{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6SGX73T4AZM5N5PMFC43EOAIZ4","short_pith_number":"pith:6SGX73T4","canonical_record":{"source":{"id":"1702.03521","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-02-12T13:07:44Z","cross_cats_sorted":[],"title_canon_sha256":"fff6fdd72d979c1a3248753a629a80c7d84797d6c95113e58b2d0e1157031eeb","abstract_canon_sha256":"f9b9c9ff032bcc8f0244ef2bb183e75ef6f47f8585b01c89aeedc4cacbf2127d"},"schema_version":"1.0"},"canonical_sha256":"f48d7fee7c0659d6f5ec28b9b23808cf16879184943e72e4982609a69ff0df2d","source":{"kind":"arxiv","id":"1702.03521","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03521","created_at":"2026-05-18T00:50:53Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03521v1","created_at":"2026-05-18T00:50:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03521","created_at":"2026-05-18T00:50:53Z"},{"alias_kind":"pith_short_12","alias_value":"6SGX73T4AZM5","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6SGX73T4AZM5N5PM","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6SGX73T4","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6SGX73T4AZM5N5PMFC43EOAIZ4","target":"record","payload":{"canonical_record":{"source":{"id":"1702.03521","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-02-12T13:07:44Z","cross_cats_sorted":[],"title_canon_sha256":"fff6fdd72d979c1a3248753a629a80c7d84797d6c95113e58b2d0e1157031eeb","abstract_canon_sha256":"f9b9c9ff032bcc8f0244ef2bb183e75ef6f47f8585b01c89aeedc4cacbf2127d"},"schema_version":"1.0"},"canonical_sha256":"f48d7fee7c0659d6f5ec28b9b23808cf16879184943e72e4982609a69ff0df2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:53.599090Z","signature_b64":"MvlILKIK6ho6S96Pfu2uf2HedPfZBPssgseAofV2XibFpe39TkcGhOGOTxUP53TW7XUC/7wOsmvWfg136w2yCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f48d7fee7c0659d6f5ec28b9b23808cf16879184943e72e4982609a69ff0df2d","last_reissued_at":"2026-05-18T00:50:53.598624Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:53.598624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.03521","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":"2026-05-18T00:50:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"91C/hI5NeGrrPjqwbOr+2xvejhSlTwK5pAWf9E0bVRjpecI6ESphDbslL0koxFVzLx2qQ1lBheZo167UdFGxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T23:34:34.142894Z"},"content_sha256":"f1b92ef5426e100972ef944e07ecadbbfa994b169333d3e30d707bad73c458a5","schema_version":"1.0","event_id":"sha256:f1b92ef5426e100972ef944e07ecadbbfa994b169333d3e30d707bad73c458a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6SGX73T4AZM5N5PMFC43EOAIZ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$(L,M)$-fuzzy convex structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Fu-Gui Shi, Zhen-Yu Xiu","submitted_at":"2017-02-12T13:07:44Z","abstract_excerpt":"In this paper, the notion of $(L,M)$-fuzzy convex structures is introduced. It is a generalization of $L$-convex structures and $M$-fuzzifying convex structures. In our definition of $(L,M)$-fuzzy convex structures, each $L$-fuzzy subset can be regarded as an $L$-convex set to some degree. The notion of convexity preserving functions is also generalized to lattice-valued case. Moreover, under the framework of $(L,M)$-fuzzy convex structures, the concepts of quotient structures, substructures and products are presented and their fundamental properties are discussed. Finally, we create a functor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03521","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":"2026-05-18T00:50:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FEEAOXmq8baSEFajXsg0+Ox4Or0u4ru1VIzh7ZGrTObNhnzwjS0Zs8zsrM+8b9NxxOe86tA/RTl5zh8d19dQCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T23:34:34.143215Z"},"content_sha256":"b8fdf3f5a7306538fe9a4a7f25185aa15730a7352d4123b04794c6a06a36d1e4","schema_version":"1.0","event_id":"sha256:b8fdf3f5a7306538fe9a4a7f25185aa15730a7352d4123b04794c6a06a36d1e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6SGX73T4AZM5N5PMFC43EOAIZ4/bundle.json","state_url":"https