{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:6M46TKUVVKX5DEKVZN4GSGKQ3U","short_pith_number":"pith:6M46TKUV","schema_version":"1.0","canonical_sha256":"f339e9aa95aaafd19155cb78691950dd30afec6351c92463aacdecc4b56a8859","source":{"kind":"arxiv","id":"1411.7537","version":1},"attestation_state":"computed","paper":{"title":"\\'Equation de Fermat et nombres premiers inertes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alain Kraus","submitted_at":"2014-11-27T10:39:51Z","abstract_excerpt":"Let $K$ be a number field and $p$ a prime number $\\geq 5$. Let us denote by $\\mu_p$ the group of the $p$th roots of unity. We define $p$ to be $K$-regular if $p$ does not divide the class number of the field $K(\\mu_p)$. Under the assumption that $p$ is $K$-regular and inert in $K$, we establish the second case of Fermat's Last Theorem over $K$ for the exponent $p$. We use in the proof classical arguments, as well as Faltings' theorem stating that a curve of genus at least two over $K$ has a finite number of $K$-rational points. Moreover, if $K$ is an imaginary quadratic field, other than ${\\bf"},"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":"1411.7537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-11-27T10:39:51Z","cross_cats_sorted":[],"title_canon_sha256":"d8c80190c4cb7141b1053e8eceb8054ea939d5558a36fa3b6ab40f3292f57e01","abstract_canon_sha256":"fab57506a630b4012bf5e08c316f16f56d3d0085c04306953b4b1d287d00518b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:37.733323Z","signature_b64":"Xy2Wc1OvvmPEkvKPXJ4PcCEfpqmziBjyn2/fDh4KOlqmftNspy5Noyav+wy1s4a0JNxB0WI9E31EKQ0lS57qCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f339e9aa95aaafd19155cb78691950dd30afec6351c92463aacdecc4b56a8859","last_reissued_at":"2026-05-18T02:32:37.732905Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:37.732905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"\\'Equation de Fermat et nombres premiers inertes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alain Kraus","submitted_at":"2014-11-27T10:39:51Z","abstract_excerpt":"Let $K$ be a number field and $p$ a prime number $\\geq 5$. Let us denote by $\\mu_p$ the group of the $p$th roots of unity. We define $p$ to be $K$-regular if $p$ does not divide the class number of the field $K(\\mu_p)$. Under the assumption that $p$ is $K$-regular and inert in $K$, we establish the second case of Fermat's Last Theorem over $K$ for the exponent $p$. We use in the proof classical arguments, as well as Faltings' theorem stating that a curve of genus at least two over $K$ has a finite number of $K$-rational points. Moreover, if $K$ is an imaginary quadratic field, other than ${\\bf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7537","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":"1411.7537","created_at":"2026-05-18T02:32:37.732966+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.7537v1","created_at":"2026-05-18T02:32:37.732966+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.7537","created_at":"2026-05-18T02:32:37.732966+00:00"},{"alias_kind":"pith_short_12","alias_value":"6M46TKUVVKX5","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"6M46TKUVVKX5DEKV","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"6M46TKUV","created_at":"2026-05-18T12:28:16.859392+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/6M46TKUVVKX5DEKVZN4GSGKQ3U","json":"https://pith.science/pith/6M46TKUVVKX5DEKVZN4GSGKQ3U.json","graph_json":"https://pith.science/api/pith-number/6M46TKUVVKX5DEKVZN4GSGKQ3U/graph.json","events_json":"https://pith.science/api/pith-number/6M46TKUVVKX5DEKVZN4GSGKQ3U/events.json","paper":"https://pith.science/paper/6M46TKUV"},"agent_actions":{"view_html":"https://pith.science/pith/6M46TKUVVKX5DEKVZN4GSGKQ3U","download_json":"https://pith.science/pith/6M46TKUVVKX5DEKVZN4GSGKQ3U.json","view_paper":"https://pith.science/paper/6M46TKUV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.7537&json=true","fetch_graph":"https://pith.science/api/pith-number/6M46TKUVVKX5DEKVZN4GSGKQ3U/graph.json","fetch_events":"https://pith.science/api/pith-number/6M46TKUVVKX5DEKVZN4GSGKQ3U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6M46TKUVVKX5DEKVZN4GSGKQ3U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6M46TKUVVKX5DEKVZN4GSGKQ3U/action/storage_attestation","attest_author":"https://pith.science/pith/6M46TKUVVKX5DEKVZN4GSGKQ3U/action/author_attestation","sign_citation":"https://pith.science/pith/6M46TKUVVKX5DEKVZN4GSGKQ3U/action/citation_signature","submit_replication":"https://pith.science/pith/6M46TKUVVKX5DEKVZN4GSGKQ3U/action/replication_record"}},"created_at":"2026-05-18T02:32:37.732966+00:00","updated_at":"2026-05-18T02:32:37.732966+00:00"}