{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:AU7WES5N44BE4LGTHGGRPOSLOI","short_pith_number":"pith:AU7WES5N","canonical_record":{"source":{"id":"1803.07450","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-20T14:24:02Z","cross_cats_sorted":[],"title_canon_sha256":"7667c0ee7de672c302f0b06524c3a32715592f94671240f582209cd23ba50bec","abstract_canon_sha256":"2d44c4d55d9f02f1014f3d5692fc5ba62ea0f6ed7f0917c5c9af9f6a1a225231"},"schema_version":"1.0"},"canonical_sha256":"053f624bade7024e2cd3398d17ba4b721af1be9f782c9b7a5aeaf270b7e63731","source":{"kind":"arxiv","id":"1803.07450","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07450","created_at":"2026-05-18T00:20:33Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07450v1","created_at":"2026-05-18T00:20:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07450","created_at":"2026-05-18T00:20:33Z"},{"alias_kind":"pith_short_12","alias_value":"AU7WES5N44BE","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AU7WES5N44BE4LGT","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AU7WES5N","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:AU7WES5N44BE4LGTHGGRPOSLOI","target":"record","payload":{"canonical_record":{"source":{"id":"1803.07450","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-20T14:24:02Z","cross_cats_sorted":[],"title_canon_sha256":"7667c0ee7de672c302f0b06524c3a32715592f94671240f582209cd23ba50bec","abstract_canon_sha256":"2d44c4d55d9f02f1014f3d5692fc5ba62ea0f6ed7f0917c5c9af9f6a1a225231"},"schema_version":"1.0"},"canonical_sha256":"053f624bade7024e2cd3398d17ba4b721af1be9f782c9b7a5aeaf270b7e63731","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:33.148002Z","signature_b64":"wOxuGk/6EKVM5wkl1FE0rDWJUC3f8ZtgB5MjaAkt4DtwzGw9/YkshJNB69kIYqIeizGHmP+HYS/90ACA5/L8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"053f624bade7024e2cd3398d17ba4b721af1be9f782c9b7a5aeaf270b7e63731","last_reissued_at":"2026-05-18T00:20:33.147426Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:33.147426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.07450","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":"2026-05-18T00:20:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hkENJ8ASXg7SPfdzS+PYfyy5yPFaeDB80E+xqiTzEp7Nxpnh/RclgpsuFXKT9bDsCSb9+4HEdN6mKelzX9BqBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:37:47.422988Z"},"content_sha256":"eadba2c0339b6e0b95fc1635b876b473c4e0cd11394c941590ed8d66326a94b1","schema_version":"1.0","event_id":"sha256:eadba2c0339b6e0b95fc1635b876b473c4e0cd11394c941590ed8d66326a94b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:AU7WES5N44BE4LGTHGGRPOSLOI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Total Equitable List Coloring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hemanshu Kaul, Jeffrey A. Mudrock, Michael J. Pelsmajer","submitted_at":"2018-03-20T14:24:02Z","abstract_excerpt":"An equitable coloring is a proper coloring of a graph such that the sizes of the color classes differ by at most one. A graph $G$ is equitably $k$-colorable if there exists an equitable coloring of $G$ which uses $k$ colors, each one appearing on either $\\lfloor |V(G)|/k \\rfloor$ or $\\lceil |V(G)|/k \\rceil$ vertices of $G$. In 1994, Fu conjectured that for any simple graph $G$, the total graph of $G$, $T(G)$, is equitably $k$-colorable whenever $k \\geq \\max\\{\\chi(T(G)), \\Delta(G)+2\\}$ where $\\chi(T(G))$ is the chromatic number of the total graph of $G$ and $\\Delta(G)$ is the maximum degree of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07450","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":""},"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":"2026-05-18T00:20:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ToKC8E13lrfdLNHGC2TCjG1I6LI03IHhXOhnLtBq2KNRxeJ7JzH/rFSrH06qmsL1qTd4mLa4ra332oGqULYQAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:37:47.423347Z"},"content_sha256":"7da031848e7a3076b4de82f8a39cdb74b18304fad99d947590c317d6a7d239c6","schema_version":"1.0","event_id":"sha256:7da031848e7a3076b4de82f8a39cdb74b18304fad99d947590c317d6a7d239c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AU7WES5N44BE4LGTHGGRPOSLOI/bundle.json","state_url":"https