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We also show that several subalgebras of the real symmetric polydisc algebra are projective free."},"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":"1103.0899","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2011-03-04T13:37:29Z","cross_cats_sorted":["math.AC","math.FA"],"title_canon_sha256":"16c55a4a910ccf29b8ba90882c67de2d809cab75c25633abbfa19e011a910325","abstract_canon_sha256":"0ef7f7e8a0b0d16d5b31214d544b4dc71dbf16d5eba307b3054f78dbc04145f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:18.098657Z","signature_b64":"WoIk/qFyGECIhqQSCT0DD4PruGlnzTV3FZ3O04ZAX9SkUNhshoetKoNmJflTn1wqts0nSbj8UbkIa5hpj9ETBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fb83b8ba3f3ac6f326c8af1e7a38545374547e5ba00645d4ef7543ecce586a2","last_reissued_at":"2026-05-18T03:31:18.097828Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:18.097828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Projective freeness of algebras of real symmetric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.FA"],"primary_cat":"math.KT","authors_text":"Amol Sasane","submitted_at":"2011-03-04T13:37:29Z","abstract_excerpt":"Let D^n be the closed unit polydisk in C^n. 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