{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:JL7RU3DI5DER34RZAYPLXFDHSR","short_pith_number":"pith:JL7RU3DI","canonical_record":{"source":{"id":"2411.16888","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-11-25T19:39:56Z","cross_cats_sorted":[],"title_canon_sha256":"4a98354d6a09763e0f09065bc010645c1a24c7fd2de5a22d41ed1786d820a9bf","abstract_canon_sha256":"4e8079848abc31a491b011d4f0d814a5e45eab3567924e914bc984ace156edec"},"schema_version":"1.0"},"canonical_sha256":"4aff1a6c68e8c91df239061ebb9467946400ec719d19be5d7d0fb37289966f67","source":{"kind":"arxiv","id":"2411.16888","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.16888","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"arxiv_version","alias_value":"2411.16888v1","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16888","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"pith_short_12","alias_value":"JL7RU3DI5DER","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"pith_short_16","alias_value":"JL7RU3DI5DER34RZ","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"pith_short_8","alias_value":"JL7RU3DI","created_at":"2026-07-05T09:40:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:JL7RU3DI5DER34RZAYPLXFDHSR","target":"record","payload":{"canonical_record":{"source":{"id":"2411.16888","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-11-25T19:39:56Z","cross_cats_sorted":[],"title_canon_sha256":"4a98354d6a09763e0f09065bc010645c1a24c7fd2de5a22d41ed1786d820a9bf","abstract_canon_sha256":"4e8079848abc31a491b011d4f0d814a5e45eab3567924e914bc984ace156edec"},"schema_version":"1.0"},"canonical_sha256":"4aff1a6c68e8c91df239061ebb9467946400ec719d19be5d7d0fb37289966f67","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:40:24.305274Z","signature_b64":"U+gjopoQQj8nt6ipyUCTdySxtz3QDF0250qWF0UScX1UPXzkMWLyzuxPd/OoURcPmStpR3pkMXjEepSdqQsCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4aff1a6c68e8c91df239061ebb9467946400ec719d19be5d7d0fb37289966f67","last_reissued_at":"2026-07-05T09:40:24.304854Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:40:24.304854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.16888","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":"2026-07-05T09:40:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Veh8pQO4Hgu6igxO6pTHmQm9w0rnpRfOvW2bhYVbT97b3x65CnjpjTloavrlAZM/g6En4d2YHHMd4S6AlfMADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T04:17:56.150247Z"},"content_sha256":"adfeea4bf798db619a19b9fa76f9ab67b39491a42a2bd9792c0f833d365bf3eb","schema_version":"1.0","event_id":"sha256:adfeea4bf798db619a19b9fa76f9ab67b39491a42a2bd9792c0f833d365bf3eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:JL7RU3DI5DER34RZAYPLXFDHSR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the prime spectrum of the amalgamations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Y. Azimi","submitted_at":"2024-11-25T19:39:56Z","abstract_excerpt":"Let $f:R\\to S$ be a ring homomorphism and $J$ be an ideal of $S$. Then the subring $R\\bowtie^fJ:=\\{(r,f(r)+j)\\mid r\\in R$ and $j\\in J\\}$ of $R\\times S$ is called the amalgamation of $R$ with $S$ along $J$ with respect to $f$. In this paper, we will deepen the study of the prime spectrum of the amalgamations and characterize when $R\\bowtie^fJ$ is a pm-ring. We also investigate the transfer of compactly packed and properly zipped property on amalgamated constructions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16888","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/2411.16888/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":"2026-07-05T09:40:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"05SRPGNxgWEPCetLLb97e7jIPHVe+5B/UTMyhDt2OPw4V4FsKki6csP7Te51wkr+w3VKMVRm6twp/Q2ekN9yCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T04:17:56.150764Z"},"content_sha256":"752f16509620e1ece8a87a85549970018602c06ab0ab454bb45c06e0cb1430ec","schema_version":"1.0","event_id":"sha256:752f16509620e1ece8a87a85549970018602c06ab0ab454bb45c06e0cb1430ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JL7RU3DI5DER34RZAYPLXFDHSR/bundle.json","state_url":"https://pith.science/pith/JL7RU3DI5DER34RZAYPLXFDHSR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JL7RU3DI5DER34RZAYPLXFDHSR/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":"2026-08-13T04:17:56Z","links":{"resolver":"https://pith.science/pith/JL7RU3DI5DER34RZAYPLXFDHSR","bundle":"https://pith.science/pith/JL7RU3DI5DER34RZAYPLXFDHSR/bundle.json","state":"https://pith.science/pith/JL7RU3DI5DER34RZAYPLXFDHSR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JL7RU3DI5DER34RZAYPLXFDHSR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:JL7RU3DI5DER34RZAYPLXFDHSR","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":"4e8079848abc31a491b011d4f0d814a5e45eab3567924e914bc984ace156edec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-11-25T19:39:56Z","title_canon_sha256":"4a98354d6a09763e0f09065bc010645c1a24c7fd2de5a22d41ed1786d820a9bf"},"schema_version":"1.0","source":{"id":"2411.16888","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.16888","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"arxiv_version","alias_value":"2411.16888v1","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16888","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"pith_short_12","alias_value":"JL7RU3DI5DER","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"pith_short_16","alias_value":"JL7RU3DI5DER34RZ","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"pith_short_8","alias_value":"JL7RU3DI","created_at":"2026-07-05T09:40:24Z"}],"graph_snapshots":[{"event_id":"sha256:752f16509620e1ece8a87a85549970018602c06ab0ab454bb45c06e0cb1430ec","target":"graph","created_at":"2026-07-05T09:40:24Z","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/2411.16888/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $f:R\\to S$ be a ring homomorphism and $J$ be an ideal of $S$. Then the subring $R\\bowtie^fJ:=\\{(r,f(r)+j)\\mid r\\in R$ and $j\\in J\\}$ of $R\\times S$ is called the amalgamation of $R$ with $S$ along $J$ with respect to $f$. In this paper, we will deepen the study of the prime spectrum of the amalgamations and characterize when $R\\bowtie^fJ$ is a pm-ring. We also investigate the transfer of compactly packed and properly zipped property on amalgamated constructions.","authors_text":"Y. Azimi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-11-25T19:39:56Z","title":"On the prime spectrum of the amalgamations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16888","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:adfeea4bf798db619a19b9fa76f9ab67b39491a42a2bd9792c0f833d365bf3eb","target":"record","created_at":"2026-07-05T09:40:24Z","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":"4e8079848abc31a491b011d4f0d814a5e45eab3567924e914bc984ace156edec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-11-25T19:39:56Z","title_canon_sha256":"4a98354d6a09763e0f09065bc010645c1a24c7fd2de5a22d41ed1786d820a9bf"},"schema_version":"1.0","source":{"id":"2411.16888","kind":"arxiv","version":1}},"canonical_sha256":"4aff1a6c68e8c91df239061ebb9467946400ec719d19be5d7d0fb37289966f67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4aff1a6c68e8c91df239061ebb9467946400ec719d19be5d7d0fb37289966f67","first_computed_at":"2026-07-05T09:40:24.304854Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:40:24.304854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U+gjopoQQj8nt6ipyUCTdySxtz3QDF0250qWF0UScX1UPXzkMWLyzuxPd/OoURcPmStpR3pkMXjEepSdqQsCDg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:40:24.305274Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.16888","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:adfeea4bf798db619a19b9fa76f9ab67b39491a42a2bd9792c0f833d365bf3eb","sha256:752f16509620e1ece8a87a85549970018602c06ab0ab454bb45c06e0cb1430ec"],"state_sha256":"f1f937bb6d68da1b56e8fdcb1464cd51a029e6abd51ce3f00b65ceda4ed13af3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LX0Qk8+myjIzeSEIxh+t46sQ7eMI6Nx6M8RbzGS4+WoMbSpEHotxZeM8Sm+e3Q3srDhP/iAvYRmHFZyFMW5/BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T04:17:56.155894Z","bundle_sha256":"b81be512eae3b4ba45299345f705d72d44229006a679a4cd0df22df56a645edf"}}