{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6D4AEW3AOXJCXNBOPNZIDO4TIR","short_pith_number":"pith:6D4AEW3A","canonical_record":{"source":{"id":"1806.06966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-18T22:10:24Z","cross_cats_sorted":[],"title_canon_sha256":"fbb07d79730750b3cf09200825dab09e8a34b65c00da5a2b124a67d0667d1ada","abstract_canon_sha256":"0a64ca700aae8693718bc689df420779bf269e001a6c8301828c8aa5479a1834"},"schema_version":"1.0"},"canonical_sha256":"f0f8025b6075d22bb42e7b7281bb9344537aa9ff0d20d270bb0d72d3b7a46187","source":{"kind":"arxiv","id":"1806.06966","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.06966","created_at":"2026-05-18T00:12:57Z"},{"alias_kind":"arxiv_version","alias_value":"1806.06966v1","created_at":"2026-05-18T00:12:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06966","created_at":"2026-05-18T00:12:57Z"},{"alias_kind":"pith_short_12","alias_value":"6D4AEW3AOXJC","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6D4AEW3AOXJCXNBO","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6D4AEW3A","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6D4AEW3AOXJCXNBOPNZIDO4TIR","target":"record","payload":{"canonical_record":{"source":{"id":"1806.06966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-18T22:10:24Z","cross_cats_sorted":[],"title_canon_sha256":"fbb07d79730750b3cf09200825dab09e8a34b65c00da5a2b124a67d0667d1ada","abstract_canon_sha256":"0a64ca700aae8693718bc689df420779bf269e001a6c8301828c8aa5479a1834"},"schema_version":"1.0"},"canonical_sha256":"f0f8025b6075d22bb42e7b7281bb9344537aa9ff0d20d270bb0d72d3b7a46187","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:57.928963Z","signature_b64":"vl31nkYy9m/5MCM/BJgYN31rAtnhUzpFCjyUTewsI9cDmPV76H0JW0jj/M+De1iqwHT6jhU8Jno/dWf72SFBCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0f8025b6075d22bb42e7b7281bb9344537aa9ff0d20d270bb0d72d3b7a46187","last_reissued_at":"2026-05-18T00:12:57.928402Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:57.928402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.06966","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":"2026-05-18T00:12:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6FTyMVFv1vo75wWAbIdWyLX6JpyK9NfPhQ6C/YX23/c7vCtiKSrRY62eWTTvHms/yEJVxEThan+0f4NpDC51Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:18:36.777886Z"},"content_sha256":"13f59dab5c928ddb55ef44ff1e064c2af4223d46ca7ac0ff0027a034bfa23006","schema_version":"1.0","event_id":"sha256:13f59dab5c928ddb55ef44ff1e064c2af4223d46ca7ac0ff0027a034bfa23006"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6D4AEW3AOXJCXNBOPNZIDO4TIR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Proportional Choosability: A New List Analogue of Equitable Coloring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Benjamin Reiniger, Hemanshu Kaul, Jeffrey A. Mudrock, Michael J. Pelsmajer","submitted_at":"2018-06-18T22:10:24Z","abstract_excerpt":"In 2003, Kostochka, Pelsmajer, and West introduced a list analogue of equitable coloring called equitable choosability. In this paper, we motivate and define a new list analogue of equitable coloring called proportional choosability. A $k$-assignment $L$ for a graph $G$ specifies a list $L(v)$ of $k$ available colors for each vertex $v$ of $G$. An $L$-coloring assigns a color to each vertex $v$ from its list $L(v)$. For each color $c$, let $\\eta(c)$ be the number of vertices $v$ whose list $L(v)$ contains $c$. A proportional $L$-coloring of $G$ is a proper $L$-coloring in which each color $c \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06966","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":"2026-05-18T00:12:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XkPr+nY0iHCnDEt5cf42fMYPMWIrecYL3SkxdogLie9YbUSmC+WHupVkrI28QZWFsHcIblde2u73AGhblgJTBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:18:36.778235Z"},"content_sha256":"bc3cf9513580d071b1bfa4fc9025ae4ceaf509961d057c4897cfe23767701902","schema_version":"1.0","event_id":"sha256:bc3cf9513580d071b1bfa4fc9025ae4ceaf509961d057c4897cfe23767701902"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6D4AEW3AOXJCXNBOPNZIDO4TIR/bundle.json","state_url":"https