{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WQG7NDN5XW676ZFUBVJZF5CM4G","short_pith_number":"pith:WQG7NDN5","canonical_record":{"source":{"id":"1309.4921","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-19T10:37:59Z","cross_cats_sorted":[],"title_canon_sha256":"e2e3d58729e14e5fdff561203ee26dd176329919f98d5c82f3dab271e6eb82a5","abstract_canon_sha256":"86e14a80d1edb3863a67e43323ec162bd7ca1092e7c0e76c15035395aea0e446"},"schema_version":"1.0"},"canonical_sha256":"b40df68dbdbdbdff64b40d5392f44ce1a5201bf240f542e21744294c140ecb8b","source":{"kind":"arxiv","id":"1309.4921","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4921","created_at":"2026-05-18T03:12:56Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4921v1","created_at":"2026-05-18T03:12:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4921","created_at":"2026-05-18T03:12:56Z"},{"alias_kind":"pith_short_12","alias_value":"WQG7NDN5XW67","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WQG7NDN5XW676ZFU","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WQG7NDN5","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WQG7NDN5XW676ZFUBVJZF5CM4G","target":"record","payload":{"canonical_record":{"source":{"id":"1309.4921","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-19T10:37:59Z","cross_cats_sorted":[],"title_canon_sha256":"e2e3d58729e14e5fdff561203ee26dd176329919f98d5c82f3dab271e6eb82a5","abstract_canon_sha256":"86e14a80d1edb3863a67e43323ec162bd7ca1092e7c0e76c15035395aea0e446"},"schema_version":"1.0"},"canonical_sha256":"b40df68dbdbdbdff64b40d5392f44ce1a5201bf240f542e21744294c140ecb8b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:56.902261Z","signature_b64":"LOjR/NYdA24wt0aB0UOFUAN2qjx5X9jsAq/BLNQZG8L8/UkQt2RD47D93fhlKqvvMZGLeipzENgHzT2Xc5QTBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b40df68dbdbdbdff64b40d5392f44ce1a5201bf240f542e21744294c140ecb8b","last_reissued_at":"2026-05-18T03:12:56.901428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:56.901428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.4921","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":"2026-05-18T03:12:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oRiRHDSzyXKJLvGTaGsKEcdh73UUhCKEtxGpEHYtxROuK3/J2gWs/Pzl4BWxUjFU1rQr93oUcnMWPSCtG9W2Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:54:09.521646Z"},"content_sha256":"6ba3760d93fec1af7cb61bcf4748d25ecfda86c78051cb226bdc554ebf4abca5","schema_version":"1.0","event_id":"sha256:6ba3760d93fec1af7cb61bcf4748d25ecfda86c78051cb226bdc554ebf4abca5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WQG7NDN5XW676ZFUBVJZF5CM4G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parameterized Norm and Parameterized Fixed-Point Theorem by Using Fuzzy Soft Set Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Abdul Razak Salleh, Adem Kilicman, Azadeh Zahedi Khameneh","submitted_at":"2013-09-19T10:37:59Z","abstract_excerpt":"From last decade, when Molodtsov introduced the theory of soft set as a new approach to deal with uncertainties, until now this theory was considered sharply by a fair number of researchers. Combination of fuzzy set theory and soft set theory, called fuzzy soft set theory, by Maji et.al opened a new way for researchers whose frame work of study is soft sets and fuzzy sets. Although published papers in this area have considered both application and theoretical aspects of fuzzy soft set theory, the concept of norm for a fuzzy soft set has not been studied yet. We begin this paper by introducing "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4921","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":"2026-05-18T03:12:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HEMz1zXtz9J0DzbM78VnrWHwkFxXW270z9bdw9YHeJdbS589GvKGCtzRTJsXO20BEIhtT6hT8cEp4pngf84FDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:54:09.522280Z"},"content_sha256":"8d05ae6bf29c40a5d757f9651b7b38aeab45a845e00f210df44f7e2bff296969","schema_version":"1.0","event_id":"sha256:8d05ae6bf29c40a5d757f9651b7b38aeab45a845e00f210df44f7e2bff296969"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WQG7NDN5XW676ZFUBVJZF5CM4G/bundle.json","state_url":"https://pith.science/pith