapshots":[{"event_id":"sha256:5fa80280f0eb6d965c5c826ba045b8f6a7a16584399f676efef1187103b7ea72","target":"graph","created_at":"2026-05-20T00:06:22Z","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/2605.18783/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G$ be a simple graph with order $n$, maximum degree $\\Delta(G)$, and chromatic index $\\chi'(G)$, respectively. A graph $G$ is edge-chromatic critical if $\\chi'(H)<\\chi'(G)$ for every proper subgraph $H$ of $G$. Assume that $G$ is an $n$-vertex connected regular Class $1$ graph, and let $G^*$ be obtained from $G$ by splitting one vertex into two vertices. Hilton and Zhao in 1997 proposed the vertex-splitting conjecture: if $\\Delta(G)>\\frac{n}{3}$, then $G^*$ is edge-chromatic critical. Recently, Cao, Chen, and Shan (Discrete Math. 2022) verified the conjecture for $\\Delta(G)\\ge\\frac{3n}{4}","authors_text":"Xuli Qi, Yanrui Feng","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-06T13:07:26Z","title":"On the Hilton-Zhao vertex-splitting conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18783","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:bb888167ab24593879e09ddba024c04852771dc5fa6747bc9894411f503e4e62","target":"record","created_at":"2026-05-20T00:06:22Z","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":"53d3dedba0fac299e71bf34c09c267081185508f04ee4a2ccf97ceeb01bd3080","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-06T13:07:26Z","title_canon_sha256":"2234e0ae0d3f31e0659ef494fa162d45e0ccb8e713c021651dc94233bf521201"},"schema_version":"1.0","source":{"id":"2605.18783","kind":"arxiv","version":1}},"canonical_sha256":"d9b0de1b040dfefae8e0fe2f24db31b8b3a20fd876dfa830449971336dcfbe2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9b0de1b040dfefae8e0fe2f24db31b8b3a20fd876dfa830449971336dcfbe2d","first_computed_at":"2026-05-20T00:06:22.016619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:06:22.016619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0qCwUmOH8yWMDh5Unxy0KMoxXjXjr8piMqs4CK/UaBzQfF/hEq2jQjGl4SSSZe3yEFZEi96T1nlgs8v0ZsXdBg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:06:22.017818Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.18783","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb888167ab24593879e09ddba024c04852771dc5fa6747bc9894411f503e4e62","sha256:5fa80280f0eb6d965c5c826ba045b8f6a7a16584399f676efef1187103b7ea72"],"state_sha256":"c7f87dc019293b804fb1697dd16a483572e621c14ff2e3d07f41862fff76a360"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X1HwlRX4ptOjIM1kLfJEiUYiJtiQ+5QgiZkXNHzyGUvwHrbBZh3gPh5Aod/P5qBIFJ/1wyrfGbdFftPCi2l7CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T09:45:41.226035Z","bundle_sha256":"2a5e40e4e2f8116e754f5831c0f10d7cc686619fc2a9e3f693309063291f0e43"}}