{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CX4DZ2BE7M4JZ3V7F7UTRK2NOH","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":"1dd970e72916d72d4df049fa85844bc26018757e40aea64eba1c5978dfaeaa16","cross_cats_sorted":["math.AC","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-19T03:31:22Z","title_canon_sha256":"5b9f8483f1f493b62c3f372aada3293ce112f8f27126d4cd9216be798de0664a"},"schema_version":"1.0","source":{"id":"1601.04785","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04785","created_at":"2026-05-18T01:22:31Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04785v1","created_at":"2026-05-18T01:22:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04785","created_at":"2026-05-18T01:22:31Z"},{"alias_kind":"pith_short_12","alias_value":"CX4DZ2BE7M4J","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CX4DZ2BE7M4JZ3V7","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CX4DZ2BE","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:c8fdf9a6980483ec1748da71fb599748ead320cc4707e0c8f640af45cda5986b","target":"graph","created_at":"2026-05-18T01:22:31Z","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":"In this paper we define and study a Dedekind-like zeta function for the algebra of multicomplex numbers. By using the idempotent representations for such numbers, we are able to identify this zeta function with the one associated to a product of copies of the field of Gaussian rationals. The approach we use is substantially different from the one previously introduced by Rochon (for the bicomplex case) and by Reid and Van Gorder (for the multicomplex case).","authors_text":"A. Sebbar, A. Vajiac, D.C. Struppa, M.B. Vajiac","cross_cats":["math.AC","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-19T03:31:22Z","title":"A Zeta Function for Multicomplex Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04785","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":"sha256:8a3874a377609434cfb55ad179f46f8e835fbfb085d9f2fa86331dcbcd136cfb","target":"record","created_at":"2026-05-18T01:22:31Z","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":"1dd970e72916d72d4df049fa85844bc26018757e40aea64eba1c5978dfaeaa16","cross_cats_sorted":["math.AC","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-19T03:31:22Z","title_canon_sha256":"5b9f8483f1f493b62c3f372aada3293ce112f8f27126d4cd9216be798de0664a"},"schema_version":"1.0","source":{"id":"1601.04785","kind":"arxiv","version":1}},"canonical_sha256":"15f83ce824fb389ceebf2fe938ab4d71f543ec5a4343db9b07aa241117cf4e24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15f83ce824fb389ceebf2fe938ab4d71f543ec5a4343db9b07aa241117cf4e24","first_computed_at":"2026-05-18T01:22:31.839461Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:31.839461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y26B1P13jafkWr6yhE+bUuL0oQaY5rf1tzjBsWCcqRhBNkX5Kx4tCZi7Xjkg0cK56NAc+1q7PlASoHlVrdRuCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:31.839897Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.04785","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a3874a377609434cfb55ad179f46f8e835fbfb085d9f2fa86331dcbcd136cfb","sha256:c8fdf9a6980483ec1748da71fb599748ead320cc4707e0c8f640af45cda5986b"],"state_sha256":"62776c903713b0ff8d73aabd6f91e6890a400c4bf6d12372122d8f81260b9bee"}