{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NOOEXLGZJAQ2RZH2BNCQW23TTN","short_pith_number":"pith:NOOEXLGZ","canonical_record":{"source":{"id":"1703.05058","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-15T10:11:45Z","cross_cats_sorted":[],"title_canon_sha256":"fe10d41f1914c80b27c8866d7c3b422c60e5f86258790b33f54522b2846b75cb","abstract_canon_sha256":"a043877585a0f21d57de802b4573dd5d587ac594a80ef3a79a7b7d8c994830c9"},"schema_version":"1.0"},"canonical_sha256":"6b9c4bacd94821a8e4fa0b450b6b739b5f2f6476fb5a082198e61b6406ccf045","source":{"kind":"arxiv","id":"1703.05058","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05058","created_at":"2026-05-17T23:43:23Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05058v3","created_at":"2026-05-17T23:43:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05058","created_at":"2026-05-17T23:43:23Z"},{"alias_kind":"pith_short_12","alias_value":"NOOEXLGZJAQ2","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NOOEXLGZJAQ2RZH2","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NOOEXLGZ","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NOOEXLGZJAQ2RZH2BNCQW23TTN","target":"record","payload":{"canonical_record":{"source":{"id":"1703.05058","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-15T10:11:45Z","cross_cats_sorted":[],"title_canon_sha256":"fe10d41f1914c80b27c8866d7c3b422c60e5f86258790b33f54522b2846b75cb","abstract_canon_sha256":"a043877585a0f21d57de802b4573dd5d587ac594a80ef3a79a7b7d8c994830c9"},"schema_version":"1.0"},"canonical_sha256":"6b9c4bacd94821a8e4fa0b450b6b739b5f2f6476fb5a082198e61b6406ccf045","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:23.991003Z","signature_b64":"EsWST4tjcgo5KEwX3loF0bSvq+/dh77F2lFLXVuoTwPXlqCm9mQMuPRHKi90PHpDiRyGsBtunZm4zyOix7IbAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b9c4bacd94821a8e4fa0b450b6b739b5f2f6476fb5a082198e61b6406ccf045","last_reissued_at":"2026-05-17T23:43:23.990330Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:23.990330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.05058","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:43:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RtoXKwDxLOKcUtbfHnsaMxbLK8TyqmKy0XIhRfRQbKkxiK8rhGOQK8y+kwxzg1vVQemORa5X6vinSxPsrE5YCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:58:55.921215Z"},"content_sha256":"87cfb8491167b4a8484fdb19875f159a9fd7212dd6b1571b4812ebb7e66eff1c","schema_version":"1.0","event_id":"sha256:87cfb8491167b4a8484fdb19875f159a9fd7212dd6b1571b4812ebb7e66eff1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NOOEXLGZJAQ2RZH2BNCQW23TTN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The generalized Fermat equation with exponents 2, 3, n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bartosz Naskrecki, Michael Stoll, Nuno Freitas","submitted_at":"2017-03-15T10:11:45Z","abstract_excerpt":"We study the Generalized Fermat Equation $x^2 + y^3 = z^p$, to be solved in coprime integers, where $p \\ge 7$ is prime. Using modularity and level lowering techniques, the problem can be reduced to the determination of the sets of rational points satisfying certain 2-adic and 3-adic conditions on a finite set of twists of the modular curve $X(p)$.\n  We first develop new local criteria to decide if two elliptic curves with certain types of potentially good reduction at 2 and 3 can have symplectically or anti-symplectically isomorphic $p$-torsion modules. Using these criteria we produce the mini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05058","kind":"arxiv","version":3},"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":"2026-05-17T23:43:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8ERwwZztoDCy1QHnxLFjHAs6MSugYlmNvnIc8J8D6DRyrMDpigi9XcSVj9/sfJdh5t02PgOb0ToKZwz6QMptBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:58:55.921885Z"},"content_sha256":"abad794de038968d034172f0ef343a305717d7206ef55da676622a285e6cacc9","schema_version":"1.0","event_id":"sha256:abad794de038968d034172f0ef343a305717d7206ef55da676622a285e6cacc9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NOOEXLGZJAQ2RZH2BNCQW23TTN/bundle.json","state_url":"https://pith.science/pith