{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:D3QSFW6CEM7XAARRZJDX6CNMCN","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":"13ce1d13f9dcca927d7f376873244b2e3d17b1267d84265ad5cbacbe2486f0d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-10-03T14:55:37Z","title_canon_sha256":"9fb7e637c4246b12a48e51489386dfa61ea13ada0032739d9dd05ea600e98fad"},"schema_version":"1.0","source":{"id":"1410.0872","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0872","created_at":"2026-05-18T02:41:09Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0872v1","created_at":"2026-05-18T02:41:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0872","created_at":"2026-05-18T02:41:09Z"},{"alias_kind":"pith_short_12","alias_value":"D3QSFW6CEM7X","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"D3QSFW6CEM7XAARR","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"D3QSFW6C","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:00f944acba29a2e38e4d43fa07037ef8d8fe2c5ab0625c998c46eed1bc051b06","target":"graph","created_at":"2026-05-18T02:41:09Z","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":"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","authors_text":"Almar Kaid, Daniel Brinkmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-10-03T14:55:37Z","title":"Rank-2 syzygy bundles on Fermat curves and an application to Hilbert-Kunz functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0872","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":"sha256:74ecef7473db7b212e468e3e7d81a73693d6f8dc254d03ffda1d69ce8ebee64a","target":"record","created_at":"2026-05-18T02:41:09Z","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":"13ce1d13f9dcca927d7f376873244b2e3d17b1267d84265ad5cbacbe2486f0d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-10-03T14:55:37Z","title_canon_sha256":"9fb7e637c4246b12a48e51489386dfa61ea13ada0032739d9dd05ea600e98fad"},"schema_version":"1.0","source":{"id":"1410.0872","kind":"arxiv","version":1}},"canonical_sha256":"1ee122dbc2233f700231ca477f09ac135bc711b85b0c9c0c02f49b0b7ea32d04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ee122dbc2233f700231ca477f09ac135bc711b85b0c9c0c02f49b0b7ea32d04","first_computed_at":"2026-05-18T02:41:09.551899Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:09.551899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g4ogawRYfk+loK+pBcS+c0tVA4DDZm47+gxvimIQvgUo5fR7AFvEgPvWRJZ+hbkU17wIyJrri6/9wK0Gq0VkBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:09.552301Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.0872","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74ecef7473db7b212e468e3e7d81a73693d6f8dc254d03ffda1d69ce8ebee64a","sha256:00f944acba29a2e38e4d43fa07037ef8d8fe2c5ab0625c998c46eed1bc051b06"],"state_sha256":"a7a5b5b751027d0b6bacd1f53e76df737f832fe6a5bd8a761ff8989e296b3312"}