{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:EPURG72AVP5MQO2AM4K4LGN2FT","short_pith_number":"pith:EPURG72A","canonical_record":{"source":{"id":"2006.04135","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2020-06-07T12:19:29Z","cross_cats_sorted":[],"title_canon_sha256":"361b9ab0d22f914919f56ce064e2b5a04d4df31231ffa49d46fd44eefeb003e6","abstract_canon_sha256":"49935658ad9fcdfbc96422681d2296265d04ba93ecd16aec8b0e024e11fa3693"},"schema_version":"1.0"},"canonical_sha256":"23e9137f40abfac83b406715c599ba2cf90c743b15c455c86b89e14439c69423","source":{"kind":"arxiv","id":"2006.04135","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.04135","created_at":"2026-07-05T02:58:22Z"},{"alias_kind":"arxiv_version","alias_value":"2006.04135v2","created_at":"2026-07-05T02:58:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.04135","created_at":"2026-07-05T02:58:22Z"},{"alias_kind":"pith_short_12","alias_value":"EPURG72AVP5M","created_at":"2026-07-05T02:58:22Z"},{"alias_kind":"pith_short_16","alias_value":"EPURG72AVP5MQO2A","created_at":"2026-07-05T02:58:22Z"},{"alias_kind":"pith_short_8","alias_value":"EPURG72A","created_at":"2026-07-05T02:58:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:EPURG72AVP5MQO2AM4K4LGN2FT","target":"record","payload":{"canonical_record":{"source":{"id":"2006.04135","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2020-06-07T12:19:29Z","cross_cats_sorted":[],"title_canon_sha256":"361b9ab0d22f914919f56ce064e2b5a04d4df31231ffa49d46fd44eefeb003e6","abstract_canon_sha256":"49935658ad9fcdfbc96422681d2296265d04ba93ecd16aec8b0e024e11fa3693"},"schema_version":"1.0"},"canonical_sha256":"23e9137f40abfac83b406715c599ba2cf90c743b15c455c86b89e14439c69423","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:58:22.137735Z","signature_b64":"1uW3HwXETj3/pBxVTQqeo10Phy0BV6dDYcLJizjV6h0TIaXRosSKkC9MlgO4EM2D7TCZtnXMA89yD970OPrtDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23e9137f40abfac83b406715c599ba2cf90c743b15c455c86b89e14439c69423","last_reissued_at":"2026-07-05T02:58:22.137382Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:58:22.137382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.04135","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":"2026-07-05T02:58:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DOl5ioXTgN41wG+Pz2CC5dRlkAXJXZxpPhHxQxvVebhZV0aqigxvRYxSZy/WI/k/KnejJSqbiip4kjhARybmDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T15:20:27.482679Z"},"content_sha256":"ae4b4288cbff1bfb5c72e8ac25c4d6072c2b23f4e805ba1814f0cefcef3a6585","schema_version":"1.0","event_id":"sha256:ae4b4288cbff1bfb5c72e8ac25c4d6072c2b23f4e805ba1814f0cefcef3a6585"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:EPURG72AVP5MQO2AM4K4LGN2FT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Domains whose ideals meet a universal restriction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Muhammad Zafrullah","submitted_at":"2020-06-07T12:19:29Z","abstract_excerpt":"Let $S(D)$ represent a set of proper nonzero ideals $I(D)$ (resp., $t$ -ideals $I_{t}(D)$) of an integral domain $D\\neq qf(D)$ and let $P$ be a valid property of ideals of $D.$ We say $S(D)$ meets $P$ (denoted $ S(D)\\vartriangleleft P)$ if each $s\\in S(D)$ is contained in an ideal satisfying $P$. If $S(D)$ $\\vartriangleleft P,$ $\\dim (D)$ can't be controlled. When $R=D[X],$ $I(D)$ $\\vartriangleleft P$ does not imply $I(R)$ $\\vartriangleleft P$ while $I_{t}(D)$ $\\vartriangleleft P$ implies $I_{t}(R)$ $\\vartriangleleft P$ usually. We say $S(D)$ meets $P$ with a twist $($ written $S(D)\\vartriangl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.04135","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.04135/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:58:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/1kJt4TbRA4GB9zbu/daBPykUuIEfm1ibfJzGZFKBZd4E4zIBhmaV1GixAZzSVyyNe437ls+H3FyklApxy6FCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T15:20:27.483094Z"},"content_sha256":"a4e5c20c8ee0252edd696df4429edb65a5bdcfbfff4a2b2a4392af9296398500","schema_version":"1.0","event_id":"sha256:a4e5c20c8ee0252edd696df4429edb65a5bdcfbfff4a2b2a4392af9296398500"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EPURG72AVP5MQO2AM4K4LGN2FT/bundle.json","state_url":"https://pith.science/