/NOOEXLGZJAQ2RZH2BNCQW23TTN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NOOEXLGZJAQ2RZH2BNCQW23TTN/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":"2026-05-30T13:58:55Z","links":{"resolver":"https://pith.science/pith/NOOEXLGZJAQ2RZH2BNCQW23TTN","bundle":"https://pith.science/pith/NOOEXLGZJAQ2RZH2BNCQW23TTN/bundle.json","state":"https://pith.science/pith/NOOEXLGZJAQ2RZH2BNCQW23TTN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NOOEXLGZJAQ2RZH2BNCQW23TTN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NOOEXLGZJAQ2RZH2BNCQW23TTN","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":"a043877585a0f21d57de802b4573dd5d587ac594a80ef3a79a7b7d8c994830c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-15T10:11:45Z","title_canon_sha256":"fe10d41f1914c80b27c8866d7c3b422c60e5f86258790b33f54522b2846b75cb"},"schema_version":"1.0","source":{"id":"1703.05058","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05058","created_at":"2026-05-17T23:43:23Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05058v3","created_at":"2026-05-17T23:43:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05058","created_at":"2026-05-17T23:43:23Z"},{"alias_kind":"pith_short_12","alias_value":"NOOEXLGZJAQ2","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NOOEXLGZJAQ2RZH2","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NOOEXLGZ","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:abad794de038968d034172f0ef343a305717d7206ef55da676622a285e6cacc9","target":"graph","created_at":"2026-05-17T23:43:23Z","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 study the Generalized Fermat Equation $x^2 + y^3 = z^p$, to be solved in coprime integers, where $p \\ge 7$ is prime. Using modularity and level lowering techniques, the problem can be reduced to the determination of the sets of rational points satisfying certain 2-adic and 3-adic conditions on a finite set of twists of the modular curve $X(p)$.\n  We first develop new local criteria to decide if two elliptic curves with certain types of potentially good reduction at 2 and 3 can have symplectically or anti-symplectically isomorphic $p$-torsion modules. Using these criteria we produce the mini","authors_text":"Bartosz Naskrecki, Michael Stoll, Nuno Freitas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-15T10:11:45Z","title":"The generalized Fermat equation with exponents 2, 3, n"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05058","kind":"arxiv","version":3},"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":"sha256:87cfb8491167b4a8484fdb19875f159a9fd7212dd6b1571b4812ebb7e66eff1c","target":"record","created_at":"2026-05-17T23:43:23Z","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":"a043877585a0f21d57de802b4573dd5d587ac594a80ef3a79a7b7d8c994830c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-15T10:11:45Z","title_canon_sha256":"fe10d41f1914c80b27c8866d7c3b422c60e5f86258790b33f54522b2846b75cb"},"schema_version":"1.0","source":{"id":"1703.05058","kind":"arxiv","version":3}},"canonical_sha256":"6b9c4bacd94821a8e4fa0b450b6b739b5f2f6476fb5a082198e61b6406ccf045","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b9c4bacd94821a8e4fa0b450b6b739b5f2f6476fb5a082198e61b6406ccf045","first_computed_at":"2026-05-17T23:43:23.990330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:23.990330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EsWST4tjcgo5KEwX3loF0bSvq+/dh77F2lFLXVuoTwPXlqCm9mQMuPRHKi90PHpDiRyGsBtunZm4zyOix7IbAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:23.991003Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05058","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87cfb8491167b4a8484fdb19875f159a9fd7212dd6b1571b4812ebb7e66eff1c","sha256:abad794de038968d034172f0ef343a305717d7206ef55da676622a285e6cacc9"],"state_sha256":"24505e36d02f2f6d5230e3d0fe758616d2dc170405b8a2a2a3f3dc4c46e5f4dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XCBdesn/EmnqmYEJfYjzokkH/XOwJBuPzdyu/iy4G4OM36pV3Xq5/uNclMMdZy6dmmSYLrvmDeE85ML7uW30AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T13:58:55.925417Z","bundle_sha256":"3093ab2d5242695b3f8f14dc7356a8bd5e1ba22431ca5ca90f176af395f8b480"}}