{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:OT5A64JXEZSCAXMASBDU6TRYV5","short_pith_number":"pith:OT5A64JX","canonical_record":{"source":{"id":"1009.3957","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-09-20T21:36:18Z","cross_cats_sorted":[],"title_canon_sha256":"ea996c823f9f3aff51186050be3032392380a52e84e88e9ae0a3762ce3a32a64","abstract_canon_sha256":"7c5f7307d3c43f002d72ebde33c62ad5d3a68fd3e4a3b7bae815b5219c228d4c"},"schema_version":"1.0"},"canonical_sha256":"74fa0f71372664205d8090474f4e38af6a65abb6daff98a96f425a9037e766db","source":{"kind":"arxiv","id":"1009.3957","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3957","created_at":"2026-05-18T03:57:37Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3957v2","created_at":"2026-05-18T03:57:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3957","created_at":"2026-05-18T03:57:37Z"},{"alias_kind":"pith_short_12","alias_value":"OT5A64JXEZSC","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OT5A64JXEZSCAXMA","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OT5A64JX","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:OT5A64JXEZSCAXMASBDU6TRYV5","target":"record","payload":{"canonical_record":{"source":{"id":"1009.3957","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-09-20T21:36:18Z","cross_cats_sorted":[],"title_canon_sha256":"ea996c823f9f3aff51186050be3032392380a52e84e88e9ae0a3762ce3a32a64","abstract_canon_sha256":"7c5f7307d3c43f002d72ebde33c62ad5d3a68fd3e4a3b7bae815b5219c228d4c"},"schema_version":"1.0"},"canonical_sha256":"74fa0f71372664205d8090474f4e38af6a65abb6daff98a96f425a9037e766db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:37.371489Z","signature_b64":"3tCC7FJnlgb75wq8tuEFfUdP8Nj6f+7l74IMFvFkpL9/WXpSHDDF56qPCGB1pYRd90Zjwm/5s5VIh29EHjptDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74fa0f71372664205d8090474f4e38af6a65abb6daff98a96f425a9037e766db","last_reissued_at":"2026-05-18T03:57:37.370844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:37.370844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.3957","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:57:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FIZByC3/iuCLm68+7xwWvBp0AyHp+QcpMNzGukQ+o609QYnDLHOqZDKrnDvXn7dekiIb6K48H51yp/nTMakiBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:42:24.906286Z"},"content_sha256":"335d12b8ee00dd4c6410f3598f8052b58f443aed5354d3333d9ad238ea3aeea5","schema_version":"1.0","event_id":"sha256:335d12b8ee00dd4c6410f3598f8052b58f443aed5354d3333d9ad238ea3aeea5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:OT5A64JXEZSCAXMASBDU6TRYV5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derivations, generic formal fibers and bad Noetherian rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Bruce Olberding","submitted_at":"2010-09-20T21:36:18Z","abstract_excerpt":"We consider a circle of ideas involving differential algebra, local Noetherian rings, and their generic formal fibers.\n  Connecting these ideas gives rise to what we term a \"twisted\" subring $R$ of a ring $S$. Each such subring $R$ arises as a pullback of a derivation taking values in an $S$-module $K$. The twisting relationship proves to be a kind of inversion of Nagata idealization: whereas idealization extends $S$ to the larger ring $S \\star K$, twisting produces a subring of $S$ which behaves much like the ring $S \\star K$.\n  The rings produced in this manner exhibit pathological features,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3957","kind":"arxiv","version":2},"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":"2026-05-18T03:57:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9fBRgXMNiAXyK2+u7qxuqG53lkYOT7ItIukaSk7MS7Zf8nTiprC3zOVaifhl0ZjAHD6sXMKsbeKh7xxS4NHvBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:42:24.906693Z"},"content_sha256":"7b3076251c401fda776e1547632e906ce9dccca0fe59f2f839ed99fc7e991623","schema_version":"1.0","event_id":"sha256:7b3076251c401fda776e1547632e906ce9dccca0fe59f2f839ed99fc7e991623"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OT5A64JXEZSCAXMASBDU6TRYV5/bundle.json","state_url":"https://pith.science/pith