{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NRMZIYUHT4WYX7VG2CUQHAXQOR","short_pith_number":"pith:NRMZIYUH","canonical_record":{"source":{"id":"1605.09228","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-30T13:39:27Z","cross_cats_sorted":[],"title_canon_sha256":"7a80f2afbd2499c4393db52a59e115a48482c7414e15e7a6e3dd64f32288bd9b","abstract_canon_sha256":"d81d5f74a6faa5f7402f3210b3e643b73bc3591d15f5941a7132a0ce9411ec8d"},"schema_version":"1.0"},"canonical_sha256":"6c599462879f2d8bfea6d0a90382f07476f446b706ca6cc12057a48c0a46aeec","source":{"kind":"arxiv","id":"1605.09228","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.09228","created_at":"2026-05-18T01:13:21Z"},{"alias_kind":"arxiv_version","alias_value":"1605.09228v1","created_at":"2026-05-18T01:13:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.09228","created_at":"2026-05-18T01:13:21Z"},{"alias_kind":"pith_short_12","alias_value":"NRMZIYUHT4WY","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NRMZIYUHT4WYX7VG","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NRMZIYUH","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NRMZIYUHT4WYX7VG2CUQHAXQOR","target":"record","payload":{"canonical_record":{"source":{"id":"1605.09228","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-30T13:39:27Z","cross_cats_sorted":[],"title_canon_sha256":"7a80f2afbd2499c4393db52a59e115a48482c7414e15e7a6e3dd64f32288bd9b","abstract_canon_sha256":"d81d5f74a6faa5f7402f3210b3e643b73bc3591d15f5941a7132a0ce9411ec8d"},"schema_version":"1.0"},"canonical_sha256":"6c599462879f2d8bfea6d0a90382f07476f446b706ca6cc12057a48c0a46aeec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:21.627661Z","signature_b64":"ZJiZ/iPAyNMcMSXoriqd9kO7JrYhndU4bbaRwHbFpRExORZcZmEB7Bvjl+cpeCzxi2t8IhZnvj6rVC0J1xoyDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c599462879f2d8bfea6d0a90382f07476f446b706ca6cc12057a48c0a46aeec","last_reissued_at":"2026-05-18T01:13:21.627137Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:21.627137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.09228","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"98h0ynM/qONpa3iG4eMtfquhdip+zlhwgAVo8u4oBxgGu5fJP3+gnZcd+iiQyPFYlIyR7/3s0ibK72ceFQHHBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:22:59.379409Z"},"content_sha256":"8b5472f19ee13f792a691ab6661d5142b1241e79df8c1a729507e023dbb6912c","schema_version":"1.0","event_id":"sha256:8b5472f19ee13f792a691ab6661d5142b1241e79df8c1a729507e023dbb6912c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NRMZIYUHT4WYX7VG2CUQHAXQOR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Noether's rationality problem for cyclic groups over $\\mathbb{Q}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bernat Plans","submitted_at":"2016-05-30T13:39:27Z","abstract_excerpt":"Let $p$ be a prime number. Let $C_p$, the cyclic group of order $p$, permute transitively a set of indeterminates $\\{ x_1,\\ldots ,x_p \\}$. We prove that the invariant field $\\mathbb{Q}(x_1,\\ldots ,x_p)^{C_p}$ is rational over $\\mathbb{Q}$ if and only if the $(p-1)$-th cyclotomic field $\\mathbb{Q}(\\zeta_{p-1})$ has class number one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09228","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cq6lfltTNG29PLVNGdI3yVNTF3vNk02DJJEflajXKMPADfxSf+iiTefdhFMQF6IJ3axtVWwgL93ErkzLSLSKBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:22:59.380142Z"},"content_sha256":"be1ea8bfe9d42340171ffee153bb78b2ce7ceabaf12fa7e350e44edada22651f","schema_version":"1.0","event_id":"sha256:be1ea8bfe9d42340171ffee153bb78b2ce7ceabaf12fa7e350e44edada22651f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NRMZIYUHT4WYX7VG2CUQHAXQOR/bundle.json","state_url":"https://pith.science/pith/NRMZIYUHT4WYX7VG2CUQHAXQOR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NRMZIYUHT4WYX7VG2CUQHAXQOR/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":"2026-06-09T19:22:59Z","links":{"resolver":"https://pith.science/pith/NRMZIYUHT4WYX7VG2CUQHAXQOR","bundle":"https://pith.science/pith/NRMZIYUHT4WYX7VG2CUQHAXQOR/bundle.json","state":"https://pith.science/pith/NRMZIYUHT4WYX7VG2CUQHAXQOR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NRMZIYUHT4WYX7VG2CUQHAXQOR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NRMZIYUHT4WYX7VG2CUQHAXQOR","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":"d81d5f74a6faa5f7402f3210b3e643b73bc3591d15f5941a7132a0ce9411ec8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-30T13:39:27Z","title_canon_sha256":"7a80f2afbd2499c4393db52a59e115a48482c7414e15e7a6e3dd64f32288bd9b"},"schema_version":"1.0","source":{"id":"1605.09228","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.09228","created_at":"2026-05-18T01:13:21Z"},{"alias_kind":"arxiv_version","alias_value":"1605.09228v1","created_at":"2026-05-18T01:13:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.09228","created_at":"2026-05-18T01:13:21Z"},{"alias_kind":"pith_short_12","alias_value":"NRMZIYUHT4WY","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NRMZIYUHT4WYX7VG","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NRMZIYUH","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:be1ea8bfe9d42340171ffee153bb78b2ce7ceabaf12fa7e350e44edada22651f","target":"graph","created_at":"2026-05-18T01:13:21Z","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":"Let $p$ be a prime number. Let $C_p$, the cyclic group of order $p$, permute transitively a set of indeterminates $\\{ x_1,\\ldots ,x_p \\}$. We prove that the invariant field $\\mathbb{Q}(x_1,\\ldots ,x_p)^{C_p}$ is rational over $\\mathbb{Q}$ if and only if the $(p-1)$-th cyclotomic field $\\mathbb{Q}(\\zeta_{p-1})$ has class number one.","authors_text":"Bernat Plans","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-30T13:39:27Z","title":"On Noether's rationality problem for cyclic groups over $\\mathbb{Q}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09228","kind":"arxiv","version":1},"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":"sha256:8b5472f19ee13f792a691ab6661d5142b1241e79df8c1a729507e023dbb6912c","target":"record","created_at":"2026-05-18T01:13:21Z","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":"d81d5f74a6faa5f7402f3210b3e643b73bc3591d15f5941a7132a0ce9411ec8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-05-30T13:39:27Z","title_canon_sha256":"7a80f2afbd2499c4393db52a59e115a48482c7414e15e7a6e3dd64f32288bd9b"},"schema_version":"1.0","source":{"id":"1605.09228","kind":"arxiv","version":1}},"canonical_sha256":"6c599462879f2d8bfea6d0a90382f07476f446b706ca6cc12057a48c0a46aeec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c599462879f2d8bfea6d0a90382f07476f446b706ca6cc12057a48c0a46aeec","first_computed_at":"2026-05-18T01:13:21.627137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:21.627137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZJiZ/iPAyNMcMSXoriqd9kO7JrYhndU4bbaRwHbFpRExORZcZmEB7Bvjl+cpeCzxi2t8IhZnvj6rVC0J1xoyDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:21.627661Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.09228","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b5472f19ee13f792a691ab6661d5142b1241e79df8c1a729507e023dbb6912c","sha256:be1ea8bfe9d42340171ffee153bb78b2ce7ceabaf12fa7e350e44edada22651f"],"state_sha256":"1219a32cd6343219f46c998f4d6637f83245c7a68d8338e2eec8b5f546d6ec17"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ja9m0m+g8VtAvyhwJ8+Ber/iZOafqMEa+SD05pSzy6o3gDNTytc0lobASSPWx+M9Toe2XgJyuWH96vGtgF39Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:22:59.384393Z","bundle_sha256":"b2d0cee2317efb96c390b66e7e7baf6309ba73c44598308349df5542977bc212"}}