{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CCSSEHDN424ZZZWV5EUYJCEM4C","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":"cd26fed9453a5073b5e85e0fe63aa32d470ba48c0eab7cec552396bd93231148","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-16T16:39:55Z","title_canon_sha256":"8f9069631e5958387065207e4f2ed82fec8eab130c7755345aed510c9ad6f91e"},"schema_version":"1.0","source":{"id":"1309.4030","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4030","created_at":"2026-05-18T03:01:10Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4030v2","created_at":"2026-05-18T03:01:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4030","created_at":"2026-05-18T03:01:10Z"},{"alias_kind":"pith_short_12","alias_value":"CCSSEHDN424Z","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CCSSEHDN424ZZZWV","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CCSSEHDN","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:7cb264ef6d3a8e7ab8182a5386b4e51bb9d6d652975da5b7e7e1fb7a4fe1aaef","target":"graph","created_at":"2026-05-18T03:01:10Z","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":"We show that the generalized Fermat equations with signatures (5,5,7), (5,5,19), and (7,7,5) (and unit coefficients) have no non-trivial primitive integer solutions. Assuming GRH, we also prove the nonexistence of non-trivial primitive integer solutions for the signatures (5,5,11), (5,5,13), and (7,7,11). The main ingredients for obtaining our results are descent techniques, the method of Chabauty-Coleman, and the modular approach to Diophantine equations.","authors_text":"Samir Siksek, Sander R. Dahmen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-16T16:39:55Z","title":"Perfect powers expressible as sums of two fifth or seventh powers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4030","kind":"arxiv","version":2},"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":"sha256:424df4900dfb5b38d036deaa5e2f9afbdd4ab32922d637d78bcd91aabe66f7db","target":"record","created_at":"2026-05-18T03:01:10Z","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":"cd26fed9453a5073b5e85e0fe63aa32d470ba48c0eab7cec552396bd93231148","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-16T16:39:55Z","title_canon_sha256":"8f9069631e5958387065207e4f2ed82fec8eab130c7755345aed510c9ad6f91e"},"schema_version":"1.0","source":{"id":"1309.4030","kind":"arxiv","version":2}},"canonical_sha256":"10a5221c6de6b99ce6d5e92984888ce09123944f20d0ea686518398bbd3cf841","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10a5221c6de6b99ce6d5e92984888ce09123944f20d0ea686518398bbd3cf841","first_computed_at":"2026-05-18T03:01:10.234148Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:10.234148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5cqhtVz6+zMAp2fcupJY0OBku2fN28bHblWgZcWc/fFgWXupit/5UAAL6bF6k3LRGXNNu74SsfI3lhP3maSeCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:10.234813Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.4030","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:424df4900dfb5b38d036deaa5e2f9afbdd4ab32922d637d78bcd91aabe66f7db","sha256:7cb264ef6d3a8e7ab8182a5386b4e51bb9d6d652975da5b7e7e1fb7a4fe1aaef"],"state_sha256":"324949983533b2ed4c2891e647182137d7a8a27c3cefd3aca032edc4e2f62c6d"}