{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:G3W7VFZFMR7IZSNTDAJBBIVA7C","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":"ce660f168cace17afdbcbd48e5fc1dff4710239d629b517b6addc1b33f3aab67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-30T08:34:53Z","title_canon_sha256":"0f5559c0c2d0406c344c49b6864e969f8bcb017ec0112c0135e926d9cd121457"},"schema_version":"1.0","source":{"id":"1606.09389","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.09389","created_at":"2026-05-18T00:47:42Z"},{"alias_kind":"arxiv_version","alias_value":"1606.09389v2","created_at":"2026-05-18T00:47:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.09389","created_at":"2026-05-18T00:47:42Z"},{"alias_kind":"pith_short_12","alias_value":"G3W7VFZFMR7I","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"G3W7VFZFMR7IZSNT","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"G3W7VFZF","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:b0878ffc044727db8a426db2a0ab4d42f23940c6237e351eaa7f957a0ed0db46","target":"graph","created_at":"2026-05-18T00:47:42Z","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 proper edge coloring of a graph $G$ with colors $1,2,\\dots,t$ is called a \\emph{cyclic interval $t$-coloring} if for each vertex $v$ of $G$ the edges incident to $v$ are colored by consecutive colors, under the condition that color $1$ is considered as consecutive to color $t$. We prove that a bipartite graph $G$ with even maximum degree $\\Delta(G)\\geq 4$ admits a cyclic interval $\\Delta(G)$-coloring if for every vertex $v$ the degree $d_G(v)$ satisfies either $d_G(v)\\geq \\Delta(G)-2$ or $d_G(v)\\leq 2$. We also prove that every Eulerian bipartite graph $G$ with maximum degree at most $8$ has","authors_text":"Armen S. Asratian, Carl Johan Casselgren, Petros A. Petrosyan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-30T08:34:53Z","title":"Some Results on Cyclic Interval Edge Colorings of Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.09389","kind":"arxiv","version":2},"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":"sha256:3ad573aa5599a544f166d8d624cf0dab9e4d7ae57574e2e64722ab273b9d5180","target":"record","created_at":"2026-05-18T00:47:42Z","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":"ce660f168cace17afdbcbd48e5fc1dff4710239d629b517b6addc1b33f3aab67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-30T08:34:53Z","title_canon_sha256":"0f5559c0c2d0406c344c49b6864e969f8bcb017ec0112c0135e926d9cd121457"},"schema_version":"1.0","source":{"id":"1606.09389","kind":"arxiv","version":2}},"canonical_sha256":"36edfa9725647e8cc9b3181210a2a0f8ac43fdedc00c7a12ba9b888b69be51f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36edfa9725647e8cc9b3181210a2a0f8ac43fdedc00c7a12ba9b888b69be51f7","first_computed_at":"2026-05-18T00:47:42.929062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:42.929062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UGeTlTJyRgGAaynSSpdkJfXqJgX8L0f6y9rLDxkloAW2DRaciAecykCjSqu1hbbm6CSplMitFkgoY1uOsg9oDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:42.929770Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.09389","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ad573aa5599a544f166d8d624cf0dab9e4d7ae57574e2e64722ab273b9d5180","sha256:b0878ffc044727db8a426db2a0ab4d42f23940c6237e351eaa7f957a0ed0db46"],"state_sha256":"fcd3aa7ccc5da8b3fe5c87fbd9dd108727e47d964c1c26dbd317bbcee39258d7"}