{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:MLWAQZ736APG4SAOJYEZ32NV6O","short_pith_number":"pith:MLWAQZ73","canonical_record":{"source":{"id":"1205.5834","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-05-25T22:37:21Z","cross_cats_sorted":[],"title_canon_sha256":"02a1f55b360cff698ba3611c9119336cf91098b9833aa48dadf3f15571108fcf","abstract_canon_sha256":"ab2810f90c2f62c8d8242e2339f8e8cecf44a5bffd841c3be036e6bf415966c9"},"schema_version":"1.0"},"canonical_sha256":"62ec0867fbf01e6e480e4e099de9b5f3b3ed2c6c1aed6fbd1f10b250b004e693","source":{"kind":"arxiv","id":"1205.5834","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5834","created_at":"2026-05-18T03:54:49Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5834v1","created_at":"2026-05-18T03:54:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5834","created_at":"2026-05-18T03:54:49Z"},{"alias_kind":"pith_short_12","alias_value":"MLWAQZ736APG","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MLWAQZ736APG4SAO","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MLWAQZ73","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:MLWAQZ736APG4SAOJYEZ32NV6O","target":"record","payload":{"canonical_record":{"source":{"id":"1205.5834","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-05-25T22:37:21Z","cross_cats_sorted":[],"title_canon_sha256":"02a1f55b360cff698ba3611c9119336cf91098b9833aa48dadf3f15571108fcf","abstract_canon_sha256":"ab2810f90c2f62c8d8242e2339f8e8cecf44a5bffd841c3be036e6bf415966c9"},"schema_version":"1.0"},"canonical_sha256":"62ec0867fbf01e6e480e4e099de9b5f3b3ed2c6c1aed6fbd1f10b250b004e693","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:49.861794Z","signature_b64":"0HmgPT0SPuuCH/pFFFn0EQsvpXw+3+bA1QfJhb1x/kUKMx8mw9V6aAcT/OzEQ3mOZjpqN0Za+xXfN0t2mzyWDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62ec0867fbf01e6e480e4e099de9b5f3b3ed2c6c1aed6fbd1f10b250b004e693","last_reissued_at":"2026-05-18T03:54:49.861349Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:49.861349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.5834","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":"2026-05-18T03:54:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hHtFvCCXMvAeGxTKKdbPmUzoE1kOBwCCfqgTv5U+awu6GiF1UbmYwWND4xgseC88tF2L4N1HWaB9K8fh12JtBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T18:31:24.255789Z"},"content_sha256":"b3c8daceecc6c00411b715e121d15947a3566a3657ab6ed03f7c6f7b9142db3b","schema_version":"1.0","event_id":"sha256:b3c8daceecc6c00411b715e121d15947a3566a3657ab6ed03f7c6f7b9142db3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:MLWAQZ736APG4SAOJYEZ32NV6O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Noether number of the non-abelian group of order 3p","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"K. Cziszter","submitted_at":"2012-05-25T22:37:21Z","abstract_excerpt":"It is proven that for any representation over a field of characteristic 0 of the non-abelian semidirect product of a cyclic group of prime order p and the group of order 3 the corresponding algebra of polynomial invariants is generated by elements of degree at most p+2. We also determine the exact degree bound for any separating system of the polynomial invariants of any representation of this group in characteristic not dividing 3p."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5834","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":"2026-05-18T03:54:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HiTMnJF4lhKYDnbpoH+c4I7eYI1lo9TF3S0ARorsrty3no2HBPw18uiJ+okMokMkWRPkVcBgsclQgSpl6bwdDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T18:31:24.256112Z"},"content_sha256":"94a198cfe295c8202663738f10b46247d03795a798b7c929ab9ae8843336585f","schema_version":"1.0","event_id":"sha256:94a198cfe295c8202663738f10b46247d03795a798b7c929ab9ae8843336585f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MLWAQZ736APG4SAOJYEZ32NV6O/bundle.json","state_url":"https://pith.science