{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6ONOLCF5NJYHEPVBOPQHH6ZUGD","short_pith_number":"pith:6ONOLCF5","canonical_record":{"source":{"id":"1408.6212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-08-26T19:07:59Z","cross_cats_sorted":[],"title_canon_sha256":"242c214c99b5dadd57496a2b1248f3537e790de493a2035bd357a67a1b5e94ed","abstract_canon_sha256":"22d442ab340c92cbd4a6a40b527950fa71b7d7ebdfcdd77fb9627b3a91fa3593"},"schema_version":"1.0"},"canonical_sha256":"f39ae588bd6a70723ea173e073fb3430d975d086eb278655b5ff43c4309319f2","source":{"kind":"arxiv","id":"1408.6212","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6212","created_at":"2026-05-18T02:44:09Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6212v1","created_at":"2026-05-18T02:44:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6212","created_at":"2026-05-18T02:44:09Z"},{"alias_kind":"pith_short_12","alias_value":"6ONOLCF5NJYH","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6ONOLCF5NJYHEPVB","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6ONOLCF5","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6ONOLCF5NJYHEPVBOPQHH6ZUGD","target":"record","payload":{"canonical_record":{"source":{"id":"1408.6212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-08-26T19:07:59Z","cross_cats_sorted":[],"title_canon_sha256":"242c214c99b5dadd57496a2b1248f3537e790de493a2035bd357a67a1b5e94ed","abstract_canon_sha256":"22d442ab340c92cbd4a6a40b527950fa71b7d7ebdfcdd77fb9627b3a91fa3593"},"schema_version":"1.0"},"canonical_sha256":"f39ae588bd6a70723ea173e073fb3430d975d086eb278655b5ff43c4309319f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:09.122813Z","signature_b64":"Ei665tqkfbheGlxFMAQUhBZfOiGHQ0rkHOD8fie542goUgjeAf9jAlgs2/kInEXmNQ6XPoKy+Loo6Q5vMsI3Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f39ae588bd6a70723ea173e073fb3430d975d086eb278655b5ff43c4309319f2","last_reissued_at":"2026-05-18T02:44:09.122175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:09.122175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.6212","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":"2026-05-18T02:44:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cch22dYnHVtk3hyeTyTCXehsGApvfHsK5id2rSKuPkrQTj/+qY6aBNHYpWKMOGKywvjl7rebcFbyGoqI4X43Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:07:42.485294Z"},"content_sha256":"465ffda14010343ca5d9bd3ed8b3236518ba54807021784725635b1d9c81daed","schema_version":"1.0","event_id":"sha256:465ffda14010343ca5d9bd3ed8b3236518ba54807021784725635b1d9c81daed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6ONOLCF5NJYHEPVBOPQHH6ZUGD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hochster's small MCM conjecture for three-dimensional weakly F-split rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Hans Schoutens","submitted_at":"2014-08-26T19:07:59Z","abstract_excerpt":"We prove Hochster's small MCM conjecture for three-dimensional complete F-pure rings. We deduce this from a more general criterion, and show that only a weakening of the notion of F-purity is needed, to wit, being weakly F-split. We conjecture that any complete ring is weakly F-split."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6212","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":"2026-05-18T02:44:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DcIN9z7cQwCcIx+iX7fDGc1dTdKqz+bG2OGAk8SLdzMLCVv18fF1Jsl/eV8unJNON98p/pT6xt2gbyRfV0E0Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:07:42.485790Z"},"content_sha256":"ff6224b87a5982477db4e9f12542989aef7e65e07bf004a116e3ee14d2f4060a","schema_version":"1.0","event_id":"sha256:ff6224b87a5982477db4e9f12542989aef7e65e07bf004a116e3ee14d2f4060a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6ONOLCF5NJYHEPVBOPQHH6ZUGD/bundle.json","state_url":"https://pith.science/pith/6ONOLCF5NJYHEPVBOPQHH6ZUGD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6ONOLCF5NJYHEPVBOPQHH6ZUGD/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":"2026-06-24T04:07:42Z","links":{"resolver":"https://pith.science/pith/6ONOLCF5NJYHEPVBOPQHH6ZUGD","bundle":"https://pith.science/pith/6ONOLCF5NJYHEPVBOPQHH6ZUGD/bundle.json","state":"https://pith.science/pith/6ONOLCF5NJYHEPVBOPQHH6ZUGD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6ONOLCF5NJYHEPVBOPQHH6ZUGD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6ONOLCF5NJYHEPVBOPQHH6ZUGD","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":"22d442ab340c92cbd4a6a40b527950fa71b7d7ebdfcdd77fb9627b3a91fa3593","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-08-26T19:07:59Z","title_canon_sha256":"242c214c99b5dadd57496a2b1248f3537e790de493a2035bd357a67a1b5e94ed"},"schema_version":"1.0","source":{"id":"1408.6212","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6212","created_at":"2026-05-18T02:44:09Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6212v1","created_at":"2026-05-18T02:44:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6212","created_at":"2026-05-18T02:44:09Z"},{"alias_kind":"pith_short_12","alias_value":"6ONOLCF5NJYH","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6ONOLCF5NJYHEPVB","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6ONOLCF5","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:ff6224b87a5982477db4e9f12542989aef7e65e07bf004a116e3ee14d2f4060a","target":"graph","created_at":"2026-05-18T02:44:09Z","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 prove Hochster's small MCM conjecture for three-dimensional complete F-pure rings. We deduce this from a more general criterion, and show that only a weakening of the notion of F-purity is needed, to wit, being weakly F-split. We conjecture that any complete ring is weakly F-split.","authors_text":"Hans Schoutens","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-08-26T19:07:59Z","title":"Hochster's small MCM conjecture for three-dimensional weakly F-split rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6212","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":"sha256:465ffda14010343ca5d9bd3ed8b3236518ba54807021784725635b1d9c81daed","target":"record","created_at":"2026-05-18T02:44:09Z","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":"22d442ab340c92cbd4a6a40b527950fa71b7d7ebdfcdd77fb9627b3a91fa3593","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-08-26T19:07:59Z","title_canon_sha256":"242c214c99b5dadd57496a2b1248f3537e790de493a2035bd357a67a1b5e94ed"},"schema_version":"1.0","source":{"id":"1408.6212","kind":"arxiv","version":1}},"canonical_sha256":"f39ae588bd6a70723ea173e073fb3430d975d086eb278655b5ff43c4309319f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f39ae588bd6a70723ea173e073fb3430d975d086eb278655b5ff43c4309319f2","first_computed_at":"2026-05-18T02:44:09.122175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:09.122175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ei665tqkfbheGlxFMAQUhBZfOiGHQ0rkHOD8fie542goUgjeAf9jAlgs2/kInEXmNQ6XPoKy+Loo6Q5vMsI3Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:09.122813Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.6212","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:465ffda14010343ca5d9bd3ed8b3236518ba54807021784725635b1d9c81daed","sha256:ff6224b87a5982477db4e9f12542989aef7e65e07bf004a116e3ee14d2f4060a"],"state_sha256":"89109039df8a069eaa5206f63e3f9f0936a4d64e7203239eb376f220f17e40c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3wGRr1G9L8e8aatTEc89sCYkrwf/V+Fhtbyz+6D6Chk70nbHwblCTHLlO6Uu+wqTXJloVrfjH6N7ajt79YcBDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:07:42.488245Z","bundle_sha256":"e0e7b611410b303bf5874f80cccb67f8b2056715cbea5648b3ba4f8dcd170118"}}