{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RXWEZ6Q7FCDV3NWRAOKCSLDVER","short_pith_number":"pith:RXWEZ6Q7","canonical_record":{"source":{"id":"1705.05317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-15T16:28:00Z","cross_cats_sorted":[],"title_canon_sha256":"d8595eea0398fb46694c6c5df5baa04cd100c1d399592b788f932a7430fe95fe","abstract_canon_sha256":"a43c704efef0f588c51058c029e449576501052978bdab057ed1dfe869bf8f95"},"schema_version":"1.0"},"canonical_sha256":"8dec4cfa1f28875db6d10394292c75245f1eb7a8189aafb5a693265839247753","source":{"kind":"arxiv","id":"1705.05317","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05317","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05317v1","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05317","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"pith_short_12","alias_value":"RXWEZ6Q7FCDV","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"RXWEZ6Q7FCDV3NWR","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"RXWEZ6Q7","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RXWEZ6Q7FCDV3NWRAOKCSLDVER","target":"record","payload":{"canonical_record":{"source":{"id":"1705.05317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-15T16:28:00Z","cross_cats_sorted":[],"title_canon_sha256":"d8595eea0398fb46694c6c5df5baa04cd100c1d399592b788f932a7430fe95fe","abstract_canon_sha256":"a43c704efef0f588c51058c029e449576501052978bdab057ed1dfe869bf8f95"},"schema_version":"1.0"},"canonical_sha256":"8dec4cfa1f28875db6d10394292c75245f1eb7a8189aafb5a693265839247753","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:30.836219Z","signature_b64":"LCehFvUN+XB+vU6drU08esid1cyqLH6CyzDIhqtcM5mIXnYyEmvOpvsPZ+f4twIRENmOBa9dG8PStnvkToi4DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8dec4cfa1f28875db6d10394292c75245f1eb7a8189aafb5a693265839247753","last_reissued_at":"2026-05-18T00:44:30.835698Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:30.835698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.05317","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tyu2UR1jPaTRjaHvLNHJapWsKlpd2DNEOMlyfm/jRUpby02AFSWYczame5eD9A2ISXkNbOscsX4sNFN1OmHhAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T23:13:42.170192Z"},"content_sha256":"b1eee7bc43b9ddc8d375683c0f16f983057d29408c82a75b11d78451c69fa91c","schema_version":"1.0","event_id":"sha256:b1eee7bc43b9ddc8d375683c0f16f983057d29408c82a75b11d78451c69fa91c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RXWEZ6Q7FCDV3NWRAOKCSLDVER","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conflict-free connection numbers of line graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo Deng, Haixing Zhao, Wenjing Li, Xueliang Li, Yaping Mao","submitted_at":"2017-05-15T16:28:00Z","abstract_excerpt":"A path in an edge-colored graph is called \\emph{conflict-free} if it contains at least one color used on exactly one of its edges. An edge-colored graph $G$ is \\emph{conflict-free connected} if for any two distinct vertices of $G$, there is a conflict-free path connecting them. For a connected graph $G$, the \\emph{conflict-free connection number} of $G$, denoted by $cfc(G)$, is defined as the minimum number of colors that are required to make $G$ conflict-free connected. In this paper, we investigate the conflict-free connection numbers of connected claw-free graphs, especially line graphs. We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05317","kind":"arxiv","version":1},"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":"2026-05-18T00:44:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lY7IywYICYiL72SkmYiBSLyWmohN+4/x1fIe7eDL8f+Z36h6M1GCEIx5qlxARD32qNKUgTZZgcuNS/Elh/RmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T23:13:42.170862Z"},"content_sha256":"c1c84b78d8ea069396253276e8a8d10f724eb533c992739e09534281915c1198","schema_version":"1.0","event_id":"sha256:c1c84b78d8ea069396253276e8a8d10f724eb533c992739e09534281915c1198"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RXWEZ6Q7FCDV3NWRAOKCSLDVER/bundle.json","state_url":"https://pith.science