{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2SE3Q2F5HCZWWSB56JXDP3AGUG","short_pith_number":"pith:2SE3Q2F5","canonical_record":{"source":{"id":"1601.02574","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-11T19:56:33Z","cross_cats_sorted":[],"title_canon_sha256":"ae4ef2ecc3baf51d4349ee434754d71f57730bf19a5481a7a36cf77e955894ee","abstract_canon_sha256":"d14bf587f1f3abf5fb3438e2a445fdec27131c91f7d8113925830819d10e0710"},"schema_version":"1.0"},"canonical_sha256":"d489b868bd38b36b483df26e37ec06a1afcc4a2dfb5be1c739780820f36947c6","source":{"kind":"arxiv","id":"1601.02574","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02574","created_at":"2026-05-18T00:48:43Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02574v1","created_at":"2026-05-18T00:48:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02574","created_at":"2026-05-18T00:48:43Z"},{"alias_kind":"pith_short_12","alias_value":"2SE3Q2F5HCZW","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2SE3Q2F5HCZWWSB5","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2SE3Q2F5","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2SE3Q2F5HCZWWSB56JXDP3AGUG","target":"record","payload":{"canonical_record":{"source":{"id":"1601.02574","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-11T19:56:33Z","cross_cats_sorted":[],"title_canon_sha256":"ae4ef2ecc3baf51d4349ee434754d71f57730bf19a5481a7a36cf77e955894ee","abstract_canon_sha256":"d14bf587f1f3abf5fb3438e2a445fdec27131c91f7d8113925830819d10e0710"},"schema_version":"1.0"},"canonical_sha256":"d489b868bd38b36b483df26e37ec06a1afcc4a2dfb5be1c739780820f36947c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:43.021609Z","signature_b64":"be8huruSaTIXN6Dzwi24aSsI7JRkHGdnb2j+w66SfgCriMaHkZoy5vwwhND3WdyXgvaJDH/jCBeXSIRbhkFqDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d489b868bd38b36b483df26e37ec06a1afcc4a2dfb5be1c739780820f36947c6","last_reissued_at":"2026-05-18T00:48:43.021167Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:43.021167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.02574","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":"2026-05-18T00:48:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5EmMzo3tz2Ebtg8YB6uaJEFHEId76/rq3Lkvssw/Dv+nReT/SnD2WwnLrddXATjArugYC73aFxNHyOI6hoBOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:12:02.987821Z"},"content_sha256":"186c5283260420145c387ed777abf7623570d07e54455ab43a22730bcc6e33d1","schema_version":"1.0","event_id":"sha256:186c5283260420145c387ed777abf7623570d07e54455ab43a22730bcc6e33d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2SE3Q2F5HCZWWSB56JXDP3AGUG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the local genus distribution of graph embeddings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christian M. Reidys, Ricky X. F. Chen","submitted_at":"2016-01-11T19:56:33Z","abstract_excerpt":"The $2$-cell embeddings of graphs on closed surfaces have been widely studied. It is well known that ($2$-cell) embedding a given graph $G$ on a closed orientable surface is equivalent to cyclically ordering the edges incident to each vertex of $G$. In this paper, we study the following problem: given a genus $g$ embedding $\\epsilon$ of the graph $G$ and a vertex of $G$, how many different ways of reembedding the vertex such that the resulting embedding $\\epsilon'$ is of genus $g+\\Delta g$? We give formulas to compute this quantity and the local minimal genus achieved by reembedding. In the pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02574","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":"2026-05-18T00:48:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"viBb2K078Sn3IPd4TxhuljGd5FDjnIiEUcrmRwOQbBG5lMxADkeY+EOJqgbct9NtJJsPJRxKGEOv3EI/oWHBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:12:02.988441Z"},"content_sha256":"bf11fff2cbf654cda79c3cb3abaf724e5881e50e32221306017b04261e251066","schema_version":"1.0","event_id":"sha256:bf11fff2cbf654cda79c3cb3abaf724e5881e50e32221306017b04261e251066"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2SE3Q2F5HCZWWSB56JXDP3AGUG/bundle.json","state_url":"https://pith.science/pith