{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GK4UISWHC2LYGUX6WP74QLO3CK","short_pith_number":"pith:GK4UISWH","canonical_record":{"source":{"id":"1103.1786","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-03-09T14:03:04Z","cross_cats_sorted":[],"title_canon_sha256":"4f2b535170a0d35aadd65bad0bef068f03df5aceb17da92fcdcdeda206230962","abstract_canon_sha256":"27fa746ce4698d5ac729fa8969c91e14a41fa522deecf08df1fbc4488bc7ad34"},"schema_version":"1.0"},"canonical_sha256":"32b9444ac716978352feb3ffc82ddb129cb535a5c66f3100a2805f48e260c381","source":{"kind":"arxiv","id":"1103.1786","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1786","created_at":"2026-05-18T03:48:45Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1786v3","created_at":"2026-05-18T03:48:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1786","created_at":"2026-05-18T03:48:45Z"},{"alias_kind":"pith_short_12","alias_value":"GK4UISWHC2LY","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GK4UISWHC2LYGUX6","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GK4UISWH","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GK4UISWHC2LYGUX6WP74QLO3CK","target":"record","payload":{"canonical_record":{"source":{"id":"1103.1786","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-03-09T14:03:04Z","cross_cats_sorted":[],"title_canon_sha256":"4f2b535170a0d35aadd65bad0bef068f03df5aceb17da92fcdcdeda206230962","abstract_canon_sha256":"27fa746ce4698d5ac729fa8969c91e14a41fa522deecf08df1fbc4488bc7ad34"},"schema_version":"1.0"},"canonical_sha256":"32b9444ac716978352feb3ffc82ddb129cb535a5c66f3100a2805f48e260c381","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:45.194861Z","signature_b64":"8jpzHxHo5vYP/Aq+cw3BvnYDU0RFOltc0MWvA0ytLFToRLaarBtpmBUzbpS3bLALVBedp1iSd5BflS3CXRgcCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32b9444ac716978352feb3ffc82ddb129cb535a5c66f3100a2805f48e260c381","last_reissued_at":"2026-05-18T03:48:45.194277Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:45.194277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.1786","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:48:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gtQULGERUpzl8M9ZOZ4cnmCrTepBfGhkrmH1u37aUPwmw4wlVGp9RcB+NlkWhUiT24yDBUQEFb4/SQJz4jZzCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:01:20.893709Z"},"content_sha256":"9c100d2d0b47817b1c971c9e639cb39395792192e73a26318e6dff37db6861a0","schema_version":"1.0","event_id":"sha256:9c100d2d0b47817b1c971c9e639cb39395792192e73a26318e6dff37db6861a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GK4UISWHC2LYGUX6WP74QLO3CK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dagger closure in regular rings containing a field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Axel St\\\"abler, Holger Brenner","submitted_at":"2011-03-09T14:03:04Z","abstract_excerpt":"We prove that dagger closure is trivial in regular domains containing a field and that graded dagger closure is trivial in polynomial rings over a field. We also prove that Heitmann's full rank one closure coincides with tight closure in positive characteristic under some mild finiteness conditions. Furthermore, we prove that dagger closure is always contained in solid closure and that the forcing algebra for an element contained in dagger closure is parasolid."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1786","kind":"arxiv","version":3},"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":"2026-05-18T03:48:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/quZ4BpnERv9u7rClVTegn/FdpcD3w+PDzbeP20RMDKrh2p1BLgMDB1Fw+bKBno5f5zTmwiwf8I3ogcn9TxtDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:01:20.894108Z"},"content_sha256":"ffae8619e8c3e3246a136d1f756441031f16c9bffc96f0c8e41547331e345189","schema_version":"1.0","event_id":"sha256:ffae8619e8c3e3246a136d1f756441031f16c9bffc96f0c8e41547331e345189"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GK4UISWHC2LYGUX6WP74QLO3CK/bundle.json","state_url":"https://pith.science/pith