{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MCOV5WKA2T6EJOLBOXLQAA45MA","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":"effea855972e012befbfde56d926504501d9c5ca402583abb6e9168a2291b50e","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-06-09T21:03:49Z","title_canon_sha256":"918bef1d8b3df136a19d3b5604d261c924e536d52881e5cf9cf389ab7d34334d"},"schema_version":"1.0","source":{"id":"1706.03126","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.03126","created_at":"2026-05-18T00:42:38Z"},{"alias_kind":"arxiv_version","alias_value":"1706.03126v1","created_at":"2026-05-18T00:42:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03126","created_at":"2026-05-18T00:42:38Z"},{"alias_kind":"pith_short_12","alias_value":"MCOV5WKA2T6E","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MCOV5WKA2T6EJOLB","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MCOV5WKA","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:bc051e1dfc045631de93a975ac06b157800a7bd5194b57573fcd31ad52aa6926","target":"graph","created_at":"2026-05-18T00:42:38Z","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":"The best known method to give a lower bound for the Noether number of a given finite group is to use the fact that it is greater than or equal to the Noether number of any of the subgroups or factor groups. The results of the present paper show in particular that these inequalities are strict for proper subgroups or factor groups. This is established by studying the algebra of coinvariants of a representation induced from a representation of a subgroup.","authors_text":"K. Cziszter, M. Domokos","cross_cats":["math.RA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-06-09T21:03:49Z","title":"Lower bounds on the Noether number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03126","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":"sha256:2949bd259f65e2b168aa5b65f06c3c2cb96bd76fbd58340428e43979f79f6317","target":"record","created_at":"2026-05-18T00:42:38Z","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":"effea855972e012befbfde56d926504501d9c5ca402583abb6e9168a2291b50e","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-06-09T21:03:49Z","title_canon_sha256":"918bef1d8b3df136a19d3b5604d261c924e536d52881e5cf9cf389ab7d34334d"},"schema_version":"1.0","source":{"id":"1706.03126","kind":"arxiv","version":1}},"canonical_sha256":"609d5ed940d4fc44b96175d700039d603af2cb07c1152f9b4818abe50e086fa8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"609d5ed940d4fc44b96175d700039d603af2cb07c1152f9b4818abe50e086fa8","first_computed_at":"2026-05-18T00:42:38.382888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:38.382888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hyXPlXFeIXl2/IKo0UGNhjfBdvlE0odVHiJvv+0BXmZ+gj38mXewjiP/gPMZVdz+d/LcmuigJJgfs3Jki05kBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:38.383675Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.03126","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2949bd259f65e2b168aa5b65f06c3c2cb96bd76fbd58340428e43979f79f6317","sha256:bc051e1dfc045631de93a975ac06b157800a7bd5194b57573fcd31ad52aa6926"],"state_sha256":"edb5e95f1e0ffeaa6e6fd2b69cbe0ee8b0ad1c00936b86ad3d88ae26ca1bd492"}