{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:YIUMC7D7SR43SZVBU362B7N232","short_pith_number":"pith:YIUMC7D7","canonical_record":{"source":{"id":"1908.10185","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-08-27T13:31:22Z","cross_cats_sorted":[],"title_canon_sha256":"ffe3904b964fca06d00acba77051399386fb68bf4dd6355a61d83cc9d59726d6","abstract_canon_sha256":"2c004a156765b866a5e7ded4d45bbee28dafeda9d8008ad8007ae40b41113641"},"schema_version":"1.0"},"canonical_sha256":"c228c17c7f9479b966a1a6fda0fdbadeb3589d632fb28fa87d3dd4754d986e3e","source":{"kind":"arxiv","id":"1908.10185","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.10185","created_at":"2026-07-04T23:59:54Z"},{"alias_kind":"arxiv_version","alias_value":"1908.10185v1","created_at":"2026-07-04T23:59:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.10185","created_at":"2026-07-04T23:59:54Z"},{"alias_kind":"pith_short_12","alias_value":"YIUMC7D7SR43","created_at":"2026-07-04T23:59:54Z"},{"alias_kind":"pith_short_16","alias_value":"YIUMC7D7SR43SZVB","created_at":"2026-07-04T23:59:54Z"},{"alias_kind":"pith_short_8","alias_value":"YIUMC7D7","created_at":"2026-07-04T23:59:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:YIUMC7D7SR43SZVBU362B7N232","target":"record","payload":{"canonical_record":{"source":{"id":"1908.10185","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-08-27T13:31:22Z","cross_cats_sorted":[],"title_canon_sha256":"ffe3904b964fca06d00acba77051399386fb68bf4dd6355a61d83cc9d59726d6","abstract_canon_sha256":"2c004a156765b866a5e7ded4d45bbee28dafeda9d8008ad8007ae40b41113641"},"schema_version":"1.0"},"canonical_sha256":"c228c17c7f9479b966a1a6fda0fdbadeb3589d632fb28fa87d3dd4754d986e3e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:59:54.715244Z","signature_b64":"ykWkVDtMGYVBUvphAq34y4qhTlpNrBrFSX+gSaci6YEA6ZpTiQjqoQTDtzhrimFP8CnAne8uIomWaU6Z9tNDBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c228c17c7f9479b966a1a6fda0fdbadeb3589d632fb28fa87d3dd4754d986e3e","last_reissued_at":"2026-07-04T23:59:54.714843Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:59:54.714843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.10185","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":"2026-07-04T23:59:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BfU32ib/bjAaUW7nJRu8sH10a4Kn7DPBgfQ6zSkwF0b1C1LQFv2elx6ExbYadCFqdmIWvYfJUyTE97zteHqJCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T14:26:34.633502Z"},"content_sha256":"1b10f2c7caf5e6da5ca49939e7bdaee2c76d4bc7cc3b2207dafef6ca4e10552a","schema_version":"1.0","event_id":"sha256:1b10f2c7caf5e6da5ca49939e7bdaee2c76d4bc7cc3b2207dafef6ca4e10552a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:YIUMC7D7SR43SZVBU362B7N232","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Powers of monomial ideals and the Ratliff-Rush operation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Oleksandra Gasanova","submitted_at":"2019-08-27T13:31:22Z","abstract_excerpt":"Powers of (monomial) ideals is a subject that still calls attraction in various ways. In this paper we present a nice presentation of high powers of ideals in a certain class in $\\mathbb K[x_1, \\ldots, x_n]$ and $\\mathbb K[[x_1, \\ldots, x_n]]$. As an interesting application it leads to an algorithm for computation of the Ratliff--Rush operation on ideals in that class. The Ratliff--Rush operation itself has several applications, for instance, if $I$ is a regular $\\mathfrak m$-primary ideal in a local ring $(R,m)$, then the Ratliff--Rush associated ideal $\\tilde I$ is the unique largest ideal c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.10185","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.10185/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":"2026-07-04T23:59:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TpohyloITiucwHmpwS3Ax0WxY/zL8bO+5cPXe8YNBt6YXEJZI6BybV3KoRg2f2ZEg2fXbc/qkShGJIxooygfDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T14:26:34.634517Z"},"content_sha256":"0e22ec890e7b62e296a0b09c19c7a1610daf8c15a6210eed8d94e2892204c4a9","schema_version":"1.0","event_id":"sha256:0e22ec890e7b62e296a0b09c19c7a1610daf8c15a6210eed8d94e2892204c4a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YIUMC7D7SR43SZVBU362B7N232/bundle.json","state_url":"https://pith.science