{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:D3QSFW6CEM7XAARRZJDX6CNMCN","short_pith_number":"pith:D3QSFW6C","schema_version":"1.0","canonical_sha256":"1ee122dbc2233f700231ca477f09ac135bc711b85b0c9c0c02f49b0b7ea32d04","source":{"kind":"arxiv","id":"1410.0872","version":1},"attestation_state":"computed","paper":{"title":"Rank-2 syzygy bundles on Fermat curves and an application to Hilbert-Kunz functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Almar Kaid, Daniel Brinkmann","submitted_at":"2014-10-03T14:55:37Z","abstract_excerpt":"In this paper we describe the Frobenius pull-backs of the syzygy bundles $Syz_C(X^a, Y^a, Z^a)$, $a \\geq 1$, on the projective Fermat curve C of degree n in characteristics coprime to n, either by giving their strong Harder-Narasimhan Filtration if $Syz_C(X^a, Y^a, Z^a)$ is not strongly semistable or in the strongly semistable case by their periodicity behavior. Moreover, we apply these results to Hilbert-Kunz functions, to find Frobenius periodicities of the restricted cotangent bundle $\\Omega_{P^2}|_C$ of arbitrary length and a problem of Brenner regarding primes with strongly semistable red"},"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":"1410.0872","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-10-03T14:55:37Z","cross_cats_sorted":[],"title_canon_sha256":"9fb7e637c4246b12a48e51489386dfa61ea13ada0032739d9dd05ea600e98fad","abstract_canon_sha256":"13ce1d13f9dcca927d7f376873244b2e3d17b1267d84265ad5cbacbe2486f0d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:09.552301Z","signature_b64":"g4ogawRYfk+loK+pBcS+c0tVA4DDZm47+gxvimIQvgUo5fR7AFvEgPvWRJZ+hbkU17wIyJrri6/9wK0Gq0VkBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ee122dbc2233f700231ca477f09ac135bc711b85b0c9c0c02f49b0b7ea32d04","last_reissued_at":"2026-05-18T02:41:09.551899Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:09.551899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rank-2 syzygy bundles on Fermat curves and an application to Hilbert-Kunz functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Almar Kaid, Daniel Brinkmann","submitted_at":"2014-10-03T14:55:37Z","abstract_excerpt":"In this paper we describe the Frobenius pull-backs of the syzygy bundles $Syz_C(X^a, Y^a, Z^a)$, $a \\geq 1$, on the projective Fermat curve C of degree n in characteristics coprime to n, either by giving their strong Harder-Narasimhan Filtration if $Syz_C(X^a, Y^a, Z^a)$ is not strongly semistable or in the strongly semistable case by their periodicity behavior. Moreover, we apply these results to Hilbert-Kunz functions, to find Frobenius periodicities of the restricted cotangent bundle $\\Omega_{P^2}|_C$ of arbitrary length and a problem of Brenner regarding primes with strongly semistable red"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0872","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":"1410.0872","created_at":"2026-05-18T02:41:09.551960+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.0872v1","created_at":"2026-05-18T02:41:09.551960+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0872","created_at":"2026-05-18T02:41:09.551960+00:00"},{"alias_kind":"pith_short_12","alias_value":"D3QSFW6CEM7X","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"D3QSFW6CEM7XAARR","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"D3QSFW6C","created_at":"2026-05-18T12:28:25.294606+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/D3QSFW6CEM7XAARRZJDX6CNMCN","json":"https://pith.science/pith/D3QSFW6CEM7XAARRZJDX6CNMCN.json","graph_json":"https://pith.science/api/pith-number/D3QSFW6CEM7XAARRZJDX6CNMCN/graph.json","events_json":"https://pith.science/api/pith-number/D3QSFW6CEM7XAARRZJDX6CNMCN/events.json","paper":"https://pith.science/paper/D3QSFW6C"},"agent_actions":{"view_html":"https://pith.science/pith/D3QSFW6CEM7XAARRZJDX6CNMCN","download_json":"https://pith.science/pith/D3QSFW6CEM7XAARRZJDX6CNMCN.json","view_paper":"https://pith.science/paper/D3QSFW6C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.0872&json=true","fetch_graph":"https://pith.science/api/pith-number/D3QSFW6CEM7XAARRZJDX6CNMCN/graph.json","fetch_events":"https://pith.science/api/pith-number/D3QSFW6CEM7XAARRZJDX6CNMCN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D3QSFW6CEM7XAARRZJDX6CNMCN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D3QSFW6CEM7XAARRZJDX6CNMCN/action/storage_attestation","attest_author":"https://pith.science/pith/D3QSFW6CEM7XAARRZJDX6CNMCN/action/author_attestation","sign_citation":"https://pith.science/pith/D3QSFW6CEM7XAARRZJDX6CNMCN/action/citation_signature","submit_replication":"https://pith.science/pith/D3QSFW6CEM7XAARRZJDX6CNMCN/action/replication_record"}},"created_at":"2026-05-18T02:41:09.551960+00:00","updated_at":"2026-05-18T02:41:09.551960+00:00"}