/pith/MLWAQZ736APG4SAOJYEZ32NV6O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MLWAQZ736APG4SAOJYEZ32NV6O/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":"2026-06-26T18:31:24Z","links":{"resolver":"https://pith.science/pith/MLWAQZ736APG4SAOJYEZ32NV6O","bundle":"https://pith.science/pith/MLWAQZ736APG4SAOJYEZ32NV6O/bundle.json","state":"https://pith.science/pith/MLWAQZ736APG4SAOJYEZ32NV6O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MLWAQZ736APG4SAOJYEZ32NV6O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MLWAQZ736APG4SAOJYEZ32NV6O","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":"ab2810f90c2f62c8d8242e2339f8e8cecf44a5bffd841c3be036e6bf415966c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-05-25T22:37:21Z","title_canon_sha256":"02a1f55b360cff698ba3611c9119336cf91098b9833aa48dadf3f15571108fcf"},"schema_version":"1.0","source":{"id":"1205.5834","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.5834","created_at":"2026-05-18T03:54:49Z"},{"alias_kind":"arxiv_version","alias_value":"1205.5834v1","created_at":"2026-05-18T03:54:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5834","created_at":"2026-05-18T03:54:49Z"},{"alias_kind":"pith_short_12","alias_value":"MLWAQZ736APG","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MLWAQZ736APG4SAO","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MLWAQZ73","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:94a198cfe295c8202663738f10b46247d03795a798b7c929ab9ae8843336585f","target":"graph","created_at":"2026-05-18T03:54:49Z","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":"It is proven that for any representation over a field of characteristic 0 of the non-abelian semidirect product of a cyclic group of prime order p and the group of order 3 the corresponding algebra of polynomial invariants is generated by elements of degree at most p+2. We also determine the exact degree bound for any separating system of the polynomial invariants of any representation of this group in characteristic not dividing 3p.","authors_text":"K. Cziszter","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-05-25T22:37:21Z","title":"The Noether number of the non-abelian group of order 3p"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5834","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:b3c8daceecc6c00411b715e121d15947a3566a3657ab6ed03f7c6f7b9142db3b","target":"record","created_at":"2026-05-18T03:54:49Z","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":"ab2810f90c2f62c8d8242e2339f8e8cecf44a5bffd841c3be036e6bf415966c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-05-25T22:37:21Z","title_canon_sha256":"02a1f55b360cff698ba3611c9119336cf91098b9833aa48dadf3f15571108fcf"},"schema_version":"1.0","source":{"id":"1205.5834","kind":"arxiv","version":1}},"canonical_sha256":"62ec0867fbf01e6e480e4e099de9b5f3b3ed2c6c1aed6fbd1f10b250b004e693","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62ec0867fbf01e6e480e4e099de9b5f3b3ed2c6c1aed6fbd1f10b250b004e693","first_computed_at":"2026-05-18T03:54:49.861349Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:49.861349Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0HmgPT0SPuuCH/pFFFn0EQsvpXw+3+bA1QfJhb1x/kUKMx8mw9V6aAcT/OzEQ3mOZjpqN0Za+xXfN0t2mzyWDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:49.861794Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.5834","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3c8daceecc6c00411b715e121d15947a3566a3657ab6ed03f7c6f7b9142db3b","sha256:94a198cfe295c8202663738f10b46247d03795a798b7c929ab9ae8843336585f"],"state_sha256":"9f0bc55e96ec2e546193892ffdd10acacecd0615e8acfee6b3c7516dbe547a11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aJRZLBbf04NGkPnUHQ4P5cAUyThIwr5g2YhN3nKBCZGjJWpV/rj5Q5fU8lOcmvHp3ykqWd2fEX0BVarComLSCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T18:31:24.258219Z","bundle_sha256":"0372ad538504ff1427db3861ca46487b88c78776eb10fecb558de5b22db6064c"}}