{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AT2T7GAMRIFIIYNSWUBFB6OQ7V","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":"28bfa31bf626f011a064573da09a977b501bf079a341e63959e4f6803e2e63bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2015-11-04T15:17:18Z","title_canon_sha256":"2f08c983bc3eda7e1f58e380dac9439cd3320e214bd2c74db58085b1a41d72c5"},"schema_version":"1.0","source":{"id":"1511.02773","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.02773","created_at":"2026-05-18T01:27:29Z"},{"alias_kind":"arxiv_version","alias_value":"1511.02773v1","created_at":"2026-05-18T01:27:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02773","created_at":"2026-05-18T01:27:29Z"},{"alias_kind":"pith_short_12","alias_value":"AT2T7GAMRIFI","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AT2T7GAMRIFIIYNS","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AT2T7GAM","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:37378482977cc9a1530942d1d998cdc05cd06d9675c25e8a2ac243c5b726f86e","target":"graph","created_at":"2026-05-18T01:27:29Z","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":"We propose a new class of algebraic structure named as \\emph{$(m,n)$-semihyperring} which is a generalization of usual \\emph{semihyperring}. We define the basic properties of $(m,n)$-semihyperring like identity elements, weak distributive $(m,n)$-semihyperring, zero sum free, additively idempotent, hyperideals, homomorphism, inclusion homomorphism, congruence relation, quotient $(m,n)$-semihyperring etc. We propose some lemmas and theorems on homomorphism, congruence relation, quotient $(m,n)$-semihyperring, etc and prove these theorems. We further extend it to introduce the relationship betwe","authors_text":"Nisar Hundewale, Sultan Aljahdali, Syed Eqbal Alam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2015-11-04T15:17:18Z","title":"(m,n)-Semihyperrings and an Algebra of Fuzzy (m,n)-Semihyperrings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02773","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:ae720127a54a48aa72655e718f3eacab815e1dad0bf83a4e71ce6bedbad1c5f3","target":"record","created_at":"2026-05-18T01:27:29Z","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":"28bfa31bf626f011a064573da09a977b501bf079a341e63959e4f6803e2e63bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2015-11-04T15:17:18Z","title_canon_sha256":"2f08c983bc3eda7e1f58e380dac9439cd3320e214bd2c74db58085b1a41d72c5"},"schema_version":"1.0","source":{"id":"1511.02773","kind":"arxiv","version":1}},"canonical_sha256":"04f53f980c8a0a8461b2b50250f9d0fd75dab7e2dc8f2c9b239cc6796a2a3635","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04f53f980c8a0a8461b2b50250f9d0fd75dab7e2dc8f2c9b239cc6796a2a3635","first_computed_at":"2026-05-18T01:27:29.377200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:29.377200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dvfvgEbg5dGfODkGmHlwUK//H4+9fLgZXMCNE4BXyO0k5vONKfrV0R/sGRLgM95TIf21biDDkGMQP96vls24Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:29.377835Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.02773","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae720127a54a48aa72655e718f3eacab815e1dad0bf83a4e71ce6bedbad1c5f3","sha256:37378482977cc9a1530942d1d998cdc05cd06d9675c25e8a2ac243c5b726f86e"],"state_sha256":"898c9a219b462e83ee029c22e18a93677987c2ba7b299dc8815a0717e0fb9f44"}