{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KNIPU4AOXXEXZ2HY67LXIX2H46","short_pith_number":"pith:KNIPU4AO","canonical_record":{"source":{"id":"1310.3848","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-10-14T20:49:04Z","cross_cats_sorted":["math.AT","math.CO","math.GR"],"title_canon_sha256":"ad42d464fc286157c79f6f6e293152b2c57fc33a9475f68b032354437538cccd","abstract_canon_sha256":"36975b83235856cd79bc30998e848599277a544700d3000834fb6db1c1e4cefc"},"schema_version":"1.0"},"canonical_sha256":"5350fa700ebdc97ce8f8f7d7745f47e78e5d874b33564cc06bc4cc5ab6daddeb","source":{"kind":"arxiv","id":"1310.3848","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3848","created_at":"2026-05-18T03:10:25Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3848v1","created_at":"2026-05-18T03:10:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3848","created_at":"2026-05-18T03:10:25Z"},{"alias_kind":"pith_short_12","alias_value":"KNIPU4AOXXEX","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KNIPU4AOXXEXZ2HY","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KNIPU4AO","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KNIPU4AOXXEXZ2HY67LXIX2H46","target":"record","payload":{"canonical_record":{"source":{"id":"1310.3848","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-10-14T20:49:04Z","cross_cats_sorted":["math.AT","math.CO","math.GR"],"title_canon_sha256":"ad42d464fc286157c79f6f6e293152b2c57fc33a9475f68b032354437538cccd","abstract_canon_sha256":"36975b83235856cd79bc30998e848599277a544700d3000834fb6db1c1e4cefc"},"schema_version":"1.0"},"canonical_sha256":"5350fa700ebdc97ce8f8f7d7745f47e78e5d874b33564cc06bc4cc5ab6daddeb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:25.835369Z","signature_b64":"A+kNKWM0ra4vn/fb9EqtqqOnTJJ4Vf78nuMsovfrMK7B4ezUGfebV7IOdhGmy8yDiuBKciPTO4gXrJpt4NFHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5350fa700ebdc97ce8f8f7d7745f47e78e5d874b33564cc06bc4cc5ab6daddeb","last_reissued_at":"2026-05-18T03:10:25.834577Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:25.834577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.3848","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":"2026-05-18T03:10:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PM51C/wx2yIptlY/ve7j61khzpF8nM9jRzKF7+rLwgOrU2+i7QTi7kMp1hAJbfLWEJN/1xoOIzme5rL+6F0GCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:41:35.474471Z"},"content_sha256":"52e09ed16668539abf506e82e7435cb1c267de7e503116ecedfca5d18401ee87","schema_version":"1.0","event_id":"sha256:52e09ed16668539abf506e82e7435cb1c267de7e503116ecedfca5d18401ee87"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KNIPU4AOXXEXZ2HY67LXIX2H46","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a canonical construction of tesselated surfaces via finite group theory, Part I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CO","math.GR"],"primary_cat":"math.GT","authors_text":"Ergun Yalcin, Jonathan Pakianathan, Mark Herman","submitted_at":"2013-10-14T20:49:04Z","abstract_excerpt":"This paper is the first part in a 2 part study of an elementary functorial construction from the category of finite non-abelian groups to a category of singular compact, oriented 2-manifolds. After a desingularization process this construction results in a collection of compact, connected, oriented tesselated smooth surfaces equipped with a closed-cell structure which is face and edge transitive and which has at most 2 orbits of vertices. These tesselated surfaces can also be viewed as abstract 3-polytopes (or as graph embeddings in the corresponding surface) which are either equivar or dual t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3848","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":"2026-05-18T03:10:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dn/M9GxOORHvoBZ5nigwfX5uwZpFEKyU9R5+3etJSrRt9er2ZQnf1cm00QzVD3MsAnvjm6cse+2OwRX+y09RCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:41:35.475173Z"},"content_sha256":"e6e3db3d326bddce0df179111c800d07f8f12e98f6dd896aa4ce51c17e69e588","schema_version":"1.0","event_id":"sha256:e6e3db3d326bddce0df179111c800d07f8f12e98f6dd896aa4ce51c17e69e588"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KNIPU4AOXXEXZ2HY67LXIX2H46/bundle.json","state_url":"https://pith.science/pith