{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:WH3CBDBEUNPYJFGQUIARTWHTCM","short_pith_number":"pith:WH3CBDBE","canonical_record":{"source":{"id":"1709.04435","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-13T17:27:21Z","cross_cats_sorted":[],"title_canon_sha256":"02548262c9f1126dfbc7a3ff4e71d71e8293780563c785117dc897e494f25bd1","abstract_canon_sha256":"77f174353d77d9d2ae5f5fae5d08deb56100298d373030114f0e7a1fd957cbe9"},"schema_version":"1.0"},"canonical_sha256":"b1f6208c24a35f8494d0a20119d8f3133efc7a7d7e8fe050ea7bc545bfd180b8","source":{"kind":"arxiv","id":"1709.04435","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04435","created_at":"2026-05-17T23:53:06Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04435v5","created_at":"2026-05-17T23:53:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04435","created_at":"2026-05-17T23:53:06Z"},{"alias_kind":"pith_short_12","alias_value":"WH3CBDBEUNPY","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WH3CBDBEUNPYJFGQ","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WH3CBDBE","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:WH3CBDBEUNPYJFGQUIARTWHTCM","target":"record","payload":{"canonical_record":{"source":{"id":"1709.04435","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-13T17:27:21Z","cross_cats_sorted":[],"title_canon_sha256":"02548262c9f1126dfbc7a3ff4e71d71e8293780563c785117dc897e494f25bd1","abstract_canon_sha256":"77f174353d77d9d2ae5f5fae5d08deb56100298d373030114f0e7a1fd957cbe9"},"schema_version":"1.0"},"canonical_sha256":"b1f6208c24a35f8494d0a20119d8f3133efc7a7d7e8fe050ea7bc545bfd180b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:06.785409Z","signature_b64":"NGpEUzCj2dhYG4sQotPGHBgt6dxA/UYpgyP1gSFA19urWixy/nLOlQqMgil16/iqToDyhvbFxa7vfckDALRRBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1f6208c24a35f8494d0a20119d8f3133efc7a7d7e8fe050ea7bc545bfd180b8","last_reissued_at":"2026-05-17T23:53:06.784783Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:06.784783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.04435","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FT/upjHDP2OpXoMBdnNTRBUaqlovLBzjnW+yCGhsVmpdoGlJ43bjGeXcAKOiJj8Sf4pnQbzGiIumaDOHBZTvBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:13:36.098347Z"},"content_sha256":"ae11b72e390c987b4586f0370e42e09d010958cb04d3ba01cb640a149b063520","schema_version":"1.0","event_id":"sha256:ae11b72e390c987b4586f0370e42e09d010958cb04d3ba01cb640a149b063520"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:WH3CBDBEUNPYJFGQUIARTWHTCM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Presentations for subrings and subalgebras of finite co-rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Nik Ruskuc, Peter Mayr","submitted_at":"2017-09-13T17:27:21Z","abstract_excerpt":"Let $K$ be a commutative Noetherian ring with identity, let $A$ be a $K$-algebra, and let $B$ be a subalgebra of $A$ such that $A/B$ is finitely generated as a $K$-module. The main result of the paper is that $A$ is finitely presented (resp. finitely generated) if and only if $B$ is finitely presented (resp. finitely generated). As corollaries we obtain: a subring of finite index in a finitely presented ring is finitely presented; a subalgebra of finite co-dimension in a finitely presented algebra over a field is finitely presented (already shown by Voden in 2009). We also discuss the role of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04435","kind":"arxiv","version":5},"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":"2026-05-17T23:53:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UemRJJ7bhg+v284fvPQYylTSO+aeKkH0/AV/rKUGFGBvNwOHU+RWRyyg36OOoaWbRyhRaioOiSsUE5nEMyf6Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:13:36.098714Z"},"content_sha256":"f689ec63fbce86ec60628cce0ba78c26fbaac6a933d80c22e957155e5b90ac10","schema_version":"1.0","event_id":"sha256:f689ec63fbce86ec60628cce0ba78c26fbaac6a933d80c22e957155e5b90ac10"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WH3CBDBEUNPYJFGQUIARTWHTCM/bundle.json","state_url":"https://pith.science/pith/WH3CBDBEUNPYJFGQUIARTWHTCM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WH3CBDBEUNPYJFGQUIARTWHTCM/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":"2026-05-27T03:13:36Z","links":{"resolver":"https://pith.science/pith/WH3CBDBEUNPYJFGQUIARTWHTCM","bundle":"https://pith.science/pith/WH3CBDBEUNPYJFGQUIARTWHTCM/bundle.json","state":"https://pith.science/pith/WH3CBDBEUNPYJFGQUIARTWHTCM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WH3CBDBEUNPYJFGQUIARTWHTCM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WH3CBDBEUNPYJFGQUIARTWHTCM","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":"77f174353d77d9d2ae5f5fae5d08deb56100298d373030114f0e7a1fd957cbe9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-13T17:27:21Z","title_canon_sha256":"02548262c9f1126dfbc7a3ff4e71d71e8293780563c785117dc897e494f25bd1"},"schema_version":"1.0","source":{"id":"1709.04435","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04435","created_at":"2026-05-17T23:53:06Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04435v5","created_at":"2026-05-17T23:53:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04435","created_at":"2026-05-17T23:53:06Z"},{"alias_kind":"pith_short_12","alias_value":"WH3CBDBEUNPY","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WH3CBDBEUNPYJFGQ","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WH3CBDBE","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:f689ec63fbce86ec60628cce0ba78c26fbaac6a933d80c22e957155e5b90ac10","target":"graph","created_at":"2026-05-17T23:53:06Z","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 a commutative Noetherian ring with identity, let $A$ be a $K$-algebra, and let $B$ be a subalgebra of $A$ such that $A/B$ is finitely generated as a $K$-module. The main result of the paper is that $A$ is finitely presented (resp. finitely generated) if and only if $B$ is finitely presented (resp. finitely generated). As corollaries we obtain: a subring of finite index in a finitely presented ring is finitely presented; a subalgebra of finite co-dimension in a finitely presented algebra over a field is finitely presented (already shown by Voden in 2009). We also discuss the role of ","authors_text":"Nik Ruskuc, Peter Mayr","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-13T17:27:21Z","title":"Presentations for subrings and subalgebras of finite co-rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04435","kind":"arxiv","version":5},"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:ae11b72e390c987b4586f0370e42e09d010958cb04d3ba01cb640a149b063520","target":"record","created_at":"2026-05-17T23:53:06Z","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":"77f174353d77d9d2ae5f5fae5d08deb56100298d373030114f0e7a1fd957cbe9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-09-13T17:27:21Z","title_canon_sha256":"02548262c9f1126dfbc7a3ff4e71d71e8293780563c785117dc897e494f25bd1"},"schema_version":"1.0","source":{"id":"1709.04435","kind":"arxiv","version":5}},"canonical_sha256":"b1f6208c24a35f8494d0a20119d8f3133efc7a7d7e8fe050ea7bc545bfd180b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1f6208c24a35f8494d0a20119d8f3133efc7a7d7e8fe050ea7bc545bfd180b8","first_computed_at":"2026-05-17T23:53:06.784783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:06.784783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NGpEUzCj2dhYG4sQotPGHBgt6dxA/UYpgyP1gSFA19urWixy/nLOlQqMgil16/iqToDyhvbFxa7vfckDALRRBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:06.785409Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.04435","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae11b72e390c987b4586f0370e42e09d010958cb04d3ba01cb640a149b063520","sha256:f689ec63fbce86ec60628cce0ba78c26fbaac6a933d80c22e957155e5b90ac10"],"state_sha256":"cda21e409cb5cb7930f3e945503943feda2b7f5efa81c8c30883b2e38ff94d08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wU4wG1mViXtG67i8iXkaa2mtWKoLlj+fTic4USznlvaw3QI9qyvZXc1Qn2rZyUMyvPy+gnJVghEFS3O0YMisAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T03:13:36.103630Z","bundle_sha256":"a841041d74f3de53d5d652c852a91c4dda99f42bbb5dacf1630354705d1709ce"}}