{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:CRSGINJW7DZ3CGQHKYTHD65VGH","short_pith_number":"pith:CRSGINJW","canonical_record":{"source":{"id":"2505.17193","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-22T18:03:55Z","cross_cats_sorted":[],"title_canon_sha256":"a69f9970c575789f9e1c8ed27a6057b60ca04cfe8d408b9a54116f23d68ffa8a","abstract_canon_sha256":"6582dbe9c305d38dccbce465d1aefe75f0c1228ece27dc435970b8250c95ea62"},"schema_version":"1.0"},"canonical_sha256":"1464643536f8f3b11a07562671fbb531ee4696bacd9be3805efc67b28eb440c1","source":{"kind":"arxiv","id":"2505.17193","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.17193","created_at":"2026-07-05T11:07:48Z"},{"alias_kind":"arxiv_version","alias_value":"2505.17193v1","created_at":"2026-07-05T11:07:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.17193","created_at":"2026-07-05T11:07:48Z"},{"alias_kind":"pith_short_12","alias_value":"CRSGINJW7DZ3","created_at":"2026-07-05T11:07:48Z"},{"alias_kind":"pith_short_16","alias_value":"CRSGINJW7DZ3CGQH","created_at":"2026-07-05T11:07:48Z"},{"alias_kind":"pith_short_8","alias_value":"CRSGINJW","created_at":"2026-07-05T11:07:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:CRSGINJW7DZ3CGQHKYTHD65VGH","target":"record","payload":{"canonical_record":{"source":{"id":"2505.17193","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-22T18:03:55Z","cross_cats_sorted":[],"title_canon_sha256":"a69f9970c575789f9e1c8ed27a6057b60ca04cfe8d408b9a54116f23d68ffa8a","abstract_canon_sha256":"6582dbe9c305d38dccbce465d1aefe75f0c1228ece27dc435970b8250c95ea62"},"schema_version":"1.0"},"canonical_sha256":"1464643536f8f3b11a07562671fbb531ee4696bacd9be3805efc67b28eb440c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:07:48.473134Z","signature_b64":"kh/WjmDx8C8kCKm9LiYrEsFCm1gSYSEWB0cDhNyVHKme6VDPYzM7Hhg9AGlLOzp15PLS18QrymHfllO+12CgAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1464643536f8f3b11a07562671fbb531ee4696bacd9be3805efc67b28eb440c1","last_reissued_at":"2026-07-05T11:07:48.472617Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:07:48.472617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.17193","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":"2026-07-05T11:07:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2C02cPSOA51Y24UlllYv0T0oFGqFqip1FthsQ9R4F2fHwfK8tG0EcCprIRPgEwkvJQU1p06t9D49lrUiqG00Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T05:59:49.906771Z"},"content_sha256":"e74904e54a302de1c9f0d294f1c04c1456d480ed69b9ea0ad5b6486a58172673","schema_version":"1.0","event_id":"sha256:e74904e54a302de1c9f0d294f1c04c1456d480ed69b9ea0ad5b6486a58172673"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:CRSGINJW7DZ3CGQHKYTHD65VGH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the distinguishing chromatic number in hereditary graph classes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christoph Brause, Ingo Schiemeyer, Monika Pil\\'sniak, Rafa{\\l} Kalinowski","submitted_at":"2025-05-22T18:03:55Z","abstract_excerpt":"The distinguishing chromatic number of a graph $G$, denoted $\\chi_D(G)$, is the minimum number of colours in a proper vertex colouring of $G$ that is preserved by the identity automorphism only. Collins and Trenk proved that $\\chi_D(G)\\le 2\\Delta(G)$ for any connected graph $G$, and the equality holds for complete balanced bipartite graphs $K_{p,p}$ and for $C_6$. In this paper, we show that the upper bound on $\\chi_D(G)$ can be substantially reduced if we forbid some small graphs as induced subgraphs of $G$, that is, we study the distinguishing chromatic number in some hereditary graph classe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.17193","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/2505.17193/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":"2026-07-05T11:07:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2pAbnbdFBMf27lbHcsaOKqygd/iEzKnVY+bMZPcwECW0DBc/jvSb/YEa4KfusYEKyaCyYIOS7HZFu5M+RgUTBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T05:59:49.907142Z"},"content_sha256":"8e2dc363079fcd639a74554ed6921a71dafa3aace9238cbe3624c5bf6fbe3b06","schema_version":"1.0","event_id":"sha256:8e2dc363079fcd639a74554ed6921a71dafa3aace9238cbe3624c5bf6fbe3b06"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CRSGINJW7DZ3CGQHKYTHD65VGH/bundle.json","state_url":"https://pith