{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FI5OYPMZNMZOOCPA4LSGUXFYGR","short_pith_number":"pith:FI5OYPMZ","canonical_record":{"source":{"id":"1811.02145","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-06T03:28:33Z","cross_cats_sorted":["math.NT","math.RA"],"title_canon_sha256":"8adf2b54ba9473040ec24d184f0c30d2429af21c6872d47af7d99d31398b242e","abstract_canon_sha256":"d9858a73ca9028d3096f375259b2056fea0452850e1e1fb1e4862b13526c7588"},"schema_version":"1.0"},"canonical_sha256":"2a3aec3d996b32e709e0e2e46a5cb83446634ce6444aa263d86583d1b768b81a","source":{"kind":"arxiv","id":"1811.02145","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.02145","created_at":"2026-05-17T23:44:58Z"},{"alias_kind":"arxiv_version","alias_value":"1811.02145v4","created_at":"2026-05-17T23:44:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.02145","created_at":"2026-05-17T23:44:58Z"},{"alias_kind":"pith_short_12","alias_value":"FI5OYPMZNMZO","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FI5OYPMZNMZOOCPA","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FI5OYPMZ","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FI5OYPMZNMZOOCPA4LSGUXFYGR","target":"record","payload":{"canonical_record":{"source":{"id":"1811.02145","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-06T03:28:33Z","cross_cats_sorted":["math.NT","math.RA"],"title_canon_sha256":"8adf2b54ba9473040ec24d184f0c30d2429af21c6872d47af7d99d31398b242e","abstract_canon_sha256":"d9858a73ca9028d3096f375259b2056fea0452850e1e1fb1e4862b13526c7588"},"schema_version":"1.0"},"canonical_sha256":"2a3aec3d996b32e709e0e2e46a5cb83446634ce6444aa263d86583d1b768b81a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:58.655579Z","signature_b64":"sobkbklqJ+cNNxUwndpIxQR0Nuhaw5RjSJF2MDTkvLstoxkCxjj4VjD/Be2y6W+IHIS8EuE7sMdQVbkW33bYAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a3aec3d996b32e709e0e2e46a5cb83446634ce6444aa263d86583d1b768b81a","last_reissued_at":"2026-05-17T23:44:58.654910Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:58.654910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.02145","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MQ8gXCxql9z4KpALoo+/jtkm9RixlI8eNyAjAXmTwypTcZdpPf6tRjypbsUbUVnRl7Go4pRysTx4l2M29K8RBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:15:30.575265Z"},"content_sha256":"12d9a1321690fade098056891c808c5fde19ff46ca521381e7d774e3e2b590bd","schema_version":"1.0","event_id":"sha256:12d9a1321690fade098056891c808c5fde19ff46ca521381e7d774e3e2b590bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FI5OYPMZNMZOOCPA4LSGUXFYGR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rationality problem for norm one tori in small dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.RA"],"primary_cat":"math.AG","authors_text":"Aiichi Yamasaki, Akinari Hoshi, Sumito Hasegawa","submitted_at":"2018-11-06T03:28:33Z","abstract_excerpt":"We classify stably/retract rational norm one tori in dimension $n-1$ for $n=2^e$ $(e\\geq 1)$ is a power of $2$ and $n=12, 14, 15$. Retract non-rationality of norm one tori for primitive $G\\leq S_{2p}$ where $p$ is a prime number and for the five Mathieu groups $M_n\\leq S_n$ $(n=11,12,22,23,24)$ is also given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02145","kind":"arxiv","version":4},"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":"2026-05-17T23:44:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/6wXDH8zMitpHcCXRDrlH7ZtCT91jqezdhHJuGgcityvE9u8SV8D5RI84qAKvqur3zUNV+nGWHUutpdhAOupBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:15:30.575932Z"},"content_sha256":"65280b5e139f947967cb3d65657041a8c871867c17350523580c752a98d8d809","schema_version":"1.0","event_id":"sha256:65280b5e139f947967cb3d65657041a8c871867c17350523580c752a98d8d809"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FI5OYPMZNMZOOCPA4LSGUXFYGR/bundle.json","state_url":"https://pith.science/pith/FI5OYPMZNMZOOCPA4LSGUXFYGR