/2SE3Q2F5HCZWWSB56JXDP3AGUG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2SE3Q2F5HCZWWSB56JXDP3AGUG/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":"2026-06-05T21:12:02Z","links":{"resolver":"https://pith.science/pith/2SE3Q2F5HCZWWSB56JXDP3AGUG","bundle":"https://pith.science/pith/2SE3Q2F5HCZWWSB56JXDP3AGUG/bundle.json","state":"https://pith.science/pith/2SE3Q2F5HCZWWSB56JXDP3AGUG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2SE3Q2F5HCZWWSB56JXDP3AGUG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2SE3Q2F5HCZWWSB56JXDP3AGUG","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":"d14bf587f1f3abf5fb3438e2a445fdec27131c91f7d8113925830819d10e0710","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-11T19:56:33Z","title_canon_sha256":"ae4ef2ecc3baf51d4349ee434754d71f57730bf19a5481a7a36cf77e955894ee"},"schema_version":"1.0","source":{"id":"1601.02574","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02574","created_at":"2026-05-18T00:48:43Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02574v1","created_at":"2026-05-18T00:48:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02574","created_at":"2026-05-18T00:48:43Z"},{"alias_kind":"pith_short_12","alias_value":"2SE3Q2F5HCZW","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2SE3Q2F5HCZWWSB5","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2SE3Q2F5","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:bf11fff2cbf654cda79c3cb3abaf724e5881e50e32221306017b04261e251066","target":"graph","created_at":"2026-05-18T00:48:43Z","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":"The $2$-cell embeddings of graphs on closed surfaces have been widely studied. It is well known that ($2$-cell) embedding a given graph $G$ on a closed orientable surface is equivalent to cyclically ordering the edges incident to each vertex of $G$. In this paper, we study the following problem: given a genus $g$ embedding $\\epsilon$ of the graph $G$ and a vertex of $G$, how many different ways of reembedding the vertex such that the resulting embedding $\\epsilon'$ is of genus $g+\\Delta g$? We give formulas to compute this quantity and the local minimal genus achieved by reembedding. In the pr","authors_text":"Christian M. Reidys, Ricky X. F. Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-11T19:56:33Z","title":"On the local genus distribution of graph embeddings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02574","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":"sha256:186c5283260420145c387ed777abf7623570d07e54455ab43a22730bcc6e33d1","target":"record","created_at":"2026-05-18T00:48:43Z","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":"d14bf587f1f3abf5fb3438e2a445fdec27131c91f7d8113925830819d10e0710","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-11T19:56:33Z","title_canon_sha256":"ae4ef2ecc3baf51d4349ee434754d71f57730bf19a5481a7a36cf77e955894ee"},"schema_version":"1.0","source":{"id":"1601.02574","kind":"arxiv","version":1}},"canonical_sha256":"d489b868bd38b36b483df26e37ec06a1afcc4a2dfb5be1c739780820f36947c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d489b868bd38b36b483df26e37ec06a1afcc4a2dfb5be1c739780820f36947c6","first_computed_at":"2026-05-18T00:48:43.021167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:43.021167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"be8huruSaTIXN6Dzwi24aSsI7JRkHGdnb2j+w66SfgCriMaHkZoy5vwwhND3WdyXgvaJDH/jCBeXSIRbhkFqDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:43.021609Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.02574","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:186c5283260420145c387ed777abf7623570d07e54455ab43a22730bcc6e33d1","sha256:bf11fff2cbf654cda79c3cb3abaf724e5881e50e32221306017b04261e251066"],"state_sha256":"aada3a5de0cab8ea02eff3f3bd60657cb3e56b367fb03078a6a03bbce503254b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"imQTcopG5XnGN4TFk/g5MTu5J6FeyA9GlU7T4OFbsfrwsm+TNOylm2v7wOicY1o846mk9gWZs3kKRwaOqA95Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T21:12:02.992142Z","bundle_sha256":"c8ce6bd13f1d3a251660971360502a87a05b4e2f753d796386dedf7ee278d508"}}