/KNIPU4AOXXEXZ2HY67LXIX2H46/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KNIPU4AOXXEXZ2HY67LXIX2H46/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":"2026-05-25T17:41:35Z","links":{"resolver":"https://pith.science/pith/KNIPU4AOXXEXZ2HY67LXIX2H46","bundle":"https://pith.science/pith/KNIPU4AOXXEXZ2HY67LXIX2H46/bundle.json","state":"https://pith.science/pith/KNIPU4AOXXEXZ2HY67LXIX2H46/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KNIPU4AOXXEXZ2HY67LXIX2H46/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KNIPU4AOXXEXZ2HY67LXIX2H46","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":"36975b83235856cd79bc30998e848599277a544700d3000834fb6db1c1e4cefc","cross_cats_sorted":["math.AT","math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-10-14T20:49:04Z","title_canon_sha256":"ad42d464fc286157c79f6f6e293152b2c57fc33a9475f68b032354437538cccd"},"schema_version":"1.0","source":{"id":"1310.3848","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3848","created_at":"2026-05-18T03:10:25Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3848v1","created_at":"2026-05-18T03:10:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3848","created_at":"2026-05-18T03:10:25Z"},{"alias_kind":"pith_short_12","alias_value":"KNIPU4AOXXEX","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"KNIPU4AOXXEXZ2HY","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"KNIPU4AO","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:e6e3db3d326bddce0df179111c800d07f8f12e98f6dd896aa4ce51c17e69e588","target":"graph","created_at":"2026-05-18T03:10:25Z","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":"This paper is the first part in a 2 part study of an elementary functorial construction from the category of finite non-abelian groups to a category of singular compact, oriented 2-manifolds. After a desingularization process this construction results in a collection of compact, connected, oriented tesselated smooth surfaces equipped with a closed-cell structure which is face and edge transitive and which has at most 2 orbits of vertices. These tesselated surfaces can also be viewed as abstract 3-polytopes (or as graph embeddings in the corresponding surface) which are either equivar or dual t","authors_text":"Ergun Yalcin, Jonathan Pakianathan, Mark Herman","cross_cats":["math.AT","math.CO","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-10-14T20:49:04Z","title":"On a canonical construction of tesselated surfaces via finite group theory, Part I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3848","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":"sha256:52e09ed16668539abf506e82e7435cb1c267de7e503116ecedfca5d18401ee87","target":"record","created_at":"2026-05-18T03:10:25Z","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":"36975b83235856cd79bc30998e848599277a544700d3000834fb6db1c1e4cefc","cross_cats_sorted":["math.AT","math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-10-14T20:49:04Z","title_canon_sha256":"ad42d464fc286157c79f6f6e293152b2c57fc33a9475f68b032354437538cccd"},"schema_version":"1.0","source":{"id":"1310.3848","kind":"arxiv","version":1}},"canonical_sha256":"5350fa700ebdc97ce8f8f7d7745f47e78e5d874b33564cc06bc4cc5ab6daddeb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5350fa700ebdc97ce8f8f7d7745f47e78e5d874b33564cc06bc4cc5ab6daddeb","first_computed_at":"2026-05-18T03:10:25.834577Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:25.834577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A+kNKWM0ra4vn/fb9EqtqqOnTJJ4Vf78nuMsovfrMK7B4ezUGfebV7IOdhGmy8yDiuBKciPTO4gXrJpt4NFHAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:25.835369Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.3848","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52e09ed16668539abf506e82e7435cb1c267de7e503116ecedfca5d18401ee87","sha256:e6e3db3d326bddce0df179111c800d07f8f12e98f6dd896aa4ce51c17e69e588"],"state_sha256":"ed41ec28321d614b82a1409813f4a45f59a41a9c559052e309612dd6ad80111f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8e3fZEMvg8QPFzm4bkEopIEPzWNNzWM1kaP+chRp9kVIVmG5a8gKkjRXJGi7h/F8Vq0mNWIH5rZWQsPj+FfcAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T17:41:35.478801Z","bundle_sha256":"34535304fed876623a11626d8a9273c3e024c6de6b7481a349e61f366960719d"}}