{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YSMCBLCM5F5Z7HS4H5WDMMQJGC","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":"ab377b8dfe126aea85811367736050eab3c83ed57a9f5da011962243dd501129","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-19T11:56:48Z","title_canon_sha256":"d9f04a4be2650a5b3b586c9a2a0cf7b981d0cae1064c0b291679b87f88109fbd"},"schema_version":"1.0","source":{"id":"1608.05577","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05577","created_at":"2026-05-18T01:08:28Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05577v1","created_at":"2026-05-18T01:08:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05577","created_at":"2026-05-18T01:08:28Z"},{"alias_kind":"pith_short_12","alias_value":"YSMCBLCM5F5Z","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YSMCBLCM5F5Z7HS4","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YSMCBLCM","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:03df603da0a6407b4e618f3cab6eba5483f0d03d2c3c31d8e12bed07bd23f73e","target":"graph","created_at":"2026-05-18T01:08:28Z","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":"The packing chromatic number $\\chi_{\\rho}(G)$ of a graph $G$ is the smallest integer $k$ such that there exists a $k$-vertex coloring of $G$ in which any two vertices receiving color $i$ are at distance at least $i+1$. It is proved that in the class of subcubic graphs the packing chromatic number is bigger than $13$, thus answering an open problem from [Gastineau, Togni, $S$-packing colorings of cubic graphs, Discrete Math.\\ 339 (2016) 2461--2470]. In addition, the packing chromatic number is investigated with respect to several local operations. In particular, if $S_e(G)$ is the graph obtaine","authors_text":"Bo\\v{s}tjan Bre\\v{s}ar, Douglas F. Rall, Kirsti Wash, Sandi Klav\\v{z}ar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-19T11:56:48Z","title":"Packing chromatic number under local changes in a graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05577","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":"sha256:96b5fedc3cf61a41df304bf70a10e1cd64808064e36a6341d1c4100e0dcc6533","target":"record","created_at":"2026-05-18T01:08:28Z","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":"ab377b8dfe126aea85811367736050eab3c83ed57a9f5da011962243dd501129","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-19T11:56:48Z","title_canon_sha256":"d9f04a4be2650a5b3b586c9a2a0cf7b981d0cae1064c0b291679b87f88109fbd"},"schema_version":"1.0","source":{"id":"1608.05577","kind":"arxiv","version":1}},"canonical_sha256":"c49820ac4ce97b9f9e5c3f6c363209309b836a7b197cb9ddebb097689812eed9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c49820ac4ce97b9f9e5c3f6c363209309b836a7b197cb9ddebb097689812eed9","first_computed_at":"2026-05-18T01:08:28.133913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:28.133913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bEX8I+g0Ap3SEuril6zLodJu83YM7TSCGYH2Az/D1nBsbI2up58OAIRcvOEjLecvG4s7Vv9/hfafYiOBIDYWCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:28.134580Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.05577","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96b5fedc3cf61a41df304bf70a10e1cd64808064e36a6341d1c4100e0dcc6533","sha256:03df603da0a6407b4e618f3cab6eba5483f0d03d2c3c31d8e12bed07bd23f73e"],"state_sha256":"ff6662458ee6c95e4aaa1b02d4c58290b08b201a80b1a94061d0b5b73800d1b0"}