/WQG7NDN5XW676ZFUBVJZF5CM4G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WQG7NDN5XW676ZFUBVJZF5CM4G/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":"2026-06-07T22:54:09Z","links":{"resolver":"https://pith.science/pith/WQG7NDN5XW676ZFUBVJZF5CM4G","bundle":"https://pith.science/pith/WQG7NDN5XW676ZFUBVJZF5CM4G/bundle.json","state":"https://pith.science/pith/WQG7NDN5XW676ZFUBVJZF5CM4G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WQG7NDN5XW676ZFUBVJZF5CM4G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WQG7NDN5XW676ZFUBVJZF5CM4G","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":"86e14a80d1edb3863a67e43323ec162bd7ca1092e7c0e76c15035395aea0e446","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-19T10:37:59Z","title_canon_sha256":"e2e3d58729e14e5fdff561203ee26dd176329919f98d5c82f3dab271e6eb82a5"},"schema_version":"1.0","source":{"id":"1309.4921","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.4921","created_at":"2026-05-18T03:12:56Z"},{"alias_kind":"arxiv_version","alias_value":"1309.4921v1","created_at":"2026-05-18T03:12:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.4921","created_at":"2026-05-18T03:12:56Z"},{"alias_kind":"pith_short_12","alias_value":"WQG7NDN5XW67","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WQG7NDN5XW676ZFU","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WQG7NDN5","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:8d05ae6bf29c40a5d757f9651b7b38aeab45a845e00f210df44f7e2bff296969","target":"graph","created_at":"2026-05-18T03:12:56Z","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":"From last decade, when Molodtsov introduced the theory of soft set as a new approach to deal with uncertainties, until now this theory was considered sharply by a fair number of researchers. Combination of fuzzy set theory and soft set theory, called fuzzy soft set theory, by Maji et.al opened a new way for researchers whose frame work of study is soft sets and fuzzy sets. Although published papers in this area have considered both application and theoretical aspects of fuzzy soft set theory, the concept of norm for a fuzzy soft set has not been studied yet. We begin this paper by introducing ","authors_text":"Abdul Razak Salleh, Adem Kilicman, Azadeh Zahedi Khameneh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-19T10:37:59Z","title":"Parameterized Norm and Parameterized Fixed-Point Theorem by Using Fuzzy Soft Set Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4921","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":"sha256:6ba3760d93fec1af7cb61bcf4748d25ecfda86c78051cb226bdc554ebf4abca5","target":"record","created_at":"2026-05-18T03:12:56Z","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":"86e14a80d1edb3863a67e43323ec162bd7ca1092e7c0e76c15035395aea0e446","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-09-19T10:37:59Z","title_canon_sha256":"e2e3d58729e14e5fdff561203ee26dd176329919f98d5c82f3dab271e6eb82a5"},"schema_version":"1.0","source":{"id":"1309.4921","kind":"arxiv","version":1}},"canonical_sha256":"b40df68dbdbdbdff64b40d5392f44ce1a5201bf240f542e21744294c140ecb8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b40df68dbdbdbdff64b40d5392f44ce1a5201bf240f542e21744294c140ecb8b","first_computed_at":"2026-05-18T03:12:56.901428Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:56.901428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LOjR/NYdA24wt0aB0UOFUAN2qjx5X9jsAq/BLNQZG8L8/UkQt2RD47D93fhlKqvvMZGLeipzENgHzT2Xc5QTBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:56.902261Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.4921","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ba3760d93fec1af7cb61bcf4748d25ecfda86c78051cb226bdc554ebf4abca5","sha256:8d05ae6bf29c40a5d757f9651b7b38aeab45a845e00f210df44f7e2bff296969"],"state_sha256":"326c88d88ad85937cbeb4987a05720a06ada8f616722a66f88cafb8677bbcd7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"doochkJGuhvAWhLcPVZoUFWup0i6zExyQdsiPvNcndIXE7Aq0fuXE/aEL2xjqKXmjvrcUhg4wGOd4+vVibsRCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T22:54:09.526365Z","bundle_sha256":"d9f02da216fbcd9c3ade318e2e907093d91fb6e9fcce21775921d4afecd1d006"}}