{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6O6RLUYZ6DDEMVUSDQ62WERTAJ","short_pith_number":"pith:6O6RLUYZ","schema_version":"1.0","canonical_sha256":"f3bd15d319f0c64656921c3dab12330279cbf555aec4ef6b19c301acc90c646d","source":{"kind":"arxiv","id":"1709.08356","version":1},"attestation_state":"computed","paper":{"title":"Le th\\'eor\\`eme de Fermat sur certains corps de nombres totalement r\\'eels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alain Kraus","submitted_at":"2017-09-25T07:49:57Z","abstract_excerpt":"Let $K$ be a totally real number field. For all prime number $p\\geq 5$, let us denote by $F_p$ the Fermat curve of equation $x^p+y^p+z^p=0$. Under the assumption that $2$ is totally ramified in $K$, we establish some results about the set $F_p(K)$ of points of $F_p$ rational over $K$. We obtain a criterion so that the asymptotic Fermat's Last Theorem is true over $K$, criterion related to the set of Hilbert modular cusp newforms over $K$, of parallel weight $2$ and of level the prime ideal above $2$. It is often simply testable numerically, particularly if the narrow class number of $K$ is $1$"},"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":"1709.08356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-25T07:49:57Z","cross_cats_sorted":[],"title_canon_sha256":"5cd6386cbd34d5058601e5ef0f4fc8f6fa0516a2ad2f4d15f15b937d418fb139","abstract_canon_sha256":"e5646ce7845e73e3da22780b28356fc098d6a59b565dc740985e6d1ff8253075"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:16.393810Z","signature_b64":"AR9F5Wdqkl5S7WutUxNRiyOU1VDGJiiTWLwYm1fIlb1SDXh4c+puErjorVbA74X6+sMrZ2b4Bv5RO2XqCazsAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3bd15d319f0c64656921c3dab12330279cbf555aec4ef6b19c301acc90c646d","last_reissued_at":"2026-05-17T23:50:16.393231Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:16.393231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Le th\\'eor\\`eme de Fermat sur certains corps de nombres totalement r\\'eels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alain Kraus","submitted_at":"2017-09-25T07:49:57Z","abstract_excerpt":"Let $K$ be a totally real number field. For all prime number $p\\geq 5$, let us denote by $F_p$ the Fermat curve of equation $x^p+y^p+z^p=0$. Under the assumption that $2$ is totally ramified in $K$, we establish some results about the set $F_p(K)$ of points of $F_p$ rational over $K$. We obtain a criterion so that the asymptotic Fermat's Last Theorem is true over $K$, criterion related to the set of Hilbert modular cusp newforms over $K$, of parallel weight $2$ and of level the prime ideal above $2$. It is often simply testable numerically, particularly if the narrow class number of $K$ is $1$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08356","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":"1709.08356","created_at":"2026-05-17T23:50:16.393303+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.08356v1","created_at":"2026-05-17T23:50:16.393303+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.08356","created_at":"2026-05-17T23:50:16.393303+00:00"},{"alias_kind":"pith_short_12","alias_value":"6O6RLUYZ6DDE","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6O6RLUYZ6DDEMVUS","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6O6RLUYZ","created_at":"2026-05-18T12:31:03.183658+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/6O6RLUYZ6DDEMVUSDQ62WERTAJ","json":"https://pith.science/pith/6O6RLUYZ6DDEMVUSDQ62WERTAJ.json","graph_json":"https://pith.science/api/pith-number/6O6RLUYZ6DDEMVUSDQ62WERTAJ/graph.json","events_json":"https://pith.science/api/pith-number/6O6RLUYZ6DDEMVUSDQ62WERTAJ/events.json","paper":"https://pith.science/paper/6O6RLUYZ"},"agent_actions":{"view_html":"https://pith.science/pith/6O6RLUYZ6DDEMVUSDQ62WERTAJ","download_json":"https://pith.science/pith/6O6RLUYZ6DDEMVUSDQ62WERTAJ.json","view_paper":"https://pith.science/paper/6O6RLUYZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.08356&json=true","fetch_graph":"https://pith.science/api/pith-number/6O6RLUYZ6DDEMVUSDQ62WERTAJ/graph.json","fetch_events":"https://pith.science/api/pith-number/6O6RLUYZ6DDEMVUSDQ62WERTAJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6O6RLUYZ6DDEMVUSDQ62WERTAJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6O6RLUYZ6DDEMVUSDQ62WERTAJ/action/storage_attestation","attest_author":"https://pith.science/pith/6O6RLUYZ6DDEMVUSDQ62WERTAJ/action/author_attestation","sign_citation":"https://pith.science/pith/6O6RLUYZ6DDEMVUSDQ62WERTAJ/action/citation_signature","submit_replication":"https://pith.science/pith/6O6RLUYZ6DDEMVUSDQ62WERTAJ/action/replication_record"}},"created_at":"2026-05-17T23:50:16.393303+00:00","updated_at":"2026-05-17T23:50:16.393303+00:00"}