{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:G3W7VFZFMR7IZSNTDAJBBIVA7C","short_pith_number":"pith:G3W7VFZF","canonical_record":{"source":{"id":"1606.09389","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-30T08:34:53Z","cross_cats_sorted":[],"title_canon_sha256":"0f5559c0c2d0406c344c49b6864e969f8bcb017ec0112c0135e926d9cd121457","abstract_canon_sha256":"ce660f168cace17afdbcbd48e5fc1dff4710239d629b517b6addc1b33f3aab67"},"schema_version":"1.0"},"canonical_sha256":"36edfa9725647e8cc9b3181210a2a0f8ac43fdedc00c7a12ba9b888b69be51f7","source":{"kind":"arxiv","id":"1606.09389","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:G3W7VFZFMR7IZSNTDAJBBIVA7C","target":"record","payload":{"canonical_record":{"source":{"id":"1606.09389","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-30T08:34:53Z","cross_cats_sorted":[],"title_canon_sha256":"0f5559c0c2d0406c344c49b6864e969f8bcb017ec0112c0135e926d9cd121457","abstract_canon_sha256":"ce660f168cace17afdbcbd48e5fc1dff4710239d629b517b6addc1b33f3aab67"},"schema_version":"1.0"},"canonical_sha256":"36edfa9725647e8cc9b3181210a2a0f8ac43fdedc00c7a12ba9b888b69be51f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:42.929770Z","signature_b64":"UGeTlTJyRgGAaynSSpdkJfXqJgX8L0f6y9rLDxkloAW2DRaciAecykCjSqu1hbbm6CSplMitFkgoY1uOsg9oDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36edfa9725647e8cc9b3181210a2a0f8ac43fdedc00c7a12ba9b888b69be51f7","last_reissued_at":"2026-05-18T00:47:42.929062Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:42.929062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.09389","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:47:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ev0Tl77hfrBfb9WPcyYY0tin3mz26F/lZgH32Y3l9zPYP4kDUykVp22GfcHV2tOpFRF3nwhFFYU3eOAJl9TiBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:37:51.045829Z"},"content_sha256":"3ad573aa5599a544f166d8d624cf0dab9e4d7ae57574e2e64722ab273b9d5180","schema_version":"1.0","event_id":"sha256:3ad573aa5599a544f166d8d624cf0dab9e4d7ae57574e2e64722ab273b9d5180"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:G3W7VFZFMR7IZSNTDAJBBIVA7C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some Results on Cyclic Interval Edge Colorings of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Armen S. Asratian, Carl Johan Casselgren, Petros A. Petrosyan","submitted_at":"2016-06-30T08:34:53Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.09389","kind":"arxiv","version":2},"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":"2026-05-18T00:47:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E0MVreiI82KEpHOP5+Y6kyzo9P4jpkK63L+eFSC3KAjSlLYn8EVHM5qGCE9i864tDfqZVFZGo5QvE54BtusADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:37:51.046565Z"},"content_sha256":"b0878ffc044727db8a426db2a0ab4d42f23940c6237e351eaa7f957a0ed0db46","schema_version":"1.0","event_id":"sha256:b0878ffc044727db8a426db2a0ab4d42f23940c6237e351eaa7f957a0ed0db46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G3W7VFZFMR7IZSNTDAJBBIVA7C/bundle.json","state_url":"https://pith.science/pith/G3W7VFZFMR7IZSNTDAJBBIVA7C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G3W7VFZFMR7IZSNTDAJBBIVA7C/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":"2026-06-06T16:37:51Z","links":{"resolver":"https://pith.science/pith/G3W7VFZFMR7IZSNTDAJBBIVA7C","bundle":"https://pith.science/pith/G3W7VFZFMR7IZSNTDAJBBIVA7C/bundle.json","state":"https://pith.science/pith/G3W7VFZFMR7IZSNTDAJBBIVA7C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G3W7VFZFMR7IZSNTDAJBBIVA7C/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GlJenxLmsF8Y18lDR8GW03twxrVpoEWUMJSV+1slcJ/BXM3vdGxqx5j4GsS8Ow2wW35JMn728lqCBOb71SDnBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:37:51.050106Z","bundle_sha256":"dd7e129dbc2301d136d262e2f122bab747693483e28958846a7838112a178185"}}