{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YVTB56NYQ5GESZRYHIRQZXVIBA","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":"244b2d0b25fe6c67fd47032da49ca96d172086db03173cb4af7f6c52d6c188ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-06T21:20:26Z","title_canon_sha256":"f06c6447d10eba0995bee26f411ee0dd7acfa787dd2e862f9a76801a16872d58"},"schema_version":"1.0","source":{"id":"1401.1226","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1226","created_at":"2026-05-18T03:03:09Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1226v1","created_at":"2026-05-18T03:03:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1226","created_at":"2026-05-18T03:03:09Z"},{"alias_kind":"pith_short_12","alias_value":"YVTB56NYQ5GE","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"YVTB56NYQ5GESZRY","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"YVTB56NY","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:b4e3fc6d07112762fa2c43a917ab5e7ebbb60eda895ac0ef73202900b65d62c2","target":"graph","created_at":"2026-05-18T03:03:09Z","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":"Given $T_1,\\dots, T_n$ commuting power-bounded operators on a Banach space we study under which conditions the equality $\\ker (T_1-\\mathrm{I})\\cdots (T_n-\\mathrm{I})=\\ker(T_1-\\mathrm{I})+\\cdots +\\ker (T_n-\\mathrm{I})$ holds true. This problem, known as the periodic decomposition problem, goes back to I. Z. Ruzsa. In this short note we consider the case when $T_j=T(t_j)$, $t_j>0$, $j=1,\\dots, n$ for some one-parameter semigroup $(T(t))_{t\\geq 0}$. We also look at a generalization of the periodic decomposition problem when instead of the cyclic semigroups $\\{T_j^n:n \\in \\mathbb{N}\\}$ more genera","authors_text":"B\\'alint Farkas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-06T21:20:26Z","title":"A note on the periodic decomposition problem for semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1226","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":"sha256:03807f0e3de0cce96283fa80bbbf398538a059ca4f0b3081ef00ba80eac9860c","target":"record","created_at":"2026-05-18T03:03:09Z","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":"244b2d0b25fe6c67fd47032da49ca96d172086db03173cb4af7f6c52d6c188ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-06T21:20:26Z","title_canon_sha256":"f06c6447d10eba0995bee26f411ee0dd7acfa787dd2e862f9a76801a16872d58"},"schema_version":"1.0","source":{"id":"1401.1226","kind":"arxiv","version":1}},"canonical_sha256":"c5661ef9b8874c4966383a230cdea808302f0ce28a7b907267f381645f97556f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5661ef9b8874c4966383a230cdea808302f0ce28a7b907267f381645f97556f","first_computed_at":"2026-05-18T03:03:09.314608Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:09.314608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R/ZmdOHXabI+FZ7xbr/EYunxGzaimEDY3lx7OZGadA+O9xP4z/yCofkRa9Xem1nweiiGe7dZ1soMUsTfB09BBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:09.315246Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.1226","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03807f0e3de0cce96283fa80bbbf398538a059ca4f0b3081ef00ba80eac9860c","sha256:b4e3fc6d07112762fa2c43a917ab5e7ebbb60eda895ac0ef73202900b65d62c2"],"state_sha256":"554a9aa667054fe744b204f8e0574315b82bbf2a8e47a5b8bf7c6307462cca1e"}