{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:OOBMQV667A4ZJRSUEUNG4XDQMK","short_pith_number":"pith:OOBMQV66","canonical_record":{"source":{"id":"1904.02349","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-04-04T05:06:25Z","cross_cats_sorted":[],"title_canon_sha256":"c2c30c2eeb62948def8c87bc8c6b0ac684a30ac1a15e864addf2c732a5049ba9","abstract_canon_sha256":"50bd67a4d1f485c5f25f97ecf70eadbd2fa7d293e12dd9ee7ea0bfbe1d1bace6"},"schema_version":"1.0"},"canonical_sha256":"7382c857def83994c654251a6e5c706290ef85f5d074cffeebd103f54aec9fd4","source":{"kind":"arxiv","id":"1904.02349","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02349","created_at":"2026-05-17T23:49:08Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02349v2","created_at":"2026-05-17T23:49:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02349","created_at":"2026-05-17T23:49:08Z"},{"alias_kind":"pith_short_12","alias_value":"OOBMQV667A4Z","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"OOBMQV667A4ZJRSU","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"OOBMQV66","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:OOBMQV667A4ZJRSUEUNG4XDQMK","target":"record","payload":{"canonical_record":{"source":{"id":"1904.02349","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-04-04T05:06:25Z","cross_cats_sorted":[],"title_canon_sha256":"c2c30c2eeb62948def8c87bc8c6b0ac684a30ac1a15e864addf2c732a5049ba9","abstract_canon_sha256":"50bd67a4d1f485c5f25f97ecf70eadbd2fa7d293e12dd9ee7ea0bfbe1d1bace6"},"schema_version":"1.0"},"canonical_sha256":"7382c857def83994c654251a6e5c706290ef85f5d074cffeebd103f54aec9fd4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:08.554273Z","signature_b64":"OuSwiATvZPE+757YERWUnLY2inEou6XrEUqh0FnLPhIUtJhz9dqWqGRQpLi/fW4V18YqmLlqQ7+Ro0RlaGoCBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7382c857def83994c654251a6e5c706290ef85f5d074cffeebd103f54aec9fd4","last_reissued_at":"2026-05-17T23:49:08.553616Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:08.553616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.02349","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OUyLqi/ZxfrW0upgCaNREAjN/zOiBjvjudrrXLOntFyw2PX5MPPpB2rSeKdQpmn6ShYZF3OFVv8F8Soeray8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T07:06:09.008039Z"},"content_sha256":"3e8411f5a1b3c8f5ff7e7641dc5072f699e3770cf91f5b4abbc9a5277ef80dd0","schema_version":"1.0","event_id":"sha256:3e8411f5a1b3c8f5ff7e7641dc5072f699e3770cf91f5b4abbc9a5277ef80dd0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:OOBMQV667A4ZJRSUEUNG4XDQMK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic Generalized Fermat's Last Theorem over Number Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ekin Ozman, Yasemin Kara","submitted_at":"2019-04-04T05:06:25Z","abstract_excerpt":"Recent work of Freitas and Siksek showed that an asymptotic version of Fermat's Last Theorem holds for many totally real fields. Later this result was extended by Deconinck to generalized Fermat equations of the form $Ax^p +By^p +Cz^p = 0$, where A;B;C are odd integers belonging to a totally real field. Another extension was given by Sengun and Siksek. They showed that the Fermat equation holds asymptotically for imaginary quadratic number fields satisfying usual conjectures about modularity. In this work, combining their techniques we extend their results about the generalized Fermat equatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02349","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IBJaqAOp6SICKM2XFE3ti6/RmbQLE7XtBZGISUgWx8EniF6fQkGN2knP8x7vBKZ+nsJ2GPWihSd1aTs6NCL+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T07:06:09.008799Z"},"content_sha256":"2376f4e1932251bea6c1db59623ef2bb08f7ea5353689b97769e42a1b06aaa99","schema_version":"1.0","event_id":"sha256:2376f4e1932251bea6c1db59623ef2bb08f7ea5353689b97769e42a1b06aaa99"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OOBMQV667A4ZJRSUEUNG4XDQMK/bundle.json","state_url":"https://pith.science/pith/OOBMQV667A4ZJRSUEUNG4XDQMK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