{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OHFFBGK3O4SXDSXM3CZ5CTIRNE","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":"f5beda863536ba6bb439d37b7a8c60bfae7c93737625a1bbb2baeca49dc3faed","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GR","submitted_at":"2015-02-11T19:57:40Z","title_canon_sha256":"8374992d519ee7c7818a40237b27f471d5b0af890e851571da3590e78182c61d"},"schema_version":"1.0","source":{"id":"1502.03414","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.03414","created_at":"2026-05-18T02:27:19Z"},{"alias_kind":"arxiv_version","alias_value":"1502.03414v1","created_at":"2026-05-18T02:27:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.03414","created_at":"2026-05-18T02:27:19Z"},{"alias_kind":"pith_short_12","alias_value":"OHFFBGK3O4SX","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OHFFBGK3O4SXDSXM","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OHFFBGK3","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:6afc15bcd59552e2760d569f61e3b614aa312be9c14b671c64aa8c78f29e0cfc","target":"graph","created_at":"2026-05-18T02:27:19Z","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 calculate zeta and normal zeta functions of space groups with the point group isomorphic to the cyclic group of order 2. The obtained results are applied to determine the number of subgroups, resp. normal subgroups, of a given index for each of these groups.","authors_text":"Hermina Alajbegovi\\'c, Muharem Avdispahi\\'c","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GR","submitted_at":"2015-02-11T19:57:40Z","title":"Zeta and normal zeta functions for a subclass of space groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03414","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":"sha256:1166dbb68cd766cff8af0ced6b2fcc8fa056ba235d00b70e8f4dc1838417de2c","target":"record","created_at":"2026-05-18T02:27:19Z","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":"f5beda863536ba6bb439d37b7a8c60bfae7c93737625a1bbb2baeca49dc3faed","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GR","submitted_at":"2015-02-11T19:57:40Z","title_canon_sha256":"8374992d519ee7c7818a40237b27f471d5b0af890e851571da3590e78182c61d"},"schema_version":"1.0","source":{"id":"1502.03414","kind":"arxiv","version":1}},"canonical_sha256":"71ca50995b772571caecd8b3d14d116902c71d19428c7ba45bbec3810a3d4bb0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71ca50995b772571caecd8b3d14d116902c71d19428c7ba45bbec3810a3d4bb0","first_computed_at":"2026-05-18T02:27:19.410965Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:19.410965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sk1uYZgR0t7DnADCCLmXWtJN/DA90ywJPhgr+4QQoB9B/pEpZFffYfgWFNfDszUbY1NjDo16BhkKN40q4iJcDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:19.411733Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.03414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1166dbb68cd766cff8af0ced6b2fcc8fa056ba235d00b70e8f4dc1838417de2c","sha256:6afc15bcd59552e2760d569f61e3b614aa312be9c14b671c64aa8c78f29e0cfc"],"state_sha256":"cc873c31e7ffc69ce9c2f97d54c932075498f0d0a756a078ac5d14169e8105c5"}