.science/pith/CRSGINJW7DZ3CGQHKYTHD65VGH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CRSGINJW7DZ3CGQHKYTHD65VGH/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":"2026-08-20T05:59:49Z","links":{"resolver":"https://pith.science/pith/CRSGINJW7DZ3CGQHKYTHD65VGH","bundle":"https://pith.science/pith/CRSGINJW7DZ3CGQHKYTHD65VGH/bundle.json","state":"https://pith.science/pith/CRSGINJW7DZ3CGQHKYTHD65VGH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CRSGINJW7DZ3CGQHKYTHD65VGH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CRSGINJW7DZ3CGQHKYTHD65VGH","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":"6582dbe9c305d38dccbce465d1aefe75f0c1228ece27dc435970b8250c95ea62","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-22T18:03:55Z","title_canon_sha256":"a69f9970c575789f9e1c8ed27a6057b60ca04cfe8d408b9a54116f23d68ffa8a"},"schema_version":"1.0","source":{"id":"2505.17193","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.17193","created_at":"2026-07-05T11:07:48Z"},{"alias_kind":"arxiv_version","alias_value":"2505.17193v1","created_at":"2026-07-05T11:07:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.17193","created_at":"2026-07-05T11:07:48Z"},{"alias_kind":"pith_short_12","alias_value":"CRSGINJW7DZ3","created_at":"2026-07-05T11:07:48Z"},{"alias_kind":"pith_short_16","alias_value":"CRSGINJW7DZ3CGQH","created_at":"2026-07-05T11:07:48Z"},{"alias_kind":"pith_short_8","alias_value":"CRSGINJW","created_at":"2026-07-05T11:07:48Z"}],"graph_snapshots":[{"event_id":"sha256:8e2dc363079fcd639a74554ed6921a71dafa3aace9238cbe3624c5bf6fbe3b06","target":"graph","created_at":"2026-07-05T11:07:48Z","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/2505.17193/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The distinguishing chromatic number of a graph $G$, denoted $\\chi_D(G)$, is the minimum number of colours in a proper vertex colouring of $G$ that is preserved by the identity automorphism only. Collins and Trenk proved that $\\chi_D(G)\\le 2\\Delta(G)$ for any connected graph $G$, and the equality holds for complete balanced bipartite graphs $K_{p,p}$ and for $C_6$. In this paper, we show that the upper bound on $\\chi_D(G)$ can be substantially reduced if we forbid some small graphs as induced subgraphs of $G$, that is, we study the distinguishing chromatic number in some hereditary graph classe","authors_text":"Christoph Brause, Ingo Schiemeyer, Monika Pil\\'sniak, Rafa{\\l} Kalinowski","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-22T18:03:55Z","title":"On the distinguishing chromatic number in hereditary graph classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.17193","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:e74904e54a302de1c9f0d294f1c04c1456d480ed69b9ea0ad5b6486a58172673","target":"record","created_at":"2026-07-05T11:07:48Z","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":"6582dbe9c305d38dccbce465d1aefe75f0c1228ece27dc435970b8250c95ea62","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-05-22T18:03:55Z","title_canon_sha256":"a69f9970c575789f9e1c8ed27a6057b60ca04cfe8d408b9a54116f23d68ffa8a"},"schema_version":"1.0","source":{"id":"2505.17193","kind":"arxiv","version":1}},"canonical_sha256":"1464643536f8f3b11a07562671fbb531ee4696bacd9be3805efc67b28eb440c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1464643536f8f3b11a07562671fbb531ee4696bacd9be3805efc67b28eb440c1","first_computed_at":"2026-07-05T11:07:48.472617Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:07:48.472617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kh/WjmDx8C8kCKm9LiYrEsFCm1gSYSEWB0cDhNyVHKme6VDPYzM7Hhg9AGlLOzp15PLS18QrymHfllO+12CgAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:07:48.473134Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.17193","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e74904e54a302de1c9f0d294f1c04c1456d480ed69b9ea0ad5b6486a58172673","sha256:8e2dc363079fcd639a74554ed6921a71dafa3aace9238cbe3624c5bf6fbe3b06"],"state_sha256":"2735da04d9a10cf53d7b5ae81993f406ca02917971caa51c9b0cffb4b44eff9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c+HbKHrIU2h8GqfhJxVcIF013kkcLUt02CaZ4NZUZujW3vpQgDVoVHBhEtCV+/auuHF7xL5/LfD+/F3L2Ek3Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T05:59:49.910575Z","bundle_sha256":"634cd11a98e0788eea51357bf645be3f8d8b516257a479a51688c22faa3b7b6c"}}