OOBMQV667A4ZJRSUEUNG4XDQMK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T07:06:09Z","links":{"resolver":"https://pith.science/pith/OOBMQV667A4ZJRSUEUNG4XDQMK","bundle":"https://pith.science/pith/OOBMQV667A4ZJRSUEUNG4XDQMK/bundle.json","state":"https://pith.science/pith/OOBMQV667A4ZJRSUEUNG4XDQMK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OOBMQV667A4ZJRSUEUNG4XDQMK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OOBMQV667A4ZJRSUEUNG4XDQMK","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":"50bd67a4d1f485c5f25f97ecf70eadbd2fa7d293e12dd9ee7ea0bfbe1d1bace6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-04-04T05:06:25Z","title_canon_sha256":"c2c30c2eeb62948def8c87bc8c6b0ac684a30ac1a15e864addf2c732a5049ba9"},"schema_version":"1.0","source":{"id":"1904.02349","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02349","created_at":"2026-05-17T23:49:08Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02349v2","created_at":"2026-05-17T23:49:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02349","created_at":"2026-05-17T23:49:08Z"},{"alias_kind":"pith_short_12","alias_value":"OOBMQV667A4Z","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"OOBMQV667A4ZJRSU","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"OOBMQV66","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:2376f4e1932251bea6c1db59623ef2bb08f7ea5353689b97769e42a1b06aaa99","target":"graph","created_at":"2026-05-17T23:49:08Z","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":"Recent work of Freitas and Siksek showed that an asymptotic version of Fermat's Last Theorem holds for many totally real fields. Later this result was extended by Deconinck to generalized Fermat equations of the form $Ax^p +By^p +Cz^p = 0$, where A;B;C are odd integers belonging to a totally real field. Another extension was given by Sengun and Siksek. They showed that the Fermat equation holds asymptotically for imaginary quadratic number fields satisfying usual conjectures about modularity. In this work, combining their techniques we extend their results about the generalized Fermat equatio","authors_text":"Ekin Ozman, Yasemin Kara","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-04-04T05:06:25Z","title":"Asymptotic Generalized Fermat's Last Theorem over Number Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02349","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":"sha256:3e8411f5a1b3c8f5ff7e7641dc5072f699e3770cf91f5b4abbc9a5277ef80dd0","target":"record","created_at":"2026-05-17T23:49:08Z","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":"50bd67a4d1f485c5f25f97ecf70eadbd2fa7d293e12dd9ee7ea0bfbe1d1bace6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-04-04T05:06:25Z","title_canon_sha256":"c2c30c2eeb62948def8c87bc8c6b0ac684a30ac1a15e864addf2c732a5049ba9"},"schema_version":"1.0","source":{"id":"1904.02349","kind":"arxiv","version":2}},"canonical_sha256":"7382c857def83994c654251a6e5c706290ef85f5d074cffeebd103f54aec9fd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7382c857def83994c654251a6e5c706290ef85f5d074cffeebd103f54aec9fd4","first_computed_at":"2026-05-17T23:49:08.553616Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:08.553616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OuSwiATvZPE+757YERWUnLY2inEou6XrEUqh0FnLPhIUtJhz9dqWqGRQpLi/fW4V18YqmLlqQ7+Ro0RlaGoCBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:08.554273Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.02349","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e8411f5a1b3c8f5ff7e7641dc5072f699e3770cf91f5b4abbc9a5277ef80dd0","sha256:2376f4e1932251bea6c1db59623ef2bb08f7ea5353689b97769e42a1b06aaa99"],"state_sha256":"5fcae2af67a8b603ea39531337972b5294bad776f9db34aec08f7e24d00c36c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H/t8PS/eWXHDVRJosCqKtdeZFfTaBokrNmTWnutldJZL3ihRcCWkzP6Scqz8AEo1S40teT2ttPqn1+F/r7GBBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T07:06:09.012866Z","bundle_sha256":"4c9bb6912e533e185a129eb83b862c8564a27130db764d46d988b894e797ef93"}}