{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:O3KQ76JR27IDM4AN2EVPOYJISV","short_pith_number":"pith:O3KQ76JR","canonical_record":{"source":{"id":"2312.15962","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-12-26T08:53:08Z","cross_cats_sorted":[],"title_canon_sha256":"fe522d5a1912a621aef85cfbee1b05c91f6e838a9d53989a12f10191b4853077","abstract_canon_sha256":"3240455fb0095087fc332d9c62e5679747b44905ab183b507714e61ebb0235b9"},"schema_version":"1.0"},"canonical_sha256":"76d50ff931d7d036700dd12af7612895462f8161bd47f5caebac7ca331f1b34c","source":{"kind":"arxiv","id":"2312.15962","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.15962","created_at":"2026-07-05T10:25:04Z"},{"alias_kind":"arxiv_version","alias_value":"2312.15962v2","created_at":"2026-07-05T10:25:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.15962","created_at":"2026-07-05T10:25:04Z"},{"alias_kind":"pith_short_12","alias_value":"O3KQ76JR27ID","created_at":"2026-07-05T10:25:04Z"},{"alias_kind":"pith_short_16","alias_value":"O3KQ76JR27IDM4AN","created_at":"2026-07-05T10:25:04Z"},{"alias_kind":"pith_short_8","alias_value":"O3KQ76JR","created_at":"2026-07-05T10:25:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:O3KQ76JR27IDM4AN2EVPOYJISV","target":"record","payload":{"canonical_record":{"source":{"id":"2312.15962","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-12-26T08:53:08Z","cross_cats_sorted":[],"title_canon_sha256":"fe522d5a1912a621aef85cfbee1b05c91f6e838a9d53989a12f10191b4853077","abstract_canon_sha256":"3240455fb0095087fc332d9c62e5679747b44905ab183b507714e61ebb0235b9"},"schema_version":"1.0"},"canonical_sha256":"76d50ff931d7d036700dd12af7612895462f8161bd47f5caebac7ca331f1b34c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:25:04.024302Z","signature_b64":"6qauaSo2RzmO/wbs/z0/sbJJsVjlDnb/qeJenzNTUBLVvJm91FhWfB0SnFi5kxniq4q7R2PnjUDpZQcjFtCACg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76d50ff931d7d036700dd12af7612895462f8161bd47f5caebac7ca331f1b34c","last_reissued_at":"2026-07-05T10:25:04.023293Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:25:04.023293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.15962","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:25:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kmr+yaTWY+CemsaLHgdr6eHMzDeJ5uipTsaAzmsBA9kCq+gHyjG7VKVmRefs169glzlU/Q9Y5dyu3V9bBkl7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T08:18:07.009324Z"},"content_sha256":"c12306b890c778826e7860af08d850137abd7b5f22363cb375987ebb0ae3e12e","schema_version":"1.0","event_id":"sha256:c12306b890c778826e7860af08d850137abd7b5f22363cb375987ebb0ae3e12e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:O3KQ76JR27IDM4AN2EVPOYJISV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Truncated degree DP-colourability of $K_{2,4}$-minor free graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cheng Wang, Huan Zhou, On-Hei Solomon Lo, Xuding Zhu","submitted_at":"2023-12-26T08:53:08Z","abstract_excerpt":"Assume $G$ is a graph and $k$ is a positive integer. Let $f$ from $V(G)$ to $ N$ be defined as $f(v)$ is the minimum of $k$ and $d(v)$. If $G$ is $f$-DP-colourable (respectively, $f$-choosable), then we say $G$ is $k$-truncated degree DP-colourable (respectively, $k$-truncated degree-choosable). Hutchinson proved that 2-connected maximal outerplanar graphs other than the triangle are $5$-truncated degree-choosable, and asked whether the result can be extended to all outerplanar graphs, and the question remained open.\n  This paper proves that 2-connected $K24$-minor free graphs other than cycle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.15962","kind":"arxiv","version":2},"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/2312.15962/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":"2026-07-05T10:25:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DDChJ68w6FpzEDMxRiv6sfJtOxeDDgslLgFpawsqCvlH1ugbawWxLRVPvCLpzQ6OY280//BPalrFPv88wNfYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T08:18:07.009971Z"},"content_sha256":"c8ded58ed5f0d664296e3312c7bc68830f7d44b2efead2beedb11493732fb368","schema_version":"1.0","event_id":"sha256:c8ded58ed5f0d664296e3312c7bc68830f7d44b2efead2beedb11493732fb368"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O3KQ76JR27IDM4AN2EVPOYJISV/bundle.json","state_url":"https://pith