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FI5OYPMZNMZOOCPA4LSGUXFYGR/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":"2026-06-09T19:15:30Z","links":{"resolver":"https://pith.science/pith/FI5OYPMZNMZOOCPA4LSGUXFYGR","bundle":"https://pith.science/pith/FI5OYPMZNMZOOCPA4LSGUXFYGR/bundle.json","state":"https://pith.science/pith/FI5OYPMZNMZOOCPA4LSGUXFYGR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FI5OYPMZNMZOOCPA4LSGUXFYGR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FI5OYPMZNMZOOCPA4LSGUXFYGR","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":"d9858a73ca9028d3096f375259b2056fea0452850e1e1fb1e4862b13526c7588","cross_cats_sorted":["math.NT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-06T03:28:33Z","title_canon_sha256":"8adf2b54ba9473040ec24d184f0c30d2429af21c6872d47af7d99d31398b242e"},"schema_version":"1.0","source":{"id":"1811.02145","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.02145","created_at":"2026-05-17T23:44:58Z"},{"alias_kind":"arxiv_version","alias_value":"1811.02145v4","created_at":"2026-05-17T23:44:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.02145","created_at":"2026-05-17T23:44:58Z"},{"alias_kind":"pith_short_12","alias_value":"FI5OYPMZNMZO","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"FI5OYPMZNMZOOCPA","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"FI5OYPMZ","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:65280b5e139f947967cb3d65657041a8c871867c17350523580c752a98d8d809","target":"graph","created_at":"2026-05-17T23:44:58Z","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 classify stably/retract rational norm one tori in dimension $n-1$ for $n=2^e$ $(e\\geq 1)$ is a power of $2$ and $n=12, 14, 15$. Retract non-rationality of norm one tori for primitive $G\\leq S_{2p}$ where $p$ is a prime number and for the five Mathieu groups $M_n\\leq S_n$ $(n=11,12,22,23,24)$ is also given.","authors_text":"Aiichi Yamasaki, Akinari Hoshi, Sumito Hasegawa","cross_cats":["math.NT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-06T03:28:33Z","title":"Rationality problem for norm one tori in small dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.02145","kind":"arxiv","version":4},"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":"sha256:12d9a1321690fade098056891c808c5fde19ff46ca521381e7d774e3e2b590bd","target":"record","created_at":"2026-05-17T23:44:58Z","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":"d9858a73ca9028d3096f375259b2056fea0452850e1e1fb1e4862b13526c7588","cross_cats_sorted":["math.NT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-11-06T03:28:33Z","title_canon_sha256":"8adf2b54ba9473040ec24d184f0c30d2429af21c6872d47af7d99d31398b242e"},"schema_version":"1.0","source":{"id":"1811.02145","kind":"arxiv","version":4}},"canonical_sha256":"2a3aec3d996b32e709e0e2e46a5cb83446634ce6444aa263d86583d1b768b81a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a3aec3d996b32e709e0e2e46a5cb83446634ce6444aa263d86583d1b768b81a","first_computed_at":"2026-05-17T23:44:58.654910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:58.654910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sobkbklqJ+cNNxUwndpIxQR0Nuhaw5RjSJF2MDTkvLstoxkCxjj4VjD/Be2y6W+IHIS8EuE7sMdQVbkW33bYAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:58.655579Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.02145","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12d9a1321690fade098056891c808c5fde19ff46ca521381e7d774e3e2b590bd","sha256:65280b5e139f947967cb3d65657041a8c871867c17350523580c752a98d8d809"],"state_sha256":"416bb94b868bba36de065b92ba5f95f56c16dab85d86f4a7134bcef063376130"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S2XLMkdlkjSrSz6lXz5LhlA6b/PuuZTk46Jn04RfENmArAQrSlWKdfMX381fNXTzPfn7JGLEaHlxkYVt6Q1GBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:15:30.579821Z","bundle_sha256":"26291be2f82e7c6988cf8607fcdf9abe4a9e985f21f85931a540ca698eeed886"}}