pith/EPURG72AVP5MQO2AM4K4LGN2FT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EPURG72AVP5MQO2AM4K4LGN2FT/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":"2026-07-05T15:20:27Z","links":{"resolver":"https://pith.science/pith/EPURG72AVP5MQO2AM4K4LGN2FT","bundle":"https://pith.science/pith/EPURG72AVP5MQO2AM4K4LGN2FT/bundle.json","state":"https://pith.science/pith/EPURG72AVP5MQO2AM4K4LGN2FT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EPURG72AVP5MQO2AM4K4LGN2FT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:EPURG72AVP5MQO2AM4K4LGN2FT","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":"49935658ad9fcdfbc96422681d2296265d04ba93ecd16aec8b0e024e11fa3693","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2020-06-07T12:19:29Z","title_canon_sha256":"361b9ab0d22f914919f56ce064e2b5a04d4df31231ffa49d46fd44eefeb003e6"},"schema_version":"1.0","source":{"id":"2006.04135","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.04135","created_at":"2026-07-05T02:58:22Z"},{"alias_kind":"arxiv_version","alias_value":"2006.04135v2","created_at":"2026-07-05T02:58:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.04135","created_at":"2026-07-05T02:58:22Z"},{"alias_kind":"pith_short_12","alias_value":"EPURG72AVP5M","created_at":"2026-07-05T02:58:22Z"},{"alias_kind":"pith_short_16","alias_value":"EPURG72AVP5MQO2A","created_at":"2026-07-05T02:58:22Z"},{"alias_kind":"pith_short_8","alias_value":"EPURG72A","created_at":"2026-07-05T02:58:22Z"}],"graph_snapshots":[{"event_id":"sha256:a4e5c20c8ee0252edd696df4429edb65a5bdcfbfff4a2b2a4392af9296398500","target":"graph","created_at":"2026-07-05T02:58:22Z","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/2006.04135/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $S(D)$ represent a set of proper nonzero ideals $I(D)$ (resp., $t$ -ideals $I_{t}(D)$) of an integral domain $D\\neq qf(D)$ and let $P$ be a valid property of ideals of $D.$ We say $S(D)$ meets $P$ (denoted $ S(D)\\vartriangleleft P)$ if each $s\\in S(D)$ is contained in an ideal satisfying $P$. If $S(D)$ $\\vartriangleleft P,$ $\\dim (D)$ can't be controlled. When $R=D[X],$ $I(D)$ $\\vartriangleleft P$ does not imply $I(R)$ $\\vartriangleleft P$ while $I_{t}(D)$ $\\vartriangleleft P$ implies $I_{t}(R)$ $\\vartriangleleft P$ usually. We say $S(D)$ meets $P$ with a twist $($ written $S(D)\\vartriangl","authors_text":"Muhammad Zafrullah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2020-06-07T12:19:29Z","title":"Domains whose ideals meet a universal restriction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.04135","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:ae4b4288cbff1bfb5c72e8ac25c4d6072c2b23f4e805ba1814f0cefcef3a6585","target":"record","created_at":"2026-07-05T02:58:22Z","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":"49935658ad9fcdfbc96422681d2296265d04ba93ecd16aec8b0e024e11fa3693","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2020-06-07T12:19:29Z","title_canon_sha256":"361b9ab0d22f914919f56ce064e2b5a04d4df31231ffa49d46fd44eefeb003e6"},"schema_version":"1.0","source":{"id":"2006.04135","kind":"arxiv","version":2}},"canonical_sha256":"23e9137f40abfac83b406715c599ba2cf90c743b15c455c86b89e14439c69423","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23e9137f40abfac83b406715c599ba2cf90c743b15c455c86b89e14439c69423","first_computed_at":"2026-07-05T02:58:22.137382Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:58:22.137382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1uW3HwXETj3/pBxVTQqeo10Phy0BV6dDYcLJizjV6h0TIaXRosSKkC9MlgO4EM2D7TCZtnXMA89yD970OPrtDw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:58:22.137735Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.04135","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae4b4288cbff1bfb5c72e8ac25c4d6072c2b23f4e805ba1814f0cefcef3a6585","sha256:a4e5c20c8ee0252edd696df4429edb65a5bdcfbfff4a2b2a4392af9296398500"],"state_sha256":"016a685b125d5efa2c28d56054846dbf623342acf30a938b1ebccbd292e1adb3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7+ABkw7IwjBaI5Z3F23qNc3ZqX9kuRVbUl4uOcQM0CUq4ix0B3esILFzxk/J4T6eYm+7EUKfvTwx3I1YHpY0CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T15:20:27.485501Z","bundle_sha256":"b27477a19d821800a9c2d955c228d23f21d77d7fd2a113e4084488e8a7f42a93"}}