/GK4UISWHC2LYGUX6WP74QLO3CK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GK4UISWHC2LYGUX6WP74QLO3CK/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":"2026-06-06T19:01:20Z","links":{"resolver":"https://pith.science/pith/GK4UISWHC2LYGUX6WP74QLO3CK","bundle":"https://pith.science/pith/GK4UISWHC2LYGUX6WP74QLO3CK/bundle.json","state":"https://pith.science/pith/GK4UISWHC2LYGUX6WP74QLO3CK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GK4UISWHC2LYGUX6WP74QLO3CK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GK4UISWHC2LYGUX6WP74QLO3CK","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":"27fa746ce4698d5ac729fa8969c91e14a41fa522deecf08df1fbc4488bc7ad34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-03-09T14:03:04Z","title_canon_sha256":"4f2b535170a0d35aadd65bad0bef068f03df5aceb17da92fcdcdeda206230962"},"schema_version":"1.0","source":{"id":"1103.1786","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.1786","created_at":"2026-05-18T03:48:45Z"},{"alias_kind":"arxiv_version","alias_value":"1103.1786v3","created_at":"2026-05-18T03:48:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1786","created_at":"2026-05-18T03:48:45Z"},{"alias_kind":"pith_short_12","alias_value":"GK4UISWHC2LY","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GK4UISWHC2LYGUX6","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GK4UISWH","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:ffae8619e8c3e3246a136d1f756441031f16c9bffc96f0c8e41547331e345189","target":"graph","created_at":"2026-05-18T03:48:45Z","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 that dagger closure is trivial in regular domains containing a field and that graded dagger closure is trivial in polynomial rings over a field. We also prove that Heitmann's full rank one closure coincides with tight closure in positive characteristic under some mild finiteness conditions. Furthermore, we prove that dagger closure is always contained in solid closure and that the forcing algebra for an element contained in dagger closure is parasolid.","authors_text":"Axel St\\\"abler, Holger Brenner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-03-09T14:03:04Z","title":"Dagger closure in regular rings containing a field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1786","kind":"arxiv","version":3},"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":"sha256:9c100d2d0b47817b1c971c9e639cb39395792192e73a26318e6dff37db6861a0","target":"record","created_at":"2026-05-18T03:48:45Z","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":"27fa746ce4698d5ac729fa8969c91e14a41fa522deecf08df1fbc4488bc7ad34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-03-09T14:03:04Z","title_canon_sha256":"4f2b535170a0d35aadd65bad0bef068f03df5aceb17da92fcdcdeda206230962"},"schema_version":"1.0","source":{"id":"1103.1786","kind":"arxiv","version":3}},"canonical_sha256":"32b9444ac716978352feb3ffc82ddb129cb535a5c66f3100a2805f48e260c381","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32b9444ac716978352feb3ffc82ddb129cb535a5c66f3100a2805f48e260c381","first_computed_at":"2026-05-18T03:48:45.194277Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:45.194277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8jpzHxHo5vYP/Aq+cw3BvnYDU0RFOltc0MWvA0ytLFToRLaarBtpmBUzbpS3bLALVBedp1iSd5BflS3CXRgcCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:45.194861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.1786","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c100d2d0b47817b1c971c9e639cb39395792192e73a26318e6dff37db6861a0","sha256:ffae8619e8c3e3246a136d1f756441031f16c9bffc96f0c8e41547331e345189"],"state_sha256":"bec9a7bc7ca414a60eb34c21574774b78a25d0560f3c184b2929c48eb79153a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m0iCHT8OLGgS1YDokTv3irIudqdWkvf947e9oW4SZs1yR/gQMQsIbodv8cztF7VYxOw223nySGbNsNkho5tYCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:01:20.898136Z","bundle_sha256":"5e1d5f884b0602c6a691df5d71e2a6a77394a1982ea7506c8386674c9c75a60d"}}