{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7P2RRMKWA7BCIWPRRV6AONNW5D","short_pith_number":"pith:7P2RRMKW","canonical_record":{"source":{"id":"1712.06711","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-12-18T22:59:41Z","cross_cats_sorted":[],"title_canon_sha256":"7ba38af347d96016c16668088b108f2249fc600e5201b8d320b7daa9dadd6c1a","abstract_canon_sha256":"c205aed07a5cc55b3b001cd6a3b21d81814829034703da8609c504d8e159dd17"},"schema_version":"1.0"},"canonical_sha256":"fbf518b15607c22459f18d7c0735b6e8c8cfb21b2a7e7199ebe43f849e022c2b","source":{"kind":"arxiv","id":"1712.06711","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.06711","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"arxiv_version","alias_value":"1712.06711v3","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06711","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"pith_short_12","alias_value":"7P2RRMKWA7BC","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7P2RRMKWA7BCIWPR","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7P2RRMKW","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7P2RRMKWA7BCIWPRRV6AONNW5D","target":"record","payload":{"canonical_record":{"source":{"id":"1712.06711","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-12-18T22:59:41Z","cross_cats_sorted":[],"title_canon_sha256":"7ba38af347d96016c16668088b108f2249fc600e5201b8d320b7daa9dadd6c1a","abstract_canon_sha256":"c205aed07a5cc55b3b001cd6a3b21d81814829034703da8609c504d8e159dd17"},"schema_version":"1.0"},"canonical_sha256":"fbf518b15607c22459f18d7c0735b6e8c8cfb21b2a7e7199ebe43f849e022c2b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:34.176963Z","signature_b64":"1e9KTCrPesfTun23i4UiFR4G53VZPJGfBeYRSRrOJfEuolE29VL2BYrSrkg2h1o4Zm0OuV06EstXAY0HlLq5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbf518b15607c22459f18d7c0735b6e8c8cfb21b2a7e7199ebe43f849e022c2b","last_reissued_at":"2026-05-18T00:14:34.176250Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:34.176250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.06711","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"puE0z+xgP92uvrWc3P3iPbH1mVRoFa3h5MN00Kp3cAc34HEzsDCkGD0J84ATVadesmCJGHwDt2/bOLckcJodDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:58:11.816486Z"},"content_sha256":"0435a0418b850b6ac75221fe851abc177ac5ed147be07ebab7fd42917063bd48","schema_version":"1.0","event_id":"sha256:0435a0418b850b6ac75221fe851abc177ac5ed147be07ebab7fd42917063bd48"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7P2RRMKWA7BCIWPRRV6AONNW5D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graphical virtual links and a polynomial of signed cyclic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Louis H Kauffman, Qingying Deng, Xian'an Jin","submitted_at":"2017-12-18T22:59:41Z","abstract_excerpt":"For a signed cyclic graph G, we can construct a unique virtual link L by taking the medial construction and convert 4-valent vertices of the medial graph to crossings according to the signs. If a virtual link can occur in this way then we say that the virtual link is graphical. In the article we shall prove that a virtual link L is graphical if and only if it is checkerboard colorable. On the other hand, we introduce a polynomial F[G] for signed cyclic graphs, which is defined via a deletion-marking recursion. We shall establish the relationship between F[G] of a signed cyclic graph G and the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06711","kind":"arxiv","version":3},"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":"2026-05-18T00:14:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rIqP5k0ia6bUOjSRIU9DHumJzc8KAuHVyl1RrYKaB47hIr9AzLseM8Sa5SYGWepZBQlojWOG/Z75dDgmmnLHDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:58:11.817174Z"},"content_sha256":"63facad793f8b593c371d403366a1ef1c992c2781399ae3d0a212bc9c692e0e8","schema_version":"1.0","event_id":"sha256:63facad793f8b593c371d403366a1ef1c992c2781399ae3d0a212bc9c692e0e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7P2RRMKWA7BCIWPRRV6AONNW5D/bundle.json","state_url":"https://pith.science/pith/7P2RRMKWA7BCIWPRRV6