://pith.science/pith/6SGX73T4AZM5N5PMFC43EOAIZ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6SGX73T4AZM5N5PMFC43EOAIZ4/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":"2026-08-20T23:34:34Z","links":{"resolver":"https://pith.science/pith/6SGX73T4AZM5N5PMFC43EOAIZ4","bundle":"https://pith.science/pith/6SGX73T4AZM5N5PMFC43EOAIZ4/bundle.json","state":"https://pith.science/pith/6SGX73T4AZM5N5PMFC43EOAIZ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6SGX73T4AZM5N5PMFC43EOAIZ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6SGX73T4AZM5N5PMFC43EOAIZ4","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":"f9b9c9ff032bcc8f0244ef2bb183e75ef6f47f8585b01c89aeedc4cacbf2127d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-02-12T13:07:44Z","title_canon_sha256":"fff6fdd72d979c1a3248753a629a80c7d84797d6c95113e58b2d0e1157031eeb"},"schema_version":"1.0","source":{"id":"1702.03521","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03521","created_at":"2026-05-18T00:50:53Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03521v1","created_at":"2026-05-18T00:50:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03521","created_at":"2026-05-18T00:50:53Z"},{"alias_kind":"pith_short_12","alias_value":"6SGX73T4AZM5","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6SGX73T4AZM5N5PM","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6SGX73T4","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:b8fdf3f5a7306538fe9a4a7f25185aa15730a7352d4123b04794c6a06a36d1e4","target":"graph","created_at":"2026-05-18T00:50:53Z","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 notion of $(L,M)$-fuzzy convex structures is introduced. It is a generalization of $L$-convex structures and $M$-fuzzifying convex structures. In our definition of $(L,M)$-fuzzy convex structures, each $L$-fuzzy subset can be regarded as an $L$-convex set to some degree. The notion of convexity preserving functions is also generalized to lattice-valued case. Moreover, under the framework of $(L,M)$-fuzzy convex structures, the concepts of quotient structures, substructures and products are presented and their fundamental properties are discussed. Finally, we create a functor","authors_text":"Fu-Gui Shi, Zhen-Yu Xiu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-02-12T13:07:44Z","title":"$(L,M)$-fuzzy convex structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03521","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:f1b92ef5426e100972ef944e07ecadbbfa994b169333d3e30d707bad73c458a5","target":"record","created_at":"2026-05-18T00:50:53Z","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":"f9b9c9ff032bcc8f0244ef2bb183e75ef6f47f8585b01c89aeedc4cacbf2127d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-02-12T13:07:44Z","title_canon_sha256":"fff6fdd72d979c1a3248753a629a80c7d84797d6c95113e58b2d0e1157031eeb"},"schema_version":"1.0","source":{"id":"1702.03521","kind":"arxiv","version":1}},"canonical_sha256":"f48d7fee7c0659d6f5ec28b9b23808cf16879184943e72e4982609a69ff0df2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f48d7fee7c0659d6f5ec28b9b23808cf16879184943e72e4982609a69ff0df2d","first_computed_at":"2026-05-18T00:50:53.598624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:53.598624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MvlILKIK6ho6S96Pfu2uf2HedPfZBPssgseAofV2XibFpe39TkcGhOGOTxUP53TW7XUC/7wOsmvWfg136w2yCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:53.599090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.03521","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1b92ef5426e100972ef944e07ecadbbfa994b169333d3e30d707bad73c458a5","sha256:b8fdf3f5a7306538fe9a4a7f25185aa15730a7352d4123b04794c6a06a36d1e4"],"state_sha256":"0dd13ca0bd18dbe00ce5ef00301fffc57cd9640964390c18273aae4a9d6d3b61"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uz+73g8kVBxPCXiF9vTZNNI27vzem1Ns3in4oN9xQktSdxitLW2kfMA7XzshwinliTio5jc/sRFjJH2hF6YFDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T23:34:34.146144Z","bundle_sha256":"dc354fdb7281be43c420c581bea9b0ed6bbde6ad33d37075da4d84cf9e351976"}}