/OT5A64JXEZSCAXMASBDU6TRYV5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OT5A64JXEZSCAXMASBDU6TRYV5/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":"2026-05-31T05:42:24Z","links":{"resolver":"https://pith.science/pith/OT5A64JXEZSCAXMASBDU6TRYV5","bundle":"https://pith.science/pith/OT5A64JXEZSCAXMASBDU6TRYV5/bundle.json","state":"https://pith.science/pith/OT5A64JXEZSCAXMASBDU6TRYV5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OT5A64JXEZSCAXMASBDU6TRYV5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OT5A64JXEZSCAXMASBDU6TRYV5","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":"7c5f7307d3c43f002d72ebde33c62ad5d3a68fd3e4a3b7bae815b5219c228d4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-09-20T21:36:18Z","title_canon_sha256":"ea996c823f9f3aff51186050be3032392380a52e84e88e9ae0a3762ce3a32a64"},"schema_version":"1.0","source":{"id":"1009.3957","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3957","created_at":"2026-05-18T03:57:37Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3957v2","created_at":"2026-05-18T03:57:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3957","created_at":"2026-05-18T03:57:37Z"},{"alias_kind":"pith_short_12","alias_value":"OT5A64JXEZSC","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OT5A64JXEZSCAXMA","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OT5A64JX","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:7b3076251c401fda776e1547632e906ce9dccca0fe59f2f839ed99fc7e991623","target":"graph","created_at":"2026-05-18T03:57:37Z","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 consider a circle of ideas involving differential algebra, local Noetherian rings, and their generic formal fibers.\n  Connecting these ideas gives rise to what we term a \"twisted\" subring $R$ of a ring $S$. Each such subring $R$ arises as a pullback of a derivation taking values in an $S$-module $K$. The twisting relationship proves to be a kind of inversion of Nagata idealization: whereas idealization extends $S$ to the larger ring $S \\star K$, twisting produces a subring of $S$ which behaves much like the ring $S \\star K$.\n  The rings produced in this manner exhibit pathological features,","authors_text":"Bruce Olberding","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-09-20T21:36:18Z","title":"Derivations, generic formal fibers and bad Noetherian rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3957","kind":"arxiv","version":2},"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":"sha256:335d12b8ee00dd4c6410f3598f8052b58f443aed5354d3333d9ad238ea3aeea5","target":"record","created_at":"2026-05-18T03:57:37Z","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":"7c5f7307d3c43f002d72ebde33c62ad5d3a68fd3e4a3b7bae815b5219c228d4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-09-20T21:36:18Z","title_canon_sha256":"ea996c823f9f3aff51186050be3032392380a52e84e88e9ae0a3762ce3a32a64"},"schema_version":"1.0","source":{"id":"1009.3957","kind":"arxiv","version":2}},"canonical_sha256":"74fa0f71372664205d8090474f4e38af6a65abb6daff98a96f425a9037e766db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74fa0f71372664205d8090474f4e38af6a65abb6daff98a96f425a9037e766db","first_computed_at":"2026-05-18T03:57:37.370844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:37.370844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3tCC7FJnlgb75wq8tuEFfUdP8Nj6f+7l74IMFvFkpL9/WXpSHDDF56qPCGB1pYRd90Zjwm/5s5VIh29EHjptDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:37.371489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.3957","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:335d12b8ee00dd4c6410f3598f8052b58f443aed5354d3333d9ad238ea3aeea5","sha256:7b3076251c401fda776e1547632e906ce9dccca0fe59f2f839ed99fc7e991623"],"state_sha256":"a7c13c3fbd844a02116b60d43500a20a6667ca7803db6540931bfa41326f0cfa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KhXhpZJq3wBwsdivTFR85BNDLuVUmqtEznGKgV1VDxPVZCwsI+1b/yE3lheQKkwR4wOv/VucQvnQpY3OfHKrCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:42:24.909537Z","bundle_sha256":"bddf5565ab5c58e1a1e0c6185fcecbe49ce12f6d64c7c2f8a8049d78344d78d6"}}