{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QA34VXPKMMCKSTRLFONZGFK2ZF","short_pith_number":"pith:QA34VXPK","canonical_record":{"source":{"id":"1812.02456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-12-06T10:57:46Z","cross_cats_sorted":[],"title_canon_sha256":"ca42356555ff252c7e45d5da47de3d73dbd661c3294632fe9c18053fc9f0f5b1","abstract_canon_sha256":"747716a764e289c68bc56b1f2b8f00357e9356c3769481672b76ab6fd986e5d8"},"schema_version":"1.0"},"canonical_sha256":"8037caddea6304a94e2b2b9b93155ac9497a3db847d9b3187dcb6c91619842c0","source":{"kind":"arxiv","id":"1812.02456","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02456","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02456v1","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02456","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"QA34VXPKMMCK","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QA34VXPKMMCKSTRL","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QA34VXPK","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QA34VXPKMMCKSTRLFONZGFK2ZF","target":"record","payload":{"canonical_record":{"source":{"id":"1812.02456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-12-06T10:57:46Z","cross_cats_sorted":[],"title_canon_sha256":"ca42356555ff252c7e45d5da47de3d73dbd661c3294632fe9c18053fc9f0f5b1","abstract_canon_sha256":"747716a764e289c68bc56b1f2b8f00357e9356c3769481672b76ab6fd986e5d8"},"schema_version":"1.0"},"canonical_sha256":"8037caddea6304a94e2b2b9b93155ac9497a3db847d9b3187dcb6c91619842c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:55.650985Z","signature_b64":"QQ+1fA84wOnh9rwzk8Tf+5EkgEYRIj72k2RuRU8B3KycwL6o4UYfrp16Jf/NHBoNHhpCIEYnli0xMBeEdpYqCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8037caddea6304a94e2b2b9b93155ac9497a3db847d9b3187dcb6c91619842c0","last_reissued_at":"2026-05-17T23:58:55.650515Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:55.650515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.02456","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":"2026-05-17T23:58:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"akaoK1ezruFapHcZOPO1xuCYrXi18ufN5ESI2K7egNzXk7DC7IKs6hZoWgqTlRopHnz49jgo++l6nnMUckmOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:57:41.906908Z"},"content_sha256":"bd95f2c94699020d7b3fa435eb8e7b5fb29e89bda4f6a605b66fe8f13c2333d2","schema_version":"1.0","event_id":"sha256:bd95f2c94699020d7b3fa435eb8e7b5fb29e89bda4f6a605b66fe8f13c2333d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QA34VXPKMMCKSTRLFONZGFK2ZF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasi-prime ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Abolfazl Tarizadeh, Mohsen Aghajani","submitted_at":"2018-12-06T10:57:46Z","abstract_excerpt":"In this paper, the new concept of quasi-prime ideal is introduced which at the same time generalizes the `prime ideal' and `primary ideal' notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which generalizes the Zariski topology. The basic properties of the quasi-prime spectrum are studied and several interesting results are obtained. Specially, it is proved that if the Grothendieck t-functor is applied on the quasi-prime spectrum then the prime spectrum is deduced. It is also shown that there are the cases that the prime spectrum and quasi-prime spectrum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02456","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":"2026-05-17T23:58:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b/jC1lXNNBznK70/kdhYJHsuB7I5M+ImrSvUbT0H7vB8y6aireyYE2XApl5jwlAOkehCq1AqDx4REIidexeFDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T17:57:41.907247Z"},"content_sha256":"ff9bc6b981fca022e90c2ea2610351bb3f3d9f690dd358c0b44d86bc3588bc6c","schema_version":"1.0","event_id":"sha256:ff9bc6b981fca022e90c2ea2610351bb3f3d9f690dd358c0b44d86bc3588bc6c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QA34VXPKMMCKSTRLFONZGFK2ZF/bundle.json","state_url":"https://pith.science/pith/QA34VXPKMMCKSTRLFONZGFK2ZF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QA34VXPKMMCKSTRLFONZGFK2ZF/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":"2026-06-01T17:57:41Z","links":{"resolver":"https://pith.science/pith/QA34VXPKMMCKSTRLFONZGFK2ZF","bundle":"https://pith.science/pith/QA34VXPKMMCKSTRLFONZGFK2ZF/bundle.json","state":"https://pith.science/pith/QA34VXPKMMCKSTRLFONZGFK2ZF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QA34VXPKMMCKSTRLFONZGFK2ZF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QA34VXPKMMCKSTRLFONZGFK2ZF","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":"747716a764e289c68bc56b1f2b8f00357e9356c3769481672b76ab6fd986e5d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-12-06T10:57:46Z","title_canon_sha256":"ca42356555ff252c7e45d5da47de3d73dbd661c3294632fe9c18053fc9f0f5b1"},"schema_version":"1.0","source":{"id":"1812.02456","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.02456","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1812.02456v1","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.02456","created_at":"2026-05-17T23:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"QA34VXPKMMCK","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QA34VXPKMMCKSTRL","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QA34VXPK","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:ff9bc6b981fca022e90c2ea2610351bb3f3d9f690dd358c0b44d86bc3588bc6c","target":"graph","created_at":"2026-05-17T23:58:55Z","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":"In this paper, the new concept of quasi-prime ideal is introduced which at the same time generalizes the `prime ideal' and `primary ideal' notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which generalizes the Zariski topology. The basic properties of the quasi-prime spectrum are studied and several interesting results are obtained. Specially, it is proved that if the Grothendieck t-functor is applied on the quasi-prime spectrum then the prime spectrum is deduced. It is also shown that there are the cases that the prime spectrum and quasi-prime spectrum","authors_text":"Abolfazl Tarizadeh, Mohsen Aghajani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-12-06T10:57:46Z","title":"Quasi-prime ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.02456","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:bd95f2c94699020d7b3fa435eb8e7b5fb29e89bda4f6a605b66fe8f13c2333d2","target":"record","created_at":"2026-05-17T23:58:55Z","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":"747716a764e289c68bc56b1f2b8f00357e9356c3769481672b76ab6fd986e5d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-12-06T10:57:46Z","title_canon_sha256":"ca42356555ff252c7e45d5da47de3d73dbd661c3294632fe9c18053fc9f0f5b1"},"schema_version":"1.0","source":{"id":"1812.02456","kind":"arxiv","version":1}},"canonical_sha256":"8037caddea6304a94e2b2b9b93155ac9497a3db847d9b3187dcb6c91619842c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8037caddea6304a94e2b2b9b93155ac9497a3db847d9b3187dcb6c91619842c0","first_computed_at":"2026-05-17T23:58:55.650515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:55.650515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QQ+1fA84wOnh9rwzk8Tf+5EkgEYRIj72k2RuRU8B3KycwL6o4UYfrp16Jf/NHBoNHhpCIEYnli0xMBeEdpYqCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:55.650985Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.02456","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd95f2c94699020d7b3fa435eb8e7b5fb29e89bda4f6a605b66fe8f13c2333d2","sha256:ff9bc6b981fca022e90c2ea2610351bb3f3d9f690dd358c0b44d86bc3588bc6c"],"state_sha256":"8c672fd973eaa0acd7972b68b785a718bdfa601f271dc22e341d9fdf4c946b29"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DAdYfKpEOZR5PJXBRPr8qQQOuc46cIX40psIUxxF+4L++cPQ86FCratNWu413GfJ5Nq0vfUWQcrH1EidFU5/CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T17:57:41.909206Z","bundle_sha256":"2568a2656b3ffa9e427d2b338acb8c8d32c460f89299dcbf9e130f7402a4d0bc"}}