AONNW5D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7P2RRMKWA7BCIWPRRV6AONNW5D/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":"2026-06-23T19:58:11Z","links":{"resolver":"https://pith.science/pith/7P2RRMKWA7BCIWPRRV6AONNW5D","bundle":"https://pith.science/pith/7P2RRMKWA7BCIWPRRV6AONNW5D/bundle.json","state":"https://pith.science/pith/7P2RRMKWA7BCIWPRRV6AONNW5D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7P2RRMKWA7BCIWPRRV6AONNW5D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7P2RRMKWA7BCIWPRRV6AONNW5D","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":"c205aed07a5cc55b3b001cd6a3b21d81814829034703da8609c504d8e159dd17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-12-18T22:59:41Z","title_canon_sha256":"7ba38af347d96016c16668088b108f2249fc600e5201b8d320b7daa9dadd6c1a"},"schema_version":"1.0","source":{"id":"1712.06711","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.06711","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"arxiv_version","alias_value":"1712.06711v3","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.06711","created_at":"2026-05-18T00:14:34Z"},{"alias_kind":"pith_short_12","alias_value":"7P2RRMKWA7BC","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7P2RRMKWA7BCIWPR","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7P2RRMKW","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:63facad793f8b593c371d403366a1ef1c992c2781399ae3d0a212bc9c692e0e8","target":"graph","created_at":"2026-05-18T00:14:34Z","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":"For a signed cyclic graph G, we can construct a unique virtual link L by taking the medial construction and convert 4-valent vertices of the medial graph to crossings according to the signs. If a virtual link can occur in this way then we say that the virtual link is graphical. In the article we shall prove that a virtual link L is graphical if and only if it is checkerboard colorable. On the other hand, we introduce a polynomial F[G] for signed cyclic graphs, which is defined via a deletion-marking recursion. We shall establish the relationship between F[G] of a signed cyclic graph G and the ","authors_text":"Louis H Kauffman, Qingying Deng, Xian'an Jin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-12-18T22:59:41Z","title":"Graphical virtual links and a polynomial of signed cyclic graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.06711","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":"sha256:0435a0418b850b6ac75221fe851abc177ac5ed147be07ebab7fd42917063bd48","target":"record","created_at":"2026-05-18T00:14:34Z","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":"c205aed07a5cc55b3b001cd6a3b21d81814829034703da8609c504d8e159dd17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-12-18T22:59:41Z","title_canon_sha256":"7ba38af347d96016c16668088b108f2249fc600e5201b8d320b7daa9dadd6c1a"},"schema_version":"1.0","source":{"id":"1712.06711","kind":"arxiv","version":3}},"canonical_sha256":"fbf518b15607c22459f18d7c0735b6e8c8cfb21b2a7e7199ebe43f849e022c2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbf518b15607c22459f18d7c0735b6e8c8cfb21b2a7e7199ebe43f849e022c2b","first_computed_at":"2026-05-18T00:14:34.176250Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:34.176250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1e9KTCrPesfTun23i4UiFR4G53VZPJGfBeYRSRrOJfEuolE29VL2BYrSrkg2h1o4Zm0OuV06EstXAY0HlLq5BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:34.176963Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.06711","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0435a0418b850b6ac75221fe851abc177ac5ed147be07ebab7fd42917063bd48","sha256:63facad793f8b593c371d403366a1ef1c992c2781399ae3d0a212bc9c692e0e8"],"state_sha256":"019aa0ac72cb727a88bcc0232f6bd0f440cf3f96c77186d326faadd4830798bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RHdTE1Ii35YjZ+w2+RDuTFc+yR7unYLfb8x5EQNvAgyJyZ105T+7HLxi7iJcAVdNYqhaoIoRDqN7DSmSQdryAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T19:58:11.820311Z","bundle_sha256":"d71178fe207de590716a58a126add2d2b73e0dfe7e6e72376a1a764532725b7f"}}