{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:OOQT6S33WHDVD4BAGDUS4A54SP","short_pith_number":"pith:OOQT6S33","schema_version":"1.0","canonical_sha256":"73a13f4b7bb1c751f02030e92e03bc93d673635f8ca112aa98a6e241d03f7ffe","source":{"kind":"arxiv","id":"1302.5536","version":1},"attestation_state":"computed","paper":{"title":"Power and spherical series over real alternative *-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CV","authors_text":"Alessandro Perotti, Riccardo Ghiloni","submitted_at":"2013-02-22T10:17:08Z","abstract_excerpt":"We study two types of series over a real alternative $^*$-algebra $A$. The first type are series of the form $\\sum_{n} (x-y)^{\\punto n}a_n$, where $a_n$ and $y$ belong to $A$ and $(x-y)^{\\punto n}$ denotes the $n$--th power of $x-y$ w.r.t.\\ the usual product obtained by requiring commutativity of the indeterminate $x$ with the elements of $A$. In the real and in the complex cases, the sums of power series define, respectively, the real analytic and the holomorphic functions. In the quaternionic case, a series of this type produces, in the interior of its set of convergence, a function belongin"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1302.5536","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-22T10:17:08Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"5e708db98a94e238af4bb54fe714e5380d3eef47c9a862e68e85933ed4b0617c","abstract_canon_sha256":"d29ce314405e1fe98a539d866c000f6bc523648bc87165e479572a502eb43ec3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:06.700923Z","signature_b64":"+HKUxjo48eBGk2QGY2raL0ulLGP1iNhYJLcg2/GFXg/9S2X5rdQuor4GHDlPUdSp8n1EucNyQN+E8SB+AgA5Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73a13f4b7bb1c751f02030e92e03bc93d673635f8ca112aa98a6e241d03f7ffe","last_reissued_at":"2026-05-18T00:12:06.700423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:06.700423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Power and spherical series over real alternative *-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CV","authors_text":"Alessandro Perotti, Riccardo Ghiloni","submitted_at":"2013-02-22T10:17:08Z","abstract_excerpt":"We study two types of series over a real alternative $^*$-algebra $A$. The first type are series of the form $\\sum_{n} (x-y)^{\\punto n}a_n$, where $a_n$ and $y$ belong to $A$ and $(x-y)^{\\punto n}$ denotes the $n$--th power of $x-y$ w.r.t.\\ the usual product obtained by requiring commutativity of the indeterminate $x$ with the elements of $A$. In the real and in the complex cases, the sums of power series define, respectively, the real analytic and the holomorphic functions. In the quaternionic case, a series of this type produces, in the interior of its set of convergence, a function belongin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5536","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1302.5536","created_at":"2026-05-18T00:12:06.700497+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.5536v1","created_at":"2026-05-18T00:12:06.700497+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5536","created_at":"2026-05-18T00:12:06.700497+00:00"},{"alias_kind":"pith_short_12","alias_value":"OOQT6S33WHDV","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OOQT6S33WHDVD4BA","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OOQT6S33","created_at":"2026-05-18T12:27:54.935989+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OOQT6S33WHDVD4BAGDUS4A54SP","json":"https://pith.science/pith/OOQT6S33WHDVD4BAGDUS4A54SP.json","graph_json":"https://pith.science/api/pith-number/OOQT6S33WHDVD4BAGDUS4A54SP/graph.json","events_json":"https://pith.science/api/pith-number/OOQT6S33WHDVD4BAGDUS4A54SP/events.json","paper":"https://pith.science/paper/OOQT6S33"},"agent_actions":{"view_html":"https://pith.science/pith/OOQT6S33WHDVD4BAGDUS4A54SP","download_json":"https://pith.science/pith/OOQT6S33WHDVD4BAGDUS4A54SP.json","view_paper":"https://pith.science/paper/OOQT6S33","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.5536&json=true","fetch_graph":"https://pith.science/api/pith-number/OOQT6S33WHDVD4BAGDUS4A54SP/graph.json","fetch_events":"https://pith.science/api/pith-number/OOQT6S33WHDVD4BAGDUS4A54SP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OOQT6S33WHDVD4BAGDUS4A54SP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OOQT6S33WHDVD4BAGDUS4A54SP/action/storage_attestation","attest_author":"https://pith.science/pith/OOQT6S33WHDVD4BAGDUS4A54SP/action/author_attestation","sign_citation":"https://pith.science/pith/OOQT6S33WHDVD4BAGDUS4A54SP/action/citation_signature","submit_replication":"https://pith.science/pith/OOQT6S33WHDVD4BAGDUS4A54SP/action/replication_record"}},"created_at":"2026-05-18T00:12:06.700497+00:00","updated_at":"2026-05-18T00:12:06.700497+00:00"}