{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4ENP6AYPRE2IF53DXTNOKFXTS5","short_pith_number":"pith:4ENP6AYP","canonical_record":{"source":{"id":"1708.04296","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-14T19:56:57Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"b4eeda5c8cccf190b8d0310e6bafa45879a1da89673125de910b89c883527c28","abstract_canon_sha256":"08d2f7fc0c9ce99585fd4b90240a193060f77b363b00196c6da909eafffb375f"},"schema_version":"1.0"},"canonical_sha256":"e11aff030f893482f763bcdae516f39754c48c01c03506986b64242e856eaea9","source":{"kind":"arxiv","id":"1708.04296","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04296","created_at":"2026-05-17T23:49:33Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04296v4","created_at":"2026-05-17T23:49:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04296","created_at":"2026-05-17T23:49:33Z"},{"alias_kind":"pith_short_12","alias_value":"4ENP6AYPRE2I","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4ENP6AYPRE2IF53D","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4ENP6AYP","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4ENP6AYPRE2IF53DXTNOKFXTS5","target":"record","payload":{"canonical_record":{"source":{"id":"1708.04296","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-14T19:56:57Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"b4eeda5c8cccf190b8d0310e6bafa45879a1da89673125de910b89c883527c28","abstract_canon_sha256":"08d2f7fc0c9ce99585fd4b90240a193060f77b363b00196c6da909eafffb375f"},"schema_version":"1.0"},"canonical_sha256":"e11aff030f893482f763bcdae516f39754c48c01c03506986b64242e856eaea9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:33.838688Z","signature_b64":"35wwvo7ZhemucOgaMCR5/r3fp4DbtY3TRJxSLRnbGFHxOLINeLNY/MLlnnxlPj5j4ti35sbJysZGiu3XLXjZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e11aff030f893482f763bcdae516f39754c48c01c03506986b64242e856eaea9","last_reissued_at":"2026-05-17T23:49:33.838004Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:33.838004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.04296","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zKrCG2FAfCdc2lmAz4YY3CXY/zBDNIie2Mi6XyvkZ+NiQ/uxLcmuevfXoipwERIsW6AvaToN6CMxQqWNx0VLDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:19:57.159336Z"},"content_sha256":"48ff0a1d82c4ff7568249684d72b4b4ea17a0de3ec9cf06a6a367cb413dabd61","schema_version":"1.0","event_id":"sha256:48ff0a1d82c4ff7568249684d72b4b4ea17a0de3ec9cf06a6a367cb413dabd61"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4ENP6AYPRE2IF53DXTNOKFXTS5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Z-knotted triangulations of surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CO","authors_text":"Adam Tyc, Mark Pankov","submitted_at":"2017-08-14T19:56:57Z","abstract_excerpt":"A zigzag in a map (a $2$-cell embedding of a connected graph in a connected closed $2$-dimensional surface) is a cyclic sequence of edges satisfying the following conditions: 1) any two consecutive edges lie on the same face and have a common vertex, 2) for any three consecutive edges the first and the third edges are disjoint and the face containing the first and the second edges is distinct from the face which contains the second and the third. A map is $z$-knotted if it contains a single zigzag. Such maps are closely connected to Gauss code problem and have nice homological properties. We s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04296","kind":"arxiv","version":4},"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":"2026-05-17T23:49:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pHN9yFvF/uYms8Yt3pZDmEFpvfK5bLMHnizN1AzkRuN4nBrSsW5727xGxpWZmRtM8qjtsTWiOWX0ozn4zow8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:19:57.159729Z"},"content_sha256":"815afc7dfa2ada7338b603a9c3320219dba7402a301603c66d473a06d185f4df","schema_version":"1.0","event_id":"sha256:815afc7dfa2ada7338b603a9c3320219dba7402a301603c66d473a06d185f4df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4ENP6AYPRE2IF53DXTNOKFXTS5/bundle.json","state_url":"https://pith.science/pith/4ENP6AYPRE2IF53DXTNOKFXTS5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4ENP6AYPRE2IF53DXTNOKFXTS5/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":"2026-05-30T05:19:57Z","links":{"resolver":"https://pith.science/pith/4ENP6AYPRE2IF53DXTNOKFXTS5","bundle":"https://pith.science/pith/4ENP6AYPRE2IF53DXTNOKFXTS5/bundle.json","state":"https://pith.science/pith/4ENP6AYPRE2IF53DXTNOKFXTS5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4ENP6AYPRE2IF53DXTNOKFXTS5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4ENP6AYPRE2IF53DXTNOKFXTS5","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":"08d2f7fc0c9ce99585fd4b90240a193060f77b363b00196c6da909eafffb375f","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-14T19:56:57Z","title_canon_sha256":"b4eeda5c8cccf190b8d0310e6bafa45879a1da89673125de910b89c883527c28"},"schema_version":"1.0","source":{"id":"1708.04296","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04296","created_at":"2026-05-17T23:49:33Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04296v4","created_at":"2026-05-17T23:49:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04296","created_at":"2026-05-17T23:49:33Z"},{"alias_kind":"pith_short_12","alias_value":"4ENP6AYPRE2I","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4ENP6AYPRE2IF53D","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4ENP6AYP","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:815afc7dfa2ada7338b603a9c3320219dba7402a301603c66d473a06d185f4df","target":"graph","created_at":"2026-05-17T23:49:33Z","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 zigzag in a map (a $2$-cell embedding of a connected graph in a connected closed $2$-dimensional surface) is a cyclic sequence of edges satisfying the following conditions: 1) any two consecutive edges lie on the same face and have a common vertex, 2) for any three consecutive edges the first and the third edges are disjoint and the face containing the first and the second edges is distinct from the face which contains the second and the third. A map is $z$-knotted if it contains a single zigzag. Such maps are closely connected to Gauss code problem and have nice homological properties. We s","authors_text":"Adam Tyc, Mark Pankov","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-14T19:56:57Z","title":"Z-knotted triangulations of surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04296","kind":"arxiv","version":4},"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":"sha256:48ff0a1d82c4ff7568249684d72b4b4ea17a0de3ec9cf06a6a367cb413dabd61","target":"record","created_at":"2026-05-17T23:49:33Z","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":"08d2f7fc0c9ce99585fd4b90240a193060f77b363b00196c6da909eafffb375f","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-14T19:56:57Z","title_canon_sha256":"b4eeda5c8cccf190b8d0310e6bafa45879a1da89673125de910b89c883527c28"},"schema_version":"1.0","source":{"id":"1708.04296","kind":"arxiv","version":4}},"canonical_sha256":"e11aff030f893482f763bcdae516f39754c48c01c03506986b64242e856eaea9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e11aff030f893482f763bcdae516f39754c48c01c03506986b64242e856eaea9","first_computed_at":"2026-05-17T23:49:33.838004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:33.838004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"35wwvo7ZhemucOgaMCR5/r3fp4DbtY3TRJxSLRnbGFHxOLINeLNY/MLlnnxlPj5j4ti35sbJysZGiu3XLXjZCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:33.838688Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.04296","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48ff0a1d82c4ff7568249684d72b4b4ea17a0de3ec9cf06a6a367cb413dabd61","sha256:815afc7dfa2ada7338b603a9c3320219dba7402a301603c66d473a06d185f4df"],"state_sha256":"cb6f58f9220f62074260eb961ea1f477d30acff36b84f364c4f9dd0058cf26b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oOrt87c+jQ6FjdCIiOVAyt0zUjnpnEZsCguAumdjnKVi5M+enGM3OniJfMz0Pmcu1x2WOCene50lXEEJeHUdBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:19:57.161762Z","bundle_sha256":"283fe98f209439c6647dc56c26e4f2fad4d57fd68b4a20b1fb081866bc574d4a"}}