{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RVULRCXQVZNNDG3KQE75Z2J3RM","short_pith_number":"pith:RVULRCXQ","canonical_record":{"source":{"id":"1304.6371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2013-04-22T11:43:39Z","cross_cats_sorted":[],"title_canon_sha256":"f456bce3efb7d9cfbeda6991da9c6ab9340b104b990f75b90e7b972ff73916a0","abstract_canon_sha256":"df87bba1fd1dc749472e6837fcbf76142118ce16b602386ad53d7d909ba89ea5"},"schema_version":"1.0"},"canonical_sha256":"8d68b88af0ae5ad19b6a813fdce93b8b0007a6231ff5b298d8e1fbf3fb81b901","source":{"kind":"arxiv","id":"1304.6371","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6371","created_at":"2026-05-18T03:27:21Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6371v1","created_at":"2026-05-18T03:27:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6371","created_at":"2026-05-18T03:27:21Z"},{"alias_kind":"pith_short_12","alias_value":"RVULRCXQVZNN","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RVULRCXQVZNNDG3K","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RVULRCXQ","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RVULRCXQVZNNDG3KQE75Z2J3RM","target":"record","payload":{"canonical_record":{"source":{"id":"1304.6371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2013-04-22T11:43:39Z","cross_cats_sorted":[],"title_canon_sha256":"f456bce3efb7d9cfbeda6991da9c6ab9340b104b990f75b90e7b972ff73916a0","abstract_canon_sha256":"df87bba1fd1dc749472e6837fcbf76142118ce16b602386ad53d7d909ba89ea5"},"schema_version":"1.0"},"canonical_sha256":"8d68b88af0ae5ad19b6a813fdce93b8b0007a6231ff5b298d8e1fbf3fb81b901","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:21.761377Z","signature_b64":"4lCge73W99RHh/A14Av5NHJMYV9Cidhn86hgm0CgPfdk10Xc6nh95H8963+5D//pLH6kXLZnMd0g2aRT3L5XDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d68b88af0ae5ad19b6a813fdce93b8b0007a6231ff5b298d8e1fbf3fb81b901","last_reissued_at":"2026-05-18T03:27:21.760826Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:21.760826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.6371","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":"2026-05-18T03:27:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uJARZVHVe5K93ZgeBbd6+33RGMAMYblpxCKEsyJF+dcmdWB0lkCTGnqL8n6Z62ZrhWRYGFGHMrlXMccvIiowCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:23:50.955133Z"},"content_sha256":"481c6b3710dd3b00dd81f1d31a73e0882c7424c1aad02054ed5423c1864d932f","schema_version":"1.0","event_id":"sha256:481c6b3710dd3b00dd81f1d31a73e0882c7424c1aad02054ed5423c1864d932f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RVULRCXQVZNNDG3KQE75Z2J3RM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Fuzzy semihyperrings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Aqeel Ahmed, Muhammad aslam","submitted_at":"2013-04-22T11:43:39Z","abstract_excerpt":"In this article we introduce the study of fuzzy semihyperrings and fuzzy R-semihypermodules, where R is a semihyperrings and R-semihypermodules are represntations of R. In particular, semihyperrings all of whose hyperideals are idempotent, called fully idempotent semihyperrings, are investigated in a fuzzy context. It is proved, among other results, that a semihyperring R is fully idempotent if and only if the lattics of fuzzy hyperideals of R is distributive under the sum and product of fuzzy hyperideals. It is also shown that the set of proper fuzzy prime hyperideals of a fully idempotent se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6371","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":"2026-05-18T03:27:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+6DwEhGRB+4QqX8kVEKF+rhMJYBK6icdJ/ApkaqBuuKKCIeB21ln322zFeTbGcdueLLiYFW2DGUE8QuUdXYsAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:23:50.955826Z"},"content_sha256":"6d2ce908b7b948c8c2ab7762ca4aa6a38d9d9dcfd0cd3cd265e4f4452020f381","schema_version":"1.0","event_id":"sha256:6d2ce908b7b948c8c2ab7762ca4aa6a38d9d9dcfd0cd3cd265e4f4452020f381"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RVULRCXQVZNNDG3KQE75Z2J3RM/bundle.json","state_url":"https://pith.science/pith