{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UAUOGH6HGTQ4QWJEK3TP6CUCTQ","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":"4afcd83fe985eb8f00e70771c5081933d40d89daea10dd3fe14bf26ecd2b50ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-01-30T05:07:31Z","title_canon_sha256":"5116473b936f3ca77bae63efe82d7af4333704c23b9d93c62f01d9aa64f2138d"},"schema_version":"1.0","source":{"id":"1801.09852","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09852","created_at":"2026-07-05T04:48:04Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09852v5","created_at":"2026-07-05T04:48:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09852","created_at":"2026-07-05T04:48:04Z"},{"alias_kind":"pith_short_12","alias_value":"UAUOGH6HGTQ4","created_at":"2026-07-05T04:48:04Z"},{"alias_kind":"pith_short_16","alias_value":"UAUOGH6HGTQ4QWJE","created_at":"2026-07-05T04:48:04Z"},{"alias_kind":"pith_short_8","alias_value":"UAUOGH6H","created_at":"2026-07-05T04:48:04Z"}],"graph_snapshots":[{"event_id":"sha256:ee1e6c75231da70b4abbc95603cf3857e8831b54481e6f465198d4b75ba06307","target":"graph","created_at":"2026-07-05T04:48:04Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1801.09852/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The purpose of this paper is to prove that certain limits of polynomial rings are themselves polynomial rings, and show how this observation can be used to deduce some interesting results in commutative algebra. In particular, we give two new proofs of Stillman's conjecture. The first is similar to that of Ananyan-Hochster, though more streamlined; in particular, it establishes the existence of small subalgebras. The second proof is completely different, and relies on a recent noetherianity result of Draisma.","authors_text":"Andrew Snowden, Daniel Erman, Steven V Sam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-01-30T05:07:31Z","title":"Big polynomial rings and Stillman's conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09852","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:f01807e7c266dd1b6a5ec8717d6f31cecd7cf6a06de01ec2bef59823aa37d0fc","target":"record","created_at":"2026-07-05T04:48:04Z","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":"4afcd83fe985eb8f00e70771c5081933d40d89daea10dd3fe14bf26ecd2b50ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-01-30T05:07:31Z","title_canon_sha256":"5116473b936f3ca77bae63efe82d7af4333704c23b9d93c62f01d9aa64f2138d"},"schema_version":"1.0","source":{"id":"1801.09852","kind":"arxiv","version":5}},"canonical_sha256":"a028e31fc734e1c8592456e6ff0a829c1f11b06f33e5e9a29659177e5ca716fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a028e31fc734e1c8592456e6ff0a829c1f11b06f33e5e9a29659177e5ca716fe","first_computed_at":"2026-07-05T04:48:04.812186Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:48:04.812186Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eBYhe18HUo8ERT1Hzb5KTqPS5tMVmZhpFk+7Q+2W28OR/lvH8IEbeGMi28ZoO7IlkR5uLrKxXoTTUH9lQ+FcAg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:48:04.812597Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09852","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f01807e7c266dd1b6a5ec8717d6f31cecd7cf6a06de01ec2bef59823aa37d0fc","sha256:ee1e6c75231da70b4abbc95603cf3857e8831b54481e6f465198d4b75ba06307"],"state_sha256":"345fd9db5a3468082267c6bba98ff5553108b764146af690c4ab81f17a7d379d"}