{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:OSFKKX4TFYR5DYQW4QK3EUDTHE","short_pith_number":"pith:OSFKKX4T","canonical_record":{"source":{"id":"2507.10453","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-14T16:31:11Z","cross_cats_sorted":[],"title_canon_sha256":"40356dac317eaafe5f86eaba821fe7a40019a9e42bc260d36a79ac06186eba3a","abstract_canon_sha256":"f596e56b73100372764f29cc983db75c90f20988f22f228a33dfceefcaca313d"},"schema_version":"1.0"},"canonical_sha256":"748aa55f932e23d1e216e415b2507339096093dbd85e23c67d09e7de910eaa8c","source":{"kind":"arxiv","id":"2507.10453","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.10453","created_at":"2026-07-05T11:36:51Z"},{"alias_kind":"arxiv_version","alias_value":"2507.10453v1","created_at":"2026-07-05T11:36:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.10453","created_at":"2026-07-05T11:36:51Z"},{"alias_kind":"pith_short_12","alias_value":"OSFKKX4TFYR5","created_at":"2026-07-05T11:36:51Z"},{"alias_kind":"pith_short_16","alias_value":"OSFKKX4TFYR5DYQW","created_at":"2026-07-05T11:36:51Z"},{"alias_kind":"pith_short_8","alias_value":"OSFKKX4T","created_at":"2026-07-05T11:36:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:OSFKKX4TFYR5DYQW4QK3EUDTHE","target":"record","payload":{"canonical_record":{"source":{"id":"2507.10453","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-14T16:31:11Z","cross_cats_sorted":[],"title_canon_sha256":"40356dac317eaafe5f86eaba821fe7a40019a9e42bc260d36a79ac06186eba3a","abstract_canon_sha256":"f596e56b73100372764f29cc983db75c90f20988f22f228a33dfceefcaca313d"},"schema_version":"1.0"},"canonical_sha256":"748aa55f932e23d1e216e415b2507339096093dbd85e23c67d09e7de910eaa8c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:36:51.649054Z","signature_b64":"i2fePaa5W6MNUxij2m86xwS1Zfz1Iz0a4pzbWBFFUpxITB6bcmKFlNm8bbT67Tamxn35nGoJaEZQawkHZrsJCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"748aa55f932e23d1e216e415b2507339096093dbd85e23c67d09e7de910eaa8c","last_reissued_at":"2026-07-05T11:36:51.648520Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:36:51.648520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.10453","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":"2026-07-05T11:36:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8zjUq4GGht8NKHfFZElQBehJuoHVCKKJYE/vrKo0PLpEvVSFjD9QTgGwV85L3VFNji2UGtBx1Gea3Xuq+uG4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T02:42:50.789385Z"},"content_sha256":"48ea5c001d0dc540c9103aaab76fc779f5d050fdad9f05f61f9f196c6f709c67","schema_version":"1.0","event_id":"sha256:48ea5c001d0dc540c9103aaab76fc779f5d050fdad9f05f61f9f196c6f709c67"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:OSFKKX4TFYR5DYQW4QK3EUDTHE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Degree-truncated choosability of graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huan Zhou, Jialu Zhu, Xuding Zhu","submitted_at":"2025-07-14T16:31:11Z","abstract_excerpt":"A graph $G$ is called degree-truncated $k$-choosable if for every list assignment $L$ with $|L(v)| \\ge \\min\\{d_G(v), k\\}$ for each vertex $v$, $G$ is $L$-colourable. Richter asked whether every 3-connected non-complete planar graph is degree-truncated 6-choosable. We answer this question in negative by constructing a 3-connected non-complete planar graph which is not degree-truncated 7-choosable. Then we prove that every 3-connected non-complete planar graph is degree-truncated 16-DP-colourable (and hence degree-truncated $16$-choosable). We further prove that for an arbitrary proper minor clo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.10453","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/2507.10453/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":"2026-07-05T11:36:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L86LCwdF/bYgg+lviFIKbDeFBbCMS4lqGLJhcJc1O3U9EKbUq004KRywSwR5Os/QwnjGYv76EbHo6pPrQgTtDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T02:42:50.789904Z"},"content_sha256":"bcaaf03a3608efdf614a929bab388043ee4b1e482549dfc722a6d6a8d56d2d80","schema_version":"1.0","event_id":"sha256:bcaaf03a3608efdf614a929bab388043ee4b1e482549dfc722a6d6a8d56d2d80"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OSFKKX4TFYR5DYQW4QK3EUDTHE/bundle.json","state_url":"https://pith