{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:AIGRWCZDA5MOB5N6TARQSITOAM","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":"77a71a6454e5bf9c1973ba03dcad3a8fe8745e45f2bf3dd8d4c671e8e973f7da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-29T04:22:55Z","title_canon_sha256":"d79ae98b698a2f326dcd6c69076b434bdb8d589d55db044aebca1a4f516d1b4a"},"schema_version":"1.0","source":{"id":"2411.19462","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.19462","created_at":"2026-07-05T09:42:02Z"},{"alias_kind":"arxiv_version","alias_value":"2411.19462v1","created_at":"2026-07-05T09:42:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.19462","created_at":"2026-07-05T09:42:02Z"},{"alias_kind":"pith_short_12","alias_value":"AIGRWCZDA5MO","created_at":"2026-07-05T09:42:02Z"},{"alias_kind":"pith_short_16","alias_value":"AIGRWCZDA5MOB5N6","created_at":"2026-07-05T09:42:02Z"},{"alias_kind":"pith_short_8","alias_value":"AIGRWCZD","created_at":"2026-07-05T09:42:02Z"}],"graph_snapshots":[{"event_id":"sha256:563827190954cd1e62ef256781827163bc61d1f64271b4c2bb244453d4e0bb6c","target":"graph","created_at":"2026-07-05T09:42:02Z","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/2411.19462/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the paintability, an on-line version of choosability, of complete multipartite graphs. We do this by considering an equivalent chip game introduced by Duraj, Gutowski, and Kozik. We consider complete multipartite graphs with $ n $ parts of size at most 3. Using a computational approach, we establish upper bounds on the paintability of such graphs for small values of $ n. $\n  The choosability of complete multipartite graphs is closely related to value $ p(n, m) $, the minimum number of edges in a $n$-uniform hypergraph with no panchromatic $m$-coloring. We consider an online variant of","authors_text":"Amit Krishnaiyer, Arvind Murty, Atlas Chen, Braden Dean, Grace McCourt, Peter Bradshaw, Ramon I. Garcia, Siyu Gan, Tianyue Cao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-29T04:22:55Z","title":"Chip games and multipartite graph paintability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.19462","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:e9872031fbec1e13e642985fb759898912a23817450619367fdea66e327c94f7","target":"record","created_at":"2026-07-05T09:42:02Z","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":"77a71a6454e5bf9c1973ba03dcad3a8fe8745e45f2bf3dd8d4c671e8e973f7da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-29T04:22:55Z","title_canon_sha256":"d79ae98b698a2f326dcd6c69076b434bdb8d589d55db044aebca1a4f516d1b4a"},"schema_version":"1.0","source":{"id":"2411.19462","kind":"arxiv","version":1}},"canonical_sha256":"020d1b0b230758e0f5be982309226e031167d7710da75d0c5baabfc4e783e633","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"020d1b0b230758e0f5be982309226e031167d7710da75d0c5baabfc4e783e633","first_computed_at":"2026-07-05T09:42:02.872286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:42:02.872286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i+Mn419Sli6MiRa7IwsIRTNxtpzgFokdyhlSTuteAGQIGTYequ/GP31dkp+/HfiskQNs6vCauA7NgYOj1WV1BA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:42:02.872919Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.19462","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9872031fbec1e13e642985fb759898912a23817450619367fdea66e327c94f7","sha256:563827190954cd1e62ef256781827163bc61d1f64271b4c2bb244453d4e0bb6c"],"state_sha256":"ff9f7d4495ec8f3a27f1e4dda54a674d4f30855c60f6a81c88d0b97e343bd022"}