{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Q5EZWJ23LRIBN6YFCSUYANHOL4","short_pith_number":"pith:Q5EZWJ23","canonical_record":{"source":{"id":"1503.00108","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-02-28T09:55:36Z","cross_cats_sorted":[],"title_canon_sha256":"414d23902328aae80a4aa19ce499598bcbfb65202199c1b2fd0cca35b50e98af","abstract_canon_sha256":"0603c8783f35941f32c4b93a9ab15186cac5c2ec44c6272091451dc76e9f8710"},"schema_version":"1.0"},"canonical_sha256":"87499b275b5c5016fb0514a98034ee5f0071d1b138084f921fb0df1db107d9f1","source":{"kind":"arxiv","id":"1503.00108","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00108","created_at":"2026-05-18T02:25:55Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00108v1","created_at":"2026-05-18T02:25:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00108","created_at":"2026-05-18T02:25:55Z"},{"alias_kind":"pith_short_12","alias_value":"Q5EZWJ23LRIB","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q5EZWJ23LRIBN6YF","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q5EZWJ23","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Q5EZWJ23LRIBN6YFCSUYANHOL4","target":"record","payload":{"canonical_record":{"source":{"id":"1503.00108","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-02-28T09:55:36Z","cross_cats_sorted":[],"title_canon_sha256":"414d23902328aae80a4aa19ce499598bcbfb65202199c1b2fd0cca35b50e98af","abstract_canon_sha256":"0603c8783f35941f32c4b93a9ab15186cac5c2ec44c6272091451dc76e9f8710"},"schema_version":"1.0"},"canonical_sha256":"87499b275b5c5016fb0514a98034ee5f0071d1b138084f921fb0df1db107d9f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:55.138135Z","signature_b64":"e5Rs/Mw1fGVgeyVMtkI6y0mSwNjVZ1LHaUfHs3cbsSMKpScTfLG3CemRg8avc+8wVxDSyToS4I7gy/bY5JbiDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87499b275b5c5016fb0514a98034ee5f0071d1b138084f921fb0df1db107d9f1","last_reissued_at":"2026-05-18T02:25:55.137635Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:55.137635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.00108","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":"2026-05-18T02:25:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TksPkBpmNx7Z3yORSUxhElc+XEY4jaBJSSoBTR2yte2fiRXyMonTkg6RHaST72D5JRMwNFqvXyhY+sT1aGkeCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:29:21.240206Z"},"content_sha256":"431c78664504749c3302f03ae54179d6c9d84f1eb6ce14ca2837665ca137b85b","schema_version":"1.0","event_id":"sha256:431c78664504749c3302f03ae54179d6c9d84f1eb6ce14ca2837665ca137b85b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Q5EZWJ23LRIBN6YFCSUYANHOL4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On \\phi-n-absorbing primary ideals of commutative rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ahmad Yousefian Darani, Hojjat Mostafanasab","submitted_at":"2015-02-28T09:55:36Z","abstract_excerpt":"All rings are commutative with $1$ and $n$ is a positive integer. Let $\\phi: J(R)\\to J(R)\\cup{\\emptyset}$ be a function where $J(R)$ denotes the set of all ideals of $R$. We say that a proper ideal $I$ of $R$ is $\\phi$-$n$-absorbing primary if whenever $a_1,a_2,...,a_{n+1}\\in R$ and $a_1a_2\\cdots a_{n+1}\\in I\\backslash\\phi(I)$, either $a_1a_2\\cdots a_n\\in I$ or the product of $a_{n+1}$ with $(n-1)$ of $a_1,...,a_n$ is in $\\sqrt{I}$. The aim of this paper is to investigate the concept of $\\phi$-$n$-absorbing primary ideals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00108","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":"2026-05-18T02:25:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OLumIR8gZhlQWkmhUOijMJ4jUHWj7ebpjve4BrxGlhE16Khf0yABA3JrvlETGgSAYHlcnPSkhkhQtbRp/hWhAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:29:21.240958Z"},"content_sha256":"adc19c6d457d711f07872347d645922e8d98d28784212ffa1b43591f7d5b64f8","schema_version":"1.0","event_id":"sha256:adc19c6d457d711f07872347d645922e8d98d28784212ffa1b43591f7d5b64f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q5EZWJ23LRIBN6YFCSUYANHOL4/bundle.json","state_url":"https://pith.science/pith/Q