.science/pith/OSFKKX4TFYR5DYQW4QK3EUDTHE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OSFKKX4TFYR5DYQW4QK3EUDTHE/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":"2026-08-04T02:42:50Z","links":{"resolver":"https://pith.science/pith/OSFKKX4TFYR5DYQW4QK3EUDTHE","bundle":"https://pith.science/pith/OSFKKX4TFYR5DYQW4QK3EUDTHE/bundle.json","state":"https://pith.science/pith/OSFKKX4TFYR5DYQW4QK3EUDTHE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OSFKKX4TFYR5DYQW4QK3EUDTHE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:OSFKKX4TFYR5DYQW4QK3EUDTHE","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":"f596e56b73100372764f29cc983db75c90f20988f22f228a33dfceefcaca313d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-14T16:31:11Z","title_canon_sha256":"40356dac317eaafe5f86eaba821fe7a40019a9e42bc260d36a79ac06186eba3a"},"schema_version":"1.0","source":{"id":"2507.10453","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.10453","created_at":"2026-07-05T11:36:51Z"},{"alias_kind":"arxiv_version","alias_value":"2507.10453v1","created_at":"2026-07-05T11:36:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.10453","created_at":"2026-07-05T11:36:51Z"},{"alias_kind":"pith_short_12","alias_value":"OSFKKX4TFYR5","created_at":"2026-07-05T11:36:51Z"},{"alias_kind":"pith_short_16","alias_value":"OSFKKX4TFYR5DYQW","created_at":"2026-07-05T11:36:51Z"},{"alias_kind":"pith_short_8","alias_value":"OSFKKX4T","created_at":"2026-07-05T11:36:51Z"}],"graph_snapshots":[{"event_id":"sha256:bcaaf03a3608efdf614a929bab388043ee4b1e482549dfc722a6d6a8d56d2d80","target":"graph","created_at":"2026-07-05T11:36:51Z","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/2507.10453/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A graph $G$ is called degree-truncated $k$-choosable if for every list assignment $L$ with $|L(v)| \\ge \\min\\{d_G(v), k\\}$ for each vertex $v$, $G$ is $L$-colourable. Richter asked whether every 3-connected non-complete planar graph is degree-truncated 6-choosable. We answer this question in negative by constructing a 3-connected non-complete planar graph which is not degree-truncated 7-choosable. Then we prove that every 3-connected non-complete planar graph is degree-truncated 16-DP-colourable (and hence degree-truncated $16$-choosable). We further prove that for an arbitrary proper minor clo","authors_text":"Huan Zhou, Jialu Zhu, Xuding Zhu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-14T16:31:11Z","title":"Degree-truncated choosability of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.10453","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":"sha256:48ea5c001d0dc540c9103aaab76fc779f5d050fdad9f05f61f9f196c6f709c67","target":"record","created_at":"2026-07-05T11:36:51Z","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":"f596e56b73100372764f29cc983db75c90f20988f22f228a33dfceefcaca313d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-07-14T16:31:11Z","title_canon_sha256":"40356dac317eaafe5f86eaba821fe7a40019a9e42bc260d36a79ac06186eba3a"},"schema_version":"1.0","source":{"id":"2507.10453","kind":"arxiv","version":1}},"canonical_sha256":"748aa55f932e23d1e216e415b2507339096093dbd85e23c67d09e7de910eaa8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"748aa55f932e23d1e216e415b2507339096093dbd85e23c67d09e7de910eaa8c","first_computed_at":"2026-07-05T11:36:51.648520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:36:51.648520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i2fePaa5W6MNUxij2m86xwS1Zfz1Iz0a4pzbWBFFUpxITB6bcmKFlNm8bbT67Tamxn35nGoJaEZQawkHZrsJCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:36:51.649054Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.10453","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48ea5c001d0dc540c9103aaab76fc779f5d050fdad9f05f61f9f196c6f709c67","sha256:bcaaf03a3608efdf614a929bab388043ee4b1e482549dfc722a6d6a8d56d2d80"],"state_sha256":"94fae62ca022a4d0a56cc4ee50a455f5fcbffb2ec6951608ea6dece97341192f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3S3H1cRZIpTbNOvcRq60ZPyZU8yLXmLAqZGehusR3Ywwf/vXgryesHleL0w8VAS1adi6Ez1nKkH+M3zLEYNbDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T02:42:50.794271Z","bundle_sha256":"ed8f74edac8187b2c56e0dace82515997cb714f36cb449cee71966549fa66a18"}}