://pith.science/pith/6D4AEW3AOXJCXNBOPNZIDO4TIR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6D4AEW3AOXJCXNBOPNZIDO4TIR/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":"2026-06-02T12:18:36Z","links":{"resolver":"https://pith.science/pith/6D4AEW3AOXJCXNBOPNZIDO4TIR","bundle":"https://pith.science/pith/6D4AEW3AOXJCXNBOPNZIDO4TIR/bundle.json","state":"https://pith.science/pith/6D4AEW3AOXJCXNBOPNZIDO4TIR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6D4AEW3AOXJCXNBOPNZIDO4TIR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6D4AEW3AOXJCXNBOPNZIDO4TIR","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":"0a64ca700aae8693718bc689df420779bf269e001a6c8301828c8aa5479a1834","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-18T22:10:24Z","title_canon_sha256":"fbb07d79730750b3cf09200825dab09e8a34b65c00da5a2b124a67d0667d1ada"},"schema_version":"1.0","source":{"id":"1806.06966","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.06966","created_at":"2026-05-18T00:12:57Z"},{"alias_kind":"arxiv_version","alias_value":"1806.06966v1","created_at":"2026-05-18T00:12:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06966","created_at":"2026-05-18T00:12:57Z"},{"alias_kind":"pith_short_12","alias_value":"6D4AEW3AOXJC","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6D4AEW3AOXJCXNBO","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6D4AEW3A","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:bc3cf9513580d071b1bfa4fc9025ae4ceaf509961d057c4897cfe23767701902","target":"graph","created_at":"2026-05-18T00:12:57Z","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":"In 2003, Kostochka, Pelsmajer, and West introduced a list analogue of equitable coloring called equitable choosability. In this paper, we motivate and define a new list analogue of equitable coloring called proportional choosability. A $k$-assignment $L$ for a graph $G$ specifies a list $L(v)$ of $k$ available colors for each vertex $v$ of $G$. An $L$-coloring assigns a color to each vertex $v$ from its list $L(v)$. For each color $c$, let $\\eta(c)$ be the number of vertices $v$ whose list $L(v)$ contains $c$. A proportional $L$-coloring of $G$ is a proper $L$-coloring in which each color $c \\","authors_text":"Benjamin Reiniger, 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":"2018-06-18T22:10:24Z","title":"Proportional Choosability: A New List Analogue of Equitable Coloring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06966","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":"sha256:13f59dab5c928ddb55ef44ff1e064c2af4223d46ca7ac0ff0027a034bfa23006","target":"record","created_at":"2026-05-18T00:12:57Z","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":"0a64ca700aae8693718bc689df420779bf269e001a6c8301828c8aa5479a1834","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-18T22:10:24Z","title_canon_sha256":"fbb07d79730750b3cf09200825dab09e8a34b65c00da5a2b124a67d0667d1ada"},"schema_version":"1.0","source":{"id":"1806.06966","kind":"arxiv","version":1}},"canonical_sha256":"f0f8025b6075d22bb42e7b7281bb9344537aa9ff0d20d270bb0d72d3b7a46187","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0f8025b6075d22bb42e7b7281bb9344537aa9ff0d20d270bb0d72d3b7a46187","first_computed_at":"2026-05-18T00:12:57.928402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:57.928402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vl31nkYy9m/5MCM/BJgYN31rAtnhUzpFCjyUTewsI9cDmPV76H0JW0jj/M+De1iqwHT6jhU8Jno/dWf72SFBCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:57.928963Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.06966","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13f59dab5c928ddb55ef44ff1e064c2af4223d46ca7ac0ff0027a034bfa23006","sha256:bc3cf9513580d071b1bfa4fc9025ae4ceaf509961d057c4897cfe23767701902"],"state_sha256":"055083309654e42e38f930f3461d507a124fd91a5039ebb74fb9720c17b1127c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h4ILaVgGdn5+ENu34MF/dKVOQUDce1T1q7diZ8jUUrRv/Urj10TtpzSQr1qt5UDGT34SliufkmG5vsPjlhRlDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T12:18:36.780149Z","bundle_sha256":"96de8163821a572ea0a030ab81e08ef15c67e1ef4683f41ae504072216937193"}}