{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CSEYR2JSRKTT3TIDA64XDPD72X","short_pith_number":"pith:CSEYR2JS","canonical_record":{"source":{"id":"1109.2966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-09-14T02:04:37Z","cross_cats_sorted":["math.AG","math.NT"],"title_canon_sha256":"481d329e31b724f2ac8ca384ef263210d07a543e27a901e4ebdb43ec03ff699e","abstract_canon_sha256":"110d1f25c5ca937991b081f1b509972fa23e0dddcf7512accb43d2bee1f837cb"},"schema_version":"1.0"},"canonical_sha256":"148988e9328aa73dcd0307b971bc7fd5d5f5a909f23c01f1f3c2c0c733df1a43","source":{"kind":"arxiv","id":"1109.2966","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2966","created_at":"2026-05-18T04:13:06Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2966v1","created_at":"2026-05-18T04:13:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2966","created_at":"2026-05-18T04:13:06Z"},{"alias_kind":"pith_short_12","alias_value":"CSEYR2JSRKTT","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CSEYR2JSRKTT3TID","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CSEYR2JS","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CSEYR2JSRKTT3TIDA64XDPD72X","target":"record","payload":{"canonical_record":{"source":{"id":"1109.2966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-09-14T02:04:37Z","cross_cats_sorted":["math.AG","math.NT"],"title_canon_sha256":"481d329e31b724f2ac8ca384ef263210d07a543e27a901e4ebdb43ec03ff699e","abstract_canon_sha256":"110d1f25c5ca937991b081f1b509972fa23e0dddcf7512accb43d2bee1f837cb"},"schema_version":"1.0"},"canonical_sha256":"148988e9328aa73dcd0307b971bc7fd5d5f5a909f23c01f1f3c2c0c733df1a43","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:06.615975Z","signature_b64":"w31XDm3RIgXPzQIyLNs8sYQPDVZYto0K6NWA3j38Ig/9J15ca8wOYoElMaHQG1TrlXMf9UM59VjxAJnaM9KMBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"148988e9328aa73dcd0307b971bc7fd5d5f5a909f23c01f1f3c2c0c733df1a43","last_reissued_at":"2026-05-18T04:13:06.615562Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:06.615562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.2966","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":"2026-05-18T04:13:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b6vvdS5SDQb54KQvtViwPRVmrsgu3YC8mLiusX0dyTGgATun+veu/ZLC9KnFttoYWdWjvckMVPrsuYULGv3FCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:39:43.527562Z"},"content_sha256":"2d56cac1c85d48c29677bc2567cb098f166ba9e8f246e94828a9eb4a2bca3a9b","schema_version":"1.0","event_id":"sha256:2d56cac1c85d48c29677bc2567cb098f166ba9e8f246e94828a9eb4a2bca3a9b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CSEYR2JSRKTT3TIDA64XDPD72X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unramified Brauer groups for groups of order p^5","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.AC","authors_text":"Akinari Hoshi, Ming-chang Kang","submitted_at":"2011-09-14T02:04:37Z","abstract_excerpt":"Let $k$ be any field, $G$ be a finite group acting on the rational function field $k(x_g : g\\in G)$ by $h\\cdot x_g=x_{hg}$ for any $h,g\\in G$. Define $k(G)=k(x_g : g\\in G)^G$. Noether's problem asks whether $k(G)$ is rational (= purely transcendental) over $k$. It is known that, if $\\bC(G)$ is rational over $\\bC$, then $B_0(G)=0$ where $B_0(G)$ is the unramified Brauer group of $\\bC(G)$ over $\\bC$. Bogomolov showed that, if $G$ is a $p$-group of order $p^5$, then $B_0(G)=0$. This result was disproved by Moravec for $p=3,5,7$ by computer computing. We will give a theoretic proof of the followin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2966","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":"2026-05-18T04:13:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XE3RD4a0IqUfquEdSlwgjClmWYtpYhD3I/awx8IP5DMIttZxnuqPJkyXSVR+C9EaMf4RI3DEJtdcyrBYbyqLDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:39:43.527916Z"},"content_sha256":"f7135eeeb7b5cb7318a5b6cefe207f7d435e9440cb17faeffa71e30f5515cf22","schema_version":"1.0","event_id":"sha256:f7135eeeb7b5cb7318a5b6cefe207f7d435e9440cb17faeffa71e30f5515cf22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CSEYR2JSRKTT3TIDA64XDPD72X/bundle.json","state_url":"https://pith.science/pith/CSEYR2JSRKTT3TIDA64XDPD72X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CSEYR2JSRKTT3TIDA64XDPD72X/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":"2026-05-28T16:39:43Z","links":{"resolver":"https://pith.science/pith/CSEYR2JSRKTT3TIDA64XDPD72X","bundle":"https://pith.science/pith/CSEYR2JSRKTT3TIDA64XDPD72X/bundle.json","state":"https://pith.science/pith/CSEYR2JSRKTT3TIDA64XDPD72X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CSEYR2JSRKTT3TIDA64XDPD72X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CSEYR2JSRKTT3TIDA64XDPD72X","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":"110d1f25c5ca937991b081f1b509972fa23e0dddcf7512accb43d2bee1f837cb","cross_cats_sorted":["math.AG","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-09-14T02:04:37Z","title_canon_sha256":"481d329e31b724f2ac8ca384ef263210d07a543e27a901e4ebdb43ec03ff699e"},"schema_version":"1.0","source":{"id":"1109.2966","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2966","created_at":"2026-05-18T04:13:06Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2966v1","created_at":"2026-05-18T04:13:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2966","created_at":"2026-05-18T04:13:06Z"},{"alias_kind":"pith_short_12","alias_value":"CSEYR2JSRKTT","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CSEYR2JSRKTT3TID","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CSEYR2JS","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:f7135eeeb7b5cb7318a5b6cefe207f7d435e9440cb17faeffa71e30f5515cf22","target":"graph","created_at":"2026-05-18T04:13:06Z","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 $k$ be any field, $G$ be a finite group acting on the rational function field $k(x_g : g\\in G)$ by $h\\cdot x_g=x_{hg}$ for any $h,g\\in G$. Define $k(G)=k(x_g : g\\in G)^G$. Noether's problem asks whether $k(G)$ is rational (= purely transcendental) over $k$. It is known that, if $\\bC(G)$ is rational over $\\bC$, then $B_0(G)=0$ where $B_0(G)$ is the unramified Brauer group of $\\bC(G)$ over $\\bC$. Bogomolov showed that, if $G$ is a $p$-group of order $p^5$, then $B_0(G)=0$. This result was disproved by Moravec for $p=3,5,7$ by computer computing. We will give a theoretic proof of the followin","authors_text":"Akinari Hoshi, Ming-chang Kang","cross_cats":["math.AG","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-09-14T02:04:37Z","title":"Unramified Brauer groups for groups of order p^5"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2966","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":"sha256:2d56cac1c85d48c29677bc2567cb098f166ba9e8f246e94828a9eb4a2bca3a9b","target":"record","created_at":"2026-05-18T04:13:06Z","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":"110d1f25c5ca937991b081f1b509972fa23e0dddcf7512accb43d2bee1f837cb","cross_cats_sorted":["math.AG","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-09-14T02:04:37Z","title_canon_sha256":"481d329e31b724f2ac8ca384ef263210d07a543e27a901e4ebdb43ec03ff699e"},"schema_version":"1.0","source":{"id":"1109.2966","kind":"arxiv","version":1}},"canonical_sha256":"148988e9328aa73dcd0307b971bc7fd5d5f5a909f23c01f1f3c2c0c733df1a43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"148988e9328aa73dcd0307b971bc7fd5d5f5a909f23c01f1f3c2c0c733df1a43","first_computed_at":"2026-05-18T04:13:06.615562Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:06.615562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w31XDm3RIgXPzQIyLNs8sYQPDVZYto0K6NWA3j38Ig/9J15ca8wOYoElMaHQG1TrlXMf9UM59VjxAJnaM9KMBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:06.615975Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2966","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d56cac1c85d48c29677bc2567cb098f166ba9e8f246e94828a9eb4a2bca3a9b","sha256:f7135eeeb7b5cb7318a5b6cefe207f7d435e9440cb17faeffa71e30f5515cf22"],"state_sha256":"d432e7c6270ef384779f0fb085e06646792b406a0939edca361d32db627647ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8HpV1z0dyMsfSkfCKv5444SGzRdW/pClNsFcRhlXqzwENyv+xX/JH647S1RQmqD3Dy9WswP28Wfa3m4BkVAzDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T16:39:43.529939Z","bundle_sha256":"ed747572283f0079560382cf927d4a60c97641aa3eb094ce110db189d3948137"}}