.science/pith/O3KQ76JR27IDM4AN2EVPOYJISV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O3KQ76JR27IDM4AN2EVPOYJISV/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":"2026-08-04T08:18:07Z","links":{"resolver":"https://pith.science/pith/O3KQ76JR27IDM4AN2EVPOYJISV","bundle":"https://pith.science/pith/O3KQ76JR27IDM4AN2EVPOYJISV/bundle.json","state":"https://pith.science/pith/O3KQ76JR27IDM4AN2EVPOYJISV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O3KQ76JR27IDM4AN2EVPOYJISV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:O3KQ76JR27IDM4AN2EVPOYJISV","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":"3240455fb0095087fc332d9c62e5679747b44905ab183b507714e61ebb0235b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-12-26T08:53:08Z","title_canon_sha256":"fe522d5a1912a621aef85cfbee1b05c91f6e838a9d53989a12f10191b4853077"},"schema_version":"1.0","source":{"id":"2312.15962","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.15962","created_at":"2026-07-05T10:25:04Z"},{"alias_kind":"arxiv_version","alias_value":"2312.15962v2","created_at":"2026-07-05T10:25:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.15962","created_at":"2026-07-05T10:25:04Z"},{"alias_kind":"pith_short_12","alias_value":"O3KQ76JR27ID","created_at":"2026-07-05T10:25:04Z"},{"alias_kind":"pith_short_16","alias_value":"O3KQ76JR27IDM4AN","created_at":"2026-07-05T10:25:04Z"},{"alias_kind":"pith_short_8","alias_value":"O3KQ76JR","created_at":"2026-07-05T10:25:04Z"}],"graph_snapshots":[{"event_id":"sha256:c8ded58ed5f0d664296e3312c7bc68830f7d44b2efead2beedb11493732fb368","target":"graph","created_at":"2026-07-05T10:25:04Z","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/2312.15962/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Assume $G$ is a graph and $k$ is a positive integer. Let $f$ from $V(G)$ to $ N$ be defined as $f(v)$ is the minimum of $k$ and $d(v)$. If $G$ is $f$-DP-colourable (respectively, $f$-choosable), then we say $G$ is $k$-truncated degree DP-colourable (respectively, $k$-truncated degree-choosable). Hutchinson proved that 2-connected maximal outerplanar graphs other than the triangle are $5$-truncated degree-choosable, and asked whether the result can be extended to all outerplanar graphs, and the question remained open.\n  This paper proves that 2-connected $K24$-minor free graphs other than cycle","authors_text":"Cheng Wang, Huan Zhou, On-Hei Solomon Lo, Xuding Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-12-26T08:53:08Z","title":"Truncated degree DP-colourability of $K_{2,4}$-minor free graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.15962","kind":"arxiv","version":2},"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:c12306b890c778826e7860af08d850137abd7b5f22363cb375987ebb0ae3e12e","target":"record","created_at":"2026-07-05T10:25:04Z","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":"3240455fb0095087fc332d9c62e5679747b44905ab183b507714e61ebb0235b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-12-26T08:53:08Z","title_canon_sha256":"fe522d5a1912a621aef85cfbee1b05c91f6e838a9d53989a12f10191b4853077"},"schema_version":"1.0","source":{"id":"2312.15962","kind":"arxiv","version":2}},"canonical_sha256":"76d50ff931d7d036700dd12af7612895462f8161bd47f5caebac7ca331f1b34c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76d50ff931d7d036700dd12af7612895462f8161bd47f5caebac7ca331f1b34c","first_computed_at":"2026-07-05T10:25:04.023293Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:25:04.023293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6qauaSo2RzmO/wbs/z0/sbJJsVjlDnb/qeJenzNTUBLVvJm91FhWfB0SnFi5kxniq4q7R2PnjUDpZQcjFtCACg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:25:04.024302Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.15962","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c12306b890c778826e7860af08d850137abd7b5f22363cb375987ebb0ae3e12e","sha256:c8ded58ed5f0d664296e3312c7bc68830f7d44b2efead2beedb11493732fb368"],"state_sha256":"f3f52bd8286b68e76f5260455d49c8ac76bdbc294d7b3439864fff5f999b65fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p9g7L8oH/36G8yOFwRD6IwWZATat6vzxG6MJoani1xIqK4+GpkRZkTP7SBH6shAdaonVpHBq4StOsnuhfrG6Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T08:18:07.014449Z","bundle_sha256":"93331f02990c79dacc263960f6aafc6d1a93ed9879441a9d8202497ea57231ed"}}