5EZWJ23LRIBN6YFCSUYANHOL4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q5EZWJ23LRIBN6YFCSUYANHOL4/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":"2026-05-31T20:29:21Z","links":{"resolver":"https://pith.science/pith/Q5EZWJ23LRIBN6YFCSUYANHOL4","bundle":"https://pith.science/pith/Q5EZWJ23LRIBN6YFCSUYANHOL4/bundle.json","state":"https://pith.science/pith/Q5EZWJ23LRIBN6YFCSUYANHOL4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q5EZWJ23LRIBN6YFCSUYANHOL4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Q5EZWJ23LRIBN6YFCSUYANHOL4","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":"0603c8783f35941f32c4b93a9ab15186cac5c2ec44c6272091451dc76e9f8710","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-02-28T09:55:36Z","title_canon_sha256":"414d23902328aae80a4aa19ce499598bcbfb65202199c1b2fd0cca35b50e98af"},"schema_version":"1.0","source":{"id":"1503.00108","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.00108","created_at":"2026-05-18T02:25:55Z"},{"alias_kind":"arxiv_version","alias_value":"1503.00108v1","created_at":"2026-05-18T02:25:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00108","created_at":"2026-05-18T02:25:55Z"},{"alias_kind":"pith_short_12","alias_value":"Q5EZWJ23LRIB","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q5EZWJ23LRIBN6YF","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q5EZWJ23","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:adc19c6d457d711f07872347d645922e8d98d28784212ffa1b43591f7d5b64f8","target":"graph","created_at":"2026-05-18T02:25:55Z","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":"All rings are commutative with $1$ and $n$ is a positive integer. Let $\\phi: J(R)\\to J(R)\\cup{\\emptyset}$ be a function where $J(R)$ denotes the set of all ideals of $R$. We say that a proper ideal $I$ of $R$ is $\\phi$-$n$-absorbing primary if whenever $a_1,a_2,...,a_{n+1}\\in R$ and $a_1a_2\\cdots a_{n+1}\\in I\\backslash\\phi(I)$, either $a_1a_2\\cdots a_n\\in I$ or the product of $a_{n+1}$ with $(n-1)$ of $a_1,...,a_n$ is in $\\sqrt{I}$. The aim of this paper is to investigate the concept of $\\phi$-$n$-absorbing primary ideals.","authors_text":"Ahmad Yousefian Darani, Hojjat Mostafanasab","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-02-28T09:55:36Z","title":"On \\phi-n-absorbing primary ideals of commutative rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00108","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":"sha256:431c78664504749c3302f03ae54179d6c9d84f1eb6ce14ca2837665ca137b85b","target":"record","created_at":"2026-05-18T02:25:55Z","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":"0603c8783f35941f32c4b93a9ab15186cac5c2ec44c6272091451dc76e9f8710","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-02-28T09:55:36Z","title_canon_sha256":"414d23902328aae80a4aa19ce499598bcbfb65202199c1b2fd0cca35b50e98af"},"schema_version":"1.0","source":{"id":"1503.00108","kind":"arxiv","version":1}},"canonical_sha256":"87499b275b5c5016fb0514a98034ee5f0071d1b138084f921fb0df1db107d9f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87499b275b5c5016fb0514a98034ee5f0071d1b138084f921fb0df1db107d9f1","first_computed_at":"2026-05-18T02:25:55.137635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:55.137635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e5Rs/Mw1fGVgeyVMtkI6y0mSwNjVZ1LHaUfHs3cbsSMKpScTfLG3CemRg8avc+8wVxDSyToS4I7gy/bY5JbiDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:55.138135Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.00108","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:431c78664504749c3302f03ae54179d6c9d84f1eb6ce14ca2837665ca137b85b","sha256:adc19c6d457d711f07872347d645922e8d98d28784212ffa1b43591f7d5b64f8"],"state_sha256":"afa04cea40fd932a8f3bdcc94aa91f538c6ba679f97bf80676c857bd9a3c38f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1bE304CyEigKmI2bkkhZiAO2xVSehFkLKUcy9zoJuOBJhy2F0w0+EkDnU05smhylQLci3NXCyoDI9MPLgrzqDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:29:21.244817Z","bundle_sha256":"d2968c0da4a9869d7974310e52ba4d2d05c456f962f3c8f59cbc76ec5cec05f6"}}