{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IGCLYDHDFVGRJKP6PZGHDSPH5Q","short_pith_number":"pith:IGCLYDHD","canonical_record":{"source":{"id":"1512.08263","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-22T21:08:33Z","cross_cats_sorted":[],"title_canon_sha256":"83b2cf7bfed49fcb242a24910df58155985c8c35e7b1079ca3f533d45063a10d","abstract_canon_sha256":"1897b41387ecad8bc3a9db9d9b2acf406a598541fca2be99e0269a55db5880f0"},"schema_version":"1.0"},"canonical_sha256":"4184bc0ce32d4d14a9fe7e4c71c9e7ec0a9589970ac1436f766d03d49ca94c9a","source":{"kind":"arxiv","id":"1512.08263","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08263","created_at":"2026-05-18T00:00:02Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08263v2","created_at":"2026-05-18T00:00:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08263","created_at":"2026-05-18T00:00:02Z"},{"alias_kind":"pith_short_12","alias_value":"IGCLYDHDFVGR","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IGCLYDHDFVGRJKP6","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IGCLYDHD","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IGCLYDHDFVGRJKP6PZGHDSPH5Q","target":"record","payload":{"canonical_record":{"source":{"id":"1512.08263","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-22T21:08:33Z","cross_cats_sorted":[],"title_canon_sha256":"83b2cf7bfed49fcb242a24910df58155985c8c35e7b1079ca3f533d45063a10d","abstract_canon_sha256":"1897b41387ecad8bc3a9db9d9b2acf406a598541fca2be99e0269a55db5880f0"},"schema_version":"1.0"},"canonical_sha256":"4184bc0ce32d4d14a9fe7e4c71c9e7ec0a9589970ac1436f766d03d49ca94c9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:02.829957Z","signature_b64":"TI6u1FREZJHaXm0Xav9pYrXPMytoh7pfjp1zIdtHgY/l9r+KD92a0ImpBIbfn6C1MKHZi2Av+udhN0U63/dHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4184bc0ce32d4d14a9fe7e4c71c9e7ec0a9589970ac1436f766d03d49ca94c9a","last_reissued_at":"2026-05-18T00:00:02.829495Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:02.829495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.08263","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:00:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uuiZni6bpbdhrfeUvj45lUmlvjab2+wfUKkjRah0V2MrJneP+tQDNF/QqCNs0hHSz2Htd4MQXxpnIBtc/bS8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T07:18:59.958782Z"},"content_sha256":"917b01af40f2f6936c0c97aaec05f5ce74bf4a0b864c167bddb53a04bdf14590","schema_version":"1.0","event_id":"sha256:917b01af40f2f6936c0c97aaec05f5ce74bf4a0b864c167bddb53a04bdf14590"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IGCLYDHDFVGRJKP6PZGHDSPH5Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariants and TQFT's for cut cellular surfaces from finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Diogo Bragan\\c{c}a, Roger Picken","submitted_at":"2015-12-22T21:08:33Z","abstract_excerpt":"We introduce the notion of a cut cellular surface (CCS), being a surface with boundary, which is cut in a specified way to be represented in the plane, and is composed of 0-, 1- and 2-cells. We obtain invariants of CCS's under Pachner-like moves on the cellular structure, by counting colourings of the 1-cells with elements of a finite group, subject to a \"flatness\" condition for each 2-cell. These invariants are also described in a TQFT setting, which is not the same as the usual 2-dimensional TQFT framework. We study the properties of functions which arise in this context, associated to the d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08263","kind":"arxiv","version":2},"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":"2026-05-18T00:00:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZCQfayjHcNNHjTrQ85t1/MzvlzmT9p7jA4aK2LwbUfnxj3+ITn+mTw/qo8Drp4zrNTHtIt4NYy0R101iQHl8Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T07:18:59.959113Z"},"content_sha256":"67536f5a5a4f39fb17bbdc6d9087a3b145e84b5d997a7a2138b1889b2e4ac946","schema_version":"1.0","event_id":"sha256:67536f5a5a4f39fb17bbdc6d9087a3b145e84b5d997a7a2138b1889b2e4ac946"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IGCLYDHDFVGRJKP6PZGHDSPH5Q/bundle.json","state_url":"https://pith.science/pith/IGCLYDHDFVGRJKP6PZGHDSPH5Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IGCLYDHDFVGRJKP6PZGHDSPH5Q/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":"2026-07-04T07:18:59Z","links":{"resolver":"https://pith.science/pith/IGCLYDHDFVGRJKP6PZGHDSPH5Q","bundle":"https://pith.science/pith/IGCLYDHDFVGRJKP6PZGHDSPH5Q/bundle.json","state":"https://pith.science/pith/IGCLYDHDFVGRJKP6PZGHDSPH5Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IGCLYDHDFVGRJKP6PZGHDSPH5Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IGCLYDHDFVGRJKP6PZGHDSPH5Q","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":"1897b41387ecad8bc3a9db9d9b2acf406a598541fca2be99e0269a55db5880f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-22T21:08:33Z","title_canon_sha256":"83b2cf7bfed49fcb242a24910df58155985c8c35e7b1079ca3f533d45063a10d"},"schema_version":"1.0","source":{"id":"1512.08263","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08263","created_at":"2026-05-18T00:00:02Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08263v2","created_at":"2026-05-18T00:00:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08263","created_at":"2026-05-18T00:00:02Z"},{"alias_kind":"pith_short_12","alias_value":"IGCLYDHDFVGR","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IGCLYDHDFVGRJKP6","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IGCLYDHD","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:67536f5a5a4f39fb17bbdc6d9087a3b145e84b5d997a7a2138b1889b2e4ac946","target":"graph","created_at":"2026-05-18T00:00:02Z","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":"We introduce the notion of a cut cellular surface (CCS), being a surface with boundary, which is cut in a specified way to be represented in the plane, and is composed of 0-, 1- and 2-cells. We obtain invariants of CCS's under Pachner-like moves on the cellular structure, by counting colourings of the 1-cells with elements of a finite group, subject to a \"flatness\" condition for each 2-cell. These invariants are also described in a TQFT setting, which is not the same as the usual 2-dimensional TQFT framework. We study the properties of functions which arise in this context, associated to the d","authors_text":"Diogo Bragan\\c{c}a, Roger Picken","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-22T21:08:33Z","title":"Invariants and TQFT's for cut cellular surfaces from finite groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08263","kind":"arxiv","version":2},"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":"sha256:917b01af40f2f6936c0c97aaec05f5ce74bf4a0b864c167bddb53a04bdf14590","target":"record","created_at":"2026-05-18T00:00:02Z","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":"1897b41387ecad8bc3a9db9d9b2acf406a598541fca2be99e0269a55db5880f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-22T21:08:33Z","title_canon_sha256":"83b2cf7bfed49fcb242a24910df58155985c8c35e7b1079ca3f533d45063a10d"},"schema_version":"1.0","source":{"id":"1512.08263","kind":"arxiv","version":2}},"canonical_sha256":"4184bc0ce32d4d14a9fe7e4c71c9e7ec0a9589970ac1436f766d03d49ca94c9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4184bc0ce32d4d14a9fe7e4c71c9e7ec0a9589970ac1436f766d03d49ca94c9a","first_computed_at":"2026-05-18T00:00:02.829495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:02.829495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TI6u1FREZJHaXm0Xav9pYrXPMytoh7pfjp1zIdtHgY/l9r+KD92a0ImpBIbfn6C1MKHZi2Av+udhN0U63/dHBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:02.829957Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08263","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:917b01af40f2f6936c0c97aaec05f5ce74bf4a0b864c167bddb53a04bdf14590","sha256:67536f5a5a4f39fb17bbdc6d9087a3b145e84b5d997a7a2138b1889b2e4ac946"],"state_sha256":"97d33857ac82ccdf10cdc95cd53919dcbe64c75d689f359b51da5f01db8b1cce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7S0T6UnqdF/SwdNoNXIkme6E8zd+6II2J1OlcTpdwXoDRVa7gjqyawrkT8CzIBOoRFo2vnbwJ1HZb/3JToreAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T07:18:59.960965Z","bundle_sha256":"1fb298ebad0299230fb17d5d4df2d716c606fe0c87daf1335434217d87791068"}}