/pith/YIUMC7D7SR43SZVBU362B7N232/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YIUMC7D7SR43SZVBU362B7N232/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":"2026-07-31T14:26:34Z","links":{"resolver":"https://pith.science/pith/YIUMC7D7SR43SZVBU362B7N232","bundle":"https://pith.science/pith/YIUMC7D7SR43SZVBU362B7N232/bundle.json","state":"https://pith.science/pith/YIUMC7D7SR43SZVBU362B7N232/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YIUMC7D7SR43SZVBU362B7N232/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YIUMC7D7SR43SZVBU362B7N232","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":"2c004a156765b866a5e7ded4d45bbee28dafeda9d8008ad8007ae40b41113641","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-08-27T13:31:22Z","title_canon_sha256":"ffe3904b964fca06d00acba77051399386fb68bf4dd6355a61d83cc9d59726d6"},"schema_version":"1.0","source":{"id":"1908.10185","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.10185","created_at":"2026-07-04T23:59:54Z"},{"alias_kind":"arxiv_version","alias_value":"1908.10185v1","created_at":"2026-07-04T23:59:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.10185","created_at":"2026-07-04T23:59:54Z"},{"alias_kind":"pith_short_12","alias_value":"YIUMC7D7SR43","created_at":"2026-07-04T23:59:54Z"},{"alias_kind":"pith_short_16","alias_value":"YIUMC7D7SR43SZVB","created_at":"2026-07-04T23:59:54Z"},{"alias_kind":"pith_short_8","alias_value":"YIUMC7D7","created_at":"2026-07-04T23:59:54Z"}],"graph_snapshots":[{"event_id":"sha256:0e22ec890e7b62e296a0b09c19c7a1610daf8c15a6210eed8d94e2892204c4a9","target":"graph","created_at":"2026-07-04T23:59:54Z","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/1908.10185/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Powers of (monomial) ideals is a subject that still calls attraction in various ways. In this paper we present a nice presentation of high powers of ideals in a certain class in $\\mathbb K[x_1, \\ldots, x_n]$ and $\\mathbb K[[x_1, \\ldots, x_n]]$. As an interesting application it leads to an algorithm for computation of the Ratliff--Rush operation on ideals in that class. The Ratliff--Rush operation itself has several applications, for instance, if $I$ is a regular $\\mathfrak m$-primary ideal in a local ring $(R,m)$, then the Ratliff--Rush associated ideal $\\tilde I$ is the unique largest ideal c","authors_text":"Oleksandra Gasanova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-08-27T13:31:22Z","title":"Powers of monomial ideals and the Ratliff-Rush operation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.10185","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":"sha256:1b10f2c7caf5e6da5ca49939e7bdaee2c76d4bc7cc3b2207dafef6ca4e10552a","target":"record","created_at":"2026-07-04T23:59:54Z","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":"2c004a156765b866a5e7ded4d45bbee28dafeda9d8008ad8007ae40b41113641","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-08-27T13:31:22Z","title_canon_sha256":"ffe3904b964fca06d00acba77051399386fb68bf4dd6355a61d83cc9d59726d6"},"schema_version":"1.0","source":{"id":"1908.10185","kind":"arxiv","version":1}},"canonical_sha256":"c228c17c7f9479b966a1a6fda0fdbadeb3589d632fb28fa87d3dd4754d986e3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c228c17c7f9479b966a1a6fda0fdbadeb3589d632fb28fa87d3dd4754d986e3e","first_computed_at":"2026-07-04T23:59:54.714843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:59:54.714843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ykWkVDtMGYVBUvphAq34y4qhTlpNrBrFSX+gSaci6YEA6ZpTiQjqoQTDtzhrimFP8CnAne8uIomWaU6Z9tNDBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T23:59:54.715244Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.10185","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b10f2c7caf5e6da5ca49939e7bdaee2c76d4bc7cc3b2207dafef6ca4e10552a","sha256:0e22ec890e7b62e296a0b09c19c7a1610daf8c15a6210eed8d94e2892204c4a9"],"state_sha256":"304ac0dab1b01630b430c103d4a83198dc78def472a600e381214017c1ca7296"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cw13WLootRoD4lgy1o+xX5R5tMP1ETFw/Iu5aeoyDVp0u1COWm0Zf9hbAx8P47936lI/wj5zN+nU+0HQBinZDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-31T14:26:34.639539Z","bundle_sha256":"1b1492aea3d3038699bf51caeecf1791911dcc7225c19a74b836f9357253c9f8"}}