/pith/RXWEZ6Q7FCDV3NWRAOKCSLDVER/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RXWEZ6Q7FCDV3NWRAOKCSLDVER/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":"2026-05-18T23:13:42Z","links":{"resolver":"https://pith.science/pith/RXWEZ6Q7FCDV3NWRAOKCSLDVER","bundle":"https://pith.science/pith/RXWEZ6Q7FCDV3NWRAOKCSLDVER/bundle.json","state":"https://pith.science/pith/RXWEZ6Q7FCDV3NWRAOKCSLDVER/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RXWEZ6Q7FCDV3NWRAOKCSLDVER/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RXWEZ6Q7FCDV3NWRAOKCSLDVER","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":"a43c704efef0f588c51058c029e449576501052978bdab057ed1dfe869bf8f95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-15T16:28:00Z","title_canon_sha256":"d8595eea0398fb46694c6c5df5baa04cd100c1d399592b788f932a7430fe95fe"},"schema_version":"1.0","source":{"id":"1705.05317","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05317","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05317v1","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05317","created_at":"2026-05-18T00:44:30Z"},{"alias_kind":"pith_short_12","alias_value":"RXWEZ6Q7FCDV","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"RXWEZ6Q7FCDV3NWR","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"RXWEZ6Q7","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:c1c84b78d8ea069396253276e8a8d10f724eb533c992739e09534281915c1198","target":"graph","created_at":"2026-05-18T00:44:30Z","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 \\emph{conflict-free} if it contains at least one color used on exactly one of its edges. An edge-colored graph $G$ is \\emph{conflict-free connected} if for any two distinct vertices of $G$, there is a conflict-free path connecting them. For a connected graph $G$, the \\emph{conflict-free connection number} of $G$, denoted by $cfc(G)$, is defined as the minimum number of colors that are required to make $G$ conflict-free connected. In this paper, we investigate the conflict-free connection numbers of connected claw-free graphs, especially line graphs. We","authors_text":"Bo Deng, Haixing Zhao, Wenjing Li, Xueliang Li, Yaping Mao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-15T16:28:00Z","title":"Conflict-free connection numbers of line graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05317","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:b1eee7bc43b9ddc8d375683c0f16f983057d29408c82a75b11d78451c69fa91c","target":"record","created_at":"2026-05-18T00:44:30Z","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":"a43c704efef0f588c51058c029e449576501052978bdab057ed1dfe869bf8f95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-15T16:28:00Z","title_canon_sha256":"d8595eea0398fb46694c6c5df5baa04cd100c1d399592b788f932a7430fe95fe"},"schema_version":"1.0","source":{"id":"1705.05317","kind":"arxiv","version":1}},"canonical_sha256":"8dec4cfa1f28875db6d10394292c75245f1eb7a8189aafb5a693265839247753","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8dec4cfa1f28875db6d10394292c75245f1eb7a8189aafb5a693265839247753","first_computed_at":"2026-05-18T00:44:30.835698Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:30.835698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LCehFvUN+XB+vU6drU08esid1cyqLH6CyzDIhqtcM5mIXnYyEmvOpvsPZ+f4twIRENmOBa9dG8PStnvkToi4DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:30.836219Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.05317","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1eee7bc43b9ddc8d375683c0f16f983057d29408c82a75b11d78451c69fa91c","sha256:c1c84b78d8ea069396253276e8a8d10f724eb533c992739e09534281915c1198"],"state_sha256":"9a4cd68f41186293e494498b4dc70ac66719820c679b229ccdfe6dc6440a5c3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+TdcAYw/1VLBEDhs61Q8onsPCYdkyF6R7QRT5/NdZzM2fqtfPSPc7wEmWyxUv1qo3kthu+pwhp9pktsM9lXSAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-18T23:13:42.172957Z","bundle_sha256":"da49ae350d2b9a2d39c6d0b7e5e7809fe033764f831029790d8b04616fc6d204"}}