/RVULRCXQVZNNDG3KQE75Z2J3RM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RVULRCXQVZNNDG3KQE75Z2J3RM/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":"2026-05-27T19:23:50Z","links":{"resolver":"https://pith.science/pith/RVULRCXQVZNNDG3KQE75Z2J3RM","bundle":"https://pith.science/pith/RVULRCXQVZNNDG3KQE75Z2J3RM/bundle.json","state":"https://pith.science/pith/RVULRCXQVZNNDG3KQE75Z2J3RM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RVULRCXQVZNNDG3KQE75Z2J3RM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RVULRCXQVZNNDG3KQE75Z2J3RM","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":"df87bba1fd1dc749472e6837fcbf76142118ce16b602386ad53d7d909ba89ea5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2013-04-22T11:43:39Z","title_canon_sha256":"f456bce3efb7d9cfbeda6991da9c6ab9340b104b990f75b90e7b972ff73916a0"},"schema_version":"1.0","source":{"id":"1304.6371","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6371","created_at":"2026-05-18T03:27:21Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6371v1","created_at":"2026-05-18T03:27:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6371","created_at":"2026-05-18T03:27:21Z"},{"alias_kind":"pith_short_12","alias_value":"RVULRCXQVZNN","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RVULRCXQVZNNDG3K","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RVULRCXQ","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:6d2ce908b7b948c8c2ab7762ca4aa6a38d9d9dcfd0cd3cd265e4f4452020f381","target":"graph","created_at":"2026-05-18T03:27:21Z","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 article we introduce the study of fuzzy semihyperrings and fuzzy R-semihypermodules, where R is a semihyperrings and R-semihypermodules are represntations of R. In particular, semihyperrings all of whose hyperideals are idempotent, called fully idempotent semihyperrings, are investigated in a fuzzy context. It is proved, among other results, that a semihyperring R is fully idempotent if and only if the lattics of fuzzy hyperideals of R is distributive under the sum and product of fuzzy hyperideals. It is also shown that the set of proper fuzzy prime hyperideals of a fully idempotent se","authors_text":"Aqeel Ahmed, Muhammad aslam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2013-04-22T11:43:39Z","title":"On Fuzzy semihyperrings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6371","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":"sha256:481c6b3710dd3b00dd81f1d31a73e0882c7424c1aad02054ed5423c1864d932f","target":"record","created_at":"2026-05-18T03:27:21Z","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":"df87bba1fd1dc749472e6837fcbf76142118ce16b602386ad53d7d909ba89ea5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2013-04-22T11:43:39Z","title_canon_sha256":"f456bce3efb7d9cfbeda6991da9c6ab9340b104b990f75b90e7b972ff73916a0"},"schema_version":"1.0","source":{"id":"1304.6371","kind":"arxiv","version":1}},"canonical_sha256":"8d68b88af0ae5ad19b6a813fdce93b8b0007a6231ff5b298d8e1fbf3fb81b901","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d68b88af0ae5ad19b6a813fdce93b8b0007a6231ff5b298d8e1fbf3fb81b901","first_computed_at":"2026-05-18T03:27:21.760826Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:21.760826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4lCge73W99RHh/A14Av5NHJMYV9Cidhn86hgm0CgPfdk10Xc6nh95H8963+5D//pLH6kXLZnMd0g2aRT3L5XDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:21.761377Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.6371","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:481c6b3710dd3b00dd81f1d31a73e0882c7424c1aad02054ed5423c1864d932f","sha256:6d2ce908b7b948c8c2ab7762ca4aa6a38d9d9dcfd0cd3cd265e4f4452020f381"],"state_sha256":"0d6e8e0829494babc5a3735f40f9ff5102e12f8eafc09fabda0bb66e0e7fefaf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3yByIki7CPcLlN4HCPhvaz8nDFqb3gxnnPwFor3GDSaSo1m65Q+Qs3DyisIWJR2QTPS+GtfSF81L/ARdusTCAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T19:23:50.959270Z","bundle_sha256":"aafc95346f20acca68c64b7a04ec1560d4fb51ff5f525e746705779fc1469980"}}