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We prove that there is a constant $C$ (independent of $e$) such that the regularity of $H^s_{\\mathfrak{m}}(R/J^{[p^e]})$ is bounded above by $Cp^e$ for all $e\\geq 1$ and all integers $s$ such that $s+1$ is at least the dimension of the locus where $R/J$ doesn't have finite projective dimension."},"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":"1512.00049","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-11-30T21:31:22Z","cross_cats_sorted":[],"title_canon_sha256":"2f22c4d5f9bfd50c06f8ba1dbff15e83bfe239257cd54ad5b1918292ee51392c","abstract_canon_sha256":"246963d0b1fb9017eaaac6e1a15fb6004594a6c2b02d476d7f55c576375b7a2b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:32.932365Z","signature_b64":"45+1HrWP+5G9qWyfv1lIelWO1IKhBMNNXdd/7oRkHMCTmDg5QtTGZFQ7ljThtq89Z6IAl/D3sA66DyQu+7EODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"570b33a369bb16c248d307bf00a238f2058873a447e052361f54e7dd5a9c509f","last_reissued_at":"2026-05-18T01:25:32.931690Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:32.931690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the growth of regularity with respect to Frobenius","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Wenliang Zhang","submitted_at":"2015-11-30T21:31:22Z","abstract_excerpt":"Let $R=k[x_1,\\dots,x_n]/I$ be a standard graded $k$-algebra where $k$ is a field of prime characteristic and let $J$ be a homogeneous ideal in $R$. Denote $(x_1,\\dots,x_n)$ by $\\mathfrak{m}$. We prove that there is a constant $C$ (independent of $e$) such that the regularity of $H^s_{\\mathfrak{m}}(R/J^{[p^e]})$ is bounded above by $Cp^e$ for all $e\\geq 1$ and all integers $s$ such that $s+1$ is at least the dimension of the locus where $R/J$ doesn't have finite projective dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00049","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":"1512.00049","created_at":"2026-05-18T01:25:32.931796+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.00049v1","created_at":"2026-05-18T01:25:32.931796+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00049","created_at":"2026-05-18T01:25:32.931796+00:00"},{"alias_kind":"pith_short_12","alias_value":"K4FTHI3JXMLM","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"K4FTHI3JXMLMESGT","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"K4FTHI3J","created_at":"2026-05-18T12:29:27.538025+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/K4FTHI3JXMLMESGTA67QBIRY6I","json":"https://pith.science/pith/K4FTHI3JXMLMESGTA67QBIRY6I.json","graph_json":"https://pith.science/api/pith-number/K4FTHI3JXMLMESGTA67QBIRY6I/graph.json","events_json":"https://pith.science/api/pith-number/K4FTHI3JXMLMESGTA67QBIRY6I/events.json","paper":"https://pith.science/paper/K4FTHI3J"},"agent_actions":{"view_html":"https://pith.science/pith/K4FTHI3JXMLMESGTA67QBIRY6I","download_json":"https://pith.science/pith/K4FTHI3JXMLMESGTA67QBIRY6I.json","view_paper":"https://pith.science/paper/K4FTHI3J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.00049&json=true","fetch_graph":"https://pith.science/api/pith-number/K4FTHI3JXMLMESGTA67QBIRY6I/graph.json","fetch_events":"https://pith.science/api/pith-number/K4FTHI3JXMLMESGTA67QBIRY6I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K4FTHI3JXMLMESGTA67QBIRY6I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K4FTHI3JXMLMESGTA67QBIRY6I/action/storage_attestation","attest_author":"https://pith.science/pith/K4FTHI3JXMLMESGTA67QBIRY6I/action/author_attestation","sign_citation":"https://pith.science/pith/K4FTHI3JXMLMESGTA67QBIRY6I/action/citation_signature","submit_replication":"https://pith.science/pith/K4FTHI3JXMLMESGTA67QBIRY6I/action/replication_record"}},"created_at":"2026-05-18T01:25:32.931796+00:00","updated_at":"2026-05-18T01:25:32.931796+00:00"}