{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:N5T6DYP5N5MSBZSMIQSDPUKMV2","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":"0904c67a04b1f9a34a34506a8aa8475fa0fd60a4d196b6b02ab97903d264b269","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-04-05T13:21:51Z","title_canon_sha256":"a86cfbaf877f56983c2c8dd15b1355ae90235f4143a254dafaa95fc347d2ae39"},"schema_version":"1.0","source":{"id":"1704.01403","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.01403","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"arxiv_version","alias_value":"1704.01403v2","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01403","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"pith_short_12","alias_value":"N5T6DYP5N5MS","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"N5T6DYP5N5MSBZSM","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"N5T6DYP5","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:7b50c98370c86dda2f3363e8c52fd4d37fae288eb2661a021de81b47040f251a","target":"graph","created_at":"2026-05-18T00:23:09Z","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":"The set of periodic distributions, with usual addition and convolution, forms a ring, which is isomorphic, via taking a Fourier series expansion, to the ring ${\\mathcal{S}}'({\\mathbb{Z}}^d)$ of sequences of at most polynomial growth with termwise operations. In this article, we establish several algebraic properties of these rings.","authors_text":"Amol Sasane","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-04-05T13:21:51Z","title":"A potpourri of algebraic properties of the ring of periodic distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01403","kind":"arxiv","version":2},"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":"sha256:5ecac39b98880e801904b1a108c5ab2293dc70af66e2bd200dead818655bf1a1","target":"record","created_at":"2026-05-18T00:23:09Z","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":"0904c67a04b1f9a34a34506a8aa8475fa0fd60a4d196b6b02ab97903d264b269","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-04-05T13:21:51Z","title_canon_sha256":"a86cfbaf877f56983c2c8dd15b1355ae90235f4143a254dafaa95fc347d2ae39"},"schema_version":"1.0","source":{"id":"1704.01403","kind":"arxiv","version":2}},"canonical_sha256":"6f67e1e1fd6f5920e64c442437d14caea742b366824253d782fe500a13c9723e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f67e1e1fd6f5920e64c442437d14caea742b366824253d782fe500a13c9723e","first_computed_at":"2026-05-18T00:23:09.014231Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:09.014231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LRRRrQ9U8b1yvBw8eKbFUnVmhcwuHpR8XZ39wknh0AHnAU9JI9340llRFM9l9b8GkRG9uGzuV2/M9XZKuL5kAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:09.014969Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.01403","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ecac39b98880e801904b1a108c5ab2293dc70af66e2bd200dead818655bf1a1","sha256:7b50c98370c86dda2f3363e8c52fd4d37fae288eb2661a021de81b47040f251a"],"state_sha256":"1cc34266362ca75f4014138dc8eefbd6f4fb21fc9e7ce4700e4f947dca559bf6"}