{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:CCSSEHDN424ZZZWV5EUYJCEM4C","short_pith_number":"pith:CCSSEHDN","schema_version":"1.0","canonical_sha256":"10a5221c6de6b99ce6d5e92984888ce09123944f20d0ea686518398bbd3cf841","source":{"kind":"arxiv","id":"1309.4030","version":2},"attestation_state":"computed","paper":{"title":"Perfect powers expressible as sums of two fifth or seventh powers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Samir Siksek, Sander R. Dahmen","submitted_at":"2013-09-16T16:39:55Z","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."},"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":"1309.4030","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-16T16:39:55Z","cross_cats_sorted":[],"title_canon_sha256":"8f9069631e5958387065207e4f2ed82fec8eab130c7755345aed510c9ad6f91e","abstract_canon_sha256":"cd26fed9453a5073b5e85e0fe63aa32d470ba48c0eab7cec552396bd93231148"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:10.234813Z","signature_b64":"5cqhtVz6+zMAp2fcupJY0OBku2fN28bHblWgZcWc/fFgWXupit/5UAAL6bF6k3LRGXNNu74SsfI3lhP3maSeCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10a5221c6de6b99ce6d5e92984888ce09123944f20d0ea686518398bbd3cf841","last_reissued_at":"2026-05-18T03:01:10.234148Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:10.234148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Perfect powers expressible as sums of two fifth or seventh powers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Samir Siksek, Sander R. Dahmen","submitted_at":"2013-09-16T16:39:55Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4030","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":""},"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":"1309.4030","created_at":"2026-05-18T03:01:10.234256+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.4030v2","created_at":"2026-05-18T03:01:10.234256+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4030","created_at":"2026-05-18T03:01:10.234256+00:00"},{"alias_kind":"pith_short_12","alias_value":"CCSSEHDN424Z","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"CCSSEHDN424ZZZWV","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"CCSSEHDN","created_at":"2026-05-18T12:27:40.988391+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/CCSSEHDN424ZZZWV5EUYJCEM4C","json":"https://pith.science/pith/CCSSEHDN424ZZZWV5EUYJCEM4C.json","graph_json":"https://pith.science/api/pith-number/CCSSEHDN424ZZZWV5EUYJCEM4C/graph.json","events_json":"https://pith.science/api/pith-number/CCSSEHDN424ZZZWV5EUYJCEM4C/events.json","paper":"https://pith.science/paper/CCSSEHDN"},"agent_actions":{"view_html":"https://pith.science/pith/CCSSEHDN424ZZZWV5EUYJCEM4C","download_json":"https://pith.science/pith/CCSSEHDN424ZZZWV5EUYJCEM4C.json","view_paper":"https://pith.science/paper/CCSSEHDN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.4030&json=true","fetch_graph":"https://pith.science/api/pith-number/CCSSEHDN424ZZZWV5EUYJCEM4C/graph.json","fetch_events":"https://pith.science/api/pith-number/CCSSEHDN424ZZZWV5EUYJCEM4C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CCSSEHDN424ZZZWV5EUYJCEM4C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CCSSEHDN424ZZZWV5EUYJCEM4C/action/storage_attestation","attest_author":"https://pith.science/pith/CCSSEHDN424ZZZWV5EUYJCEM4C/action/author_attestation","sign_citation":"https://pith.science/pith/CCSSEHDN424ZZZWV5EUYJCEM4C/action/citation_signature","submit_replication":"https://pith.science/pith/CCSSEHDN424ZZZWV5EUYJCEM4C/action/replication_record"}},"created_at":"2026-05-18T03:01:10.234256+00:00","updated_at":"2026-05-18T03:01:10.234256+00:00"}