://pith.science/pith/AU7WES5N44BE4LGTHGGRPOSLOI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AU7WES5N44BE4LGTHGGRPOSLOI/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":"2026-06-03T03:37:47Z","links":{"resolver":"https://pith.science/pith/AU7WES5N44BE4LGTHGGRPOSLOI","bundle":"https://pith.science/pith/AU7WES5N44BE4LGTHGGRPOSLOI/bundle.json","state":"https://pith.science/pith/AU7WES5N44BE4LGTHGGRPOSLOI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AU7WES5N44BE4LGTHGGRPOSLOI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AU7WES5N44BE4LGTHGGRPOSLOI","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":"2d44c4d55d9f02f1014f3d5692fc5ba62ea0f6ed7f0917c5c9af9f6a1a225231","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-20T14:24:02Z","title_canon_sha256":"7667c0ee7de672c302f0b06524c3a32715592f94671240f582209cd23ba50bec"},"schema_version":"1.0","source":{"id":"1803.07450","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07450","created_at":"2026-05-18T00:20:33Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07450v1","created_at":"2026-05-18T00:20:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07450","created_at":"2026-05-18T00:20:33Z"},{"alias_kind":"pith_short_12","alias_value":"AU7WES5N44BE","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AU7WES5N44BE4LGT","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AU7WES5N","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:7da031848e7a3076b4de82f8a39cdb74b18304fad99d947590c317d6a7d239c6","target":"graph","created_at":"2026-05-18T00:20:33Z","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"},"paper":{"abstract_excerpt":"An equitable coloring is a proper coloring of a graph such that the sizes of the color classes differ by at most one. A graph $G$ is equitably $k$-colorable if there exists an equitable coloring of $G$ which uses $k$ colors, each one appearing on either $\\lfloor |V(G)|/k \\rfloor$ or $\\lceil |V(G)|/k \\rceil$ vertices of $G$. In 1994, Fu conjectured that for any simple graph $G$, the total graph of $G$, $T(G)$, is equitably $k$-colorable whenever $k \\geq \\max\\{\\chi(T(G)), \\Delta(G)+2\\}$ where $\\chi(T(G))$ is the chromatic number of the total graph of $G$ and $\\Delta(G)$ is the maximum degree of ","authors_text":"Hemanshu Kaul, Jeffrey A. Mudrock, Michael J. Pelsmajer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-20T14:24:02Z","title":"Total Equitable List Coloring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07450","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:eadba2c0339b6e0b95fc1635b876b473c4e0cd11394c941590ed8d66326a94b1","target":"record","created_at":"2026-05-18T00:20:33Z","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":"2d44c4d55d9f02f1014f3d5692fc5ba62ea0f6ed7f0917c5c9af9f6a1a225231","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-20T14:24:02Z","title_canon_sha256":"7667c0ee7de672c302f0b06524c3a32715592f94671240f582209cd23ba50bec"},"schema_version":"1.0","source":{"id":"1803.07450","kind":"arxiv","version":1}},"canonical_sha256":"053f624bade7024e2cd3398d17ba4b721af1be9f782c9b7a5aeaf270b7e63731","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"053f624bade7024e2cd3398d17ba4b721af1be9f782c9b7a5aeaf270b7e63731","first_computed_at":"2026-05-18T00:20:33.147426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:33.147426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wOxuGk/6EKVM5wkl1FE0rDWJUC3f8ZtgB5MjaAkt4DtwzGw9/YkshJNB69kIYqIeizGHmP+HYS/90ACA5/L8DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:33.148002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.07450","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eadba2c0339b6e0b95fc1635b876b473c4e0cd11394c941590ed8d66326a94b1","sha256:7da031848e7a3076b4de82f8a39cdb74b18304fad99d947590c317d6a7d239c6"],"state_sha256":"66be70ebd282e79c290a7652e73e4fd77b451dd52721fbfe335ae13fd8eb101b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bxYgTSIMMGyHQipBU6gjnYMAL7u5GlBZPEa/KVkGqZHsjQfIeXYpB6XZ5SiU5ZjyEPjUp5h9qYf+knsoqx1GBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T03:37:47.425236Z","bundle_sha256":"935592a08617cb81bd271c9b627d8cf028d6ddc2cd289ef0011d03abdc297ea1"}}