{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:77QYB4JAZLX3HG4XRTNTXTMH3P","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":"992bc509c84d9b7374a8b933a0797749876b1fbec560a8451b26eaec139c5c9c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-23T14:23:48Z","title_canon_sha256":"625140d48176d4b56f48d02224a39beba0ff5d343dc38d507cdaffc92755623a"},"schema_version":"1.0","source":{"id":"1602.07163","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07163","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07163v3","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07163","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"77QYB4JAZLX3","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"77QYB4JAZLX3HG4X","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"77QYB4JA","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:5f05af293e46ae28348718379bf8ad62b3149f294d0cb75eeb66c72605d14370","target":"graph","created_at":"2026-05-18T01:18:13Z","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":"A path in an edge-colored graph is called proper if no two consecutive edges of the path receive the same color. For a connected graph $G$, the proper connection number $pc(G)$ of $G$ is defined as the minimum number of colors needed to color its edges so that every pair of distinct vertices of $G$ are connected by at least one proper path in $G$. In this paper, we consider two conjectures on the proper connection number of graphs. The first conjecture states that if $G$ is a noncomplete graph with connectivity $\\kappa(G) = 2$ and minimum degree $\\delta(G)\\ge 3$, then $pc(G) = 2$, posed by Bor","authors_text":"Colton Magnant, Fei Huang, Kenta Ozeki, Xueliang Li, Zhongmei Qin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-23T14:23:48Z","title":"On two conjectures about the proper connection number of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07163","kind":"arxiv","version":3},"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":"sha256:88683be15ed1f6400af1921536c031ac93b7b36e3159c2e0e4fb8abc65b6b4fd","target":"record","created_at":"2026-05-18T01:18:13Z","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":"992bc509c84d9b7374a8b933a0797749876b1fbec560a8451b26eaec139c5c9c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-23T14:23:48Z","title_canon_sha256":"625140d48176d4b56f48d02224a39beba0ff5d343dc38d507cdaffc92755623a"},"schema_version":"1.0","source":{"id":"1602.07163","kind":"arxiv","version":3}},"canonical_sha256":"ffe180f120caefb39b978cdb3bcd87dbeae806dfb6018394849ebecc45c7f70e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffe180f120caefb39b978cdb3bcd87dbeae806dfb6018394849ebecc45c7f70e","first_computed_at":"2026-05-18T01:18:13.759219Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:13.759219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o8N/2wwgQL5rBz6RGSzzvS4gXNKGqlHwJtTScTzV7hb8tMQNUwUA8OYKbZWc5Xb6chJC/MQzgYSVTPV6KOKpAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:13.759883Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.07163","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88683be15ed1f6400af1921536c031ac93b7b36e3159c2e0e4fb8abc65b6b4fd","sha256:5f05af293e46ae28348718379bf8ad62b3149f294d0cb75eeb66c72605d14370"],"state_sha256":"701f2e42c73fbd5df2a6f91461e615ec3314fea81de59989a0c360433914f273"}