{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:WGKEBKJ5S4AB2AQFOIFVG5PDXK","short_pith_number":"pith:WGKEBKJ5","schema_version":"1.0","canonical_sha256":"b19440a93d97001d0205720b5375e3ba964fc9262137965378b0857b7bd52d0f","source":{"kind":"arxiv","id":"2405.19506","version":2},"attestation_state":"computed","paper":{"title":"Towards higher Frobenius functors for symmetric tensor categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Johannes Flake, Kevin Coulembier","submitted_at":"2024-05-29T20:41:33Z","abstract_excerpt":"We develop theory and examples of monoidal functors on tensor categories in positive characteristic that generalise the Frobenius functor from \\cite{Os, EOf, Tann}. The latter has proved to be a powerful tool in the ongoing classification of tensor categories of moderate growth, and we demonstrate the similar potential of the generalisations. More explicitly, we describe a new construction of the generalised Verlinde categories $Ver_{p^n}$ in terms of representation categories of elementary abelian $p$-groups. This leads to families of functors relating to $Ver_{p^n}$ that we conjecture, and p"},"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":"2405.19506","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-05-29T20:41:33Z","cross_cats_sorted":[],"title_canon_sha256":"1053294d8c462c1aaa95532fb5412f77c22235f8162e97c159a7f72aa66529a9","abstract_canon_sha256":"e231a9144fabbf275e9146e06b9802efb40dc135d4c504bdd523d8de1fa05d09"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-11T01:09:08.533583Z","signature_b64":"dFul52oegM0oLA0V5ZeMa62IDYWABzizh8DS1f2Pr9eP8skdBTuxRB2vRgv8KnHL5fxHHaNR754tkzi90gFXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b19440a93d97001d0205720b5375e3ba964fc9262137965378b0857b7bd52d0f","last_reissued_at":"2026-06-11T01:09:08.532393Z","signature_status":"signed_v1","first_computed_at":"2026-06-11T01:09:08.532393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Towards higher Frobenius functors for symmetric tensor categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Johannes Flake, Kevin Coulembier","submitted_at":"2024-05-29T20:41:33Z","abstract_excerpt":"We develop theory and examples of monoidal functors on tensor categories in positive characteristic that generalise the Frobenius functor from \\cite{Os, EOf, Tann}. The latter has proved to be a powerful tool in the ongoing classification of tensor categories of moderate growth, and we demonstrate the similar potential of the generalisations. More explicitly, we describe a new construction of the generalised Verlinde categories $Ver_{p^n}$ in terms of representation categories of elementary abelian $p$-groups. This leads to families of functors relating to $Ver_{p^n}$ that we conjecture, and p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.19506","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.19506/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2405.19506","created_at":"2026-06-11T01:09:08.532561+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.19506v2","created_at":"2026-06-11T01:09:08.532561+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.19506","created_at":"2026-06-11T01:09:08.532561+00:00"},{"alias_kind":"pith_short_12","alias_value":"WGKEBKJ5S4AB","created_at":"2026-06-11T01:09:08.532561+00:00"},{"alias_kind":"pith_short_16","alias_value":"WGKEBKJ5S4AB2AQF","created_at":"2026-06-11T01:09:08.532561+00:00"},{"alias_kind":"pith_short_8","alias_value":"WGKEBKJ5","created_at":"2026-06-11T01:09:08.532561+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.07377","citing_title":"Semisimplifying categorical Heisenberg actions and periodic equivalences","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WGKEBKJ5S4AB2AQFOIFVG5PDXK","json":"https://pith.science/pith/WGKEBKJ5S4AB2AQFOIFVG5PDXK.json","graph_json":"https://pith.science/api/pith-number/WGKEBKJ5S4AB2AQFOIFVG5PDXK/graph.json","events_json":"https://pith.science/api/pith-number/WGKEBKJ5S4AB2AQFOIFVG5PDXK/events.json","paper":"https://pith.science/paper/WGKEBKJ5"},"agent_actions":{"view_html":"https://pith.science/pith/WGKEBKJ5S4AB2AQFOIFVG5PDXK","download_json":"https://pith.science/pith/WGKEBKJ5S4AB2AQFOIFVG5PDXK.json","view_paper":"https://pith.science/paper/WGKEBKJ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.19506&json=true","fetch_graph":"https://pith.science/api/pith-number/WGKEBKJ5S4AB2AQFOIFVG5PDXK/graph.json","fetch_events":"https://pith.science/api/pith-number/WGKEBKJ5S4AB2AQFOIFVG5PDXK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WGKEBKJ5S4AB2AQFOIFVG5PDXK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WGKEBKJ5S4AB2AQFOIFVG5PDXK/action/storage_attestation","attest_author":"https://pith.science/pith/WGKEBKJ5S4AB2AQFOIFVG5PDXK/action/author_attestation","sign_citation":"https://pith.science/pith/WGKEBKJ5S4AB2AQFOIFVG5PDXK/action/citation_signature","submit_replication":"https://pith.science/pith/WGKEBKJ5S4AB2AQFOIFVG5PDXK/action/replication_record"}},"created_at":"2026-06-11T01:09:08.532561+00:00","updated_at":"2026-06-11T01:09:08.532561+00:00"}