{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OOQT6S33WHDVD4BAGDUS4A54SP","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":"d29ce314405e1fe98a539d866c000f6bc523648bc87165e479572a502eb43ec3","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-22T10:17:08Z","title_canon_sha256":"5e708db98a94e238af4bb54fe714e5380d3eef47c9a862e68e85933ed4b0617c"},"schema_version":"1.0","source":{"id":"1302.5536","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5536","created_at":"2026-05-18T00:12:06Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5536v1","created_at":"2026-05-18T00:12:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5536","created_at":"2026-05-18T00:12:06Z"},{"alias_kind":"pith_short_12","alias_value":"OOQT6S33WHDV","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OOQT6S33WHDVD4BA","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OOQT6S33","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:d2672383d60913dfb8d4f7a9984dd648868267a816e8ef81aca0b9e8cff53d55","target":"graph","created_at":"2026-05-18T00:12:06Z","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 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","authors_text":"Alessandro Perotti, Riccardo Ghiloni","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-22T10:17:08Z","title":"Power and spherical series over real alternative *-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5536","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":"sha256:07024676202082c4e12a6a6d04d822914984d1d6f6538bcf56b989214cc6bbe2","target":"record","created_at":"2026-05-18T00:12:06Z","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":"d29ce314405e1fe98a539d866c000f6bc523648bc87165e479572a502eb43ec3","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-22T10:17:08Z","title_canon_sha256":"5e708db98a94e238af4bb54fe714e5380d3eef47c9a862e68e85933ed4b0617c"},"schema_version":"1.0","source":{"id":"1302.5536","kind":"arxiv","version":1}},"canonical_sha256":"73a13f4b7bb1c751f02030e92e03bc93d673635f8ca112aa98a6e241d03f7ffe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73a13f4b7bb1c751f02030e92e03bc93d673635f8ca112aa98a6e241d03f7ffe","first_computed_at":"2026-05-18T00:12:06.700423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:06.700423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+HKUxjo48eBGk2QGY2raL0ulLGP1iNhYJLcg2/GFXg/9S2X5rdQuor4GHDlPUdSp8n1EucNyQN+E8SB+AgA5Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:06.700923Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5536","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07024676202082c4e12a6a6d04d822914984d1d6f6538bcf56b989214cc6bbe2","sha256:d2672383d60913dfb8d4f7a9984dd648868267a816e8ef81aca0b9e8cff53d55"],"state_sha256":"cccd86adacfae4634f1cabfddc673ab3d3ceac00b2b4bc62e72ebb066b5b9c30"}