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Our description takes a unified form for distinct totally ramified places of degree one.","weakest_assumption":"The assumption that the place is totally ramified of degree one on the Kummer extension y^m = f(x), with the description holding uniformly without additional restrictions on the ramification or the polynomial f beyond the Kummer setup."}},"verdict_id":"f7df0384-448d-4c9a-b3b0-87cbf578e42e"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1c79dbfac7c06cf7a3118efd0a9bc139d90af568e95f2f65050b7a0f921efbb8","target":"record","created_at":"2026-05-17T23:39:05Z","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":"cac63ac7a91b745b7cfb97e4b6af66d117d7aefcc4738f986a3ae738a221c3c4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-14T08:54:10Z","title_canon_sha256":"bc14ba4a47a28998215f4728d2214ca4fac25bd095986b0d7d9e30a5ed316556"},"schema_version":"1.0","source":{"id":"2605.14583","kind":"arxiv","version":1}},"canonical_sha256":"3f3dec2a71549d2c556e035d5f2608e2509da17997f8cfa8663b086080a1903c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f3dec2a71549d2c556e035d5f2608e2509da17997f8cfa8663b086080a1903c","first_computed_at":"2026-05-17T23:39:05.338853Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:05.338853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fSqTM1bae/JMAn/dwiWomUHZ1GJKanECCb67WSHIwpUQSBzlnKvasCfXumi2AMcxkoIn2iakdBeBU15XeDH7Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:05.339490Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.14583","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c79dbfac7c06cf7a3118efd0a9bc139d90af568e95f2f65050b7a0f921efbb8","sha256:d6c8ebf74e5465f41c5ac0b725e241ee9535141ef68c2c670c1f34b6542ab6f8"],"state_sha256":"c57cc305fdbfd69a59a8c21aab343d2e6ae692a2483636097138861551aa974d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ojaWPz+QDZJS1V0LbL2qz68nhVVOhWnJ7EMM0dSvAaMfu25bBIlQOS2TJ77IP0ccNUkR2PlBAYaORBJsMvwrDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T03:27:53.620472Z","bundle_sha256":"b18bf35b2dbae4a4b67b2cbcc71f5471987c5593c02f589920eb93ee3d2469af"}}