{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:Y2KYCSN4W2C6PCPAQKPEP53NTI","short_pith_number":"pith:Y2KYCSN4","schema_version":"1.0","canonical_sha256":"c6958149bcb685e789e0829e47f76d9a0966871b9e8f357bb4bc93f4e8c7af31","source":{"kind":"arxiv","id":"1707.08617","version":1},"attestation_state":"computed","paper":{"title":"n-Dimensional Fuzzy Negations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Benjam\\'in Bedregal, Ivan Mezzomo, Renata Hax Sander Reiser","submitted_at":"2017-07-26T19:27:13Z","abstract_excerpt":"n-Dimensional fuzzy sets is a fuzzy set extension where the membership values are n-tuples of real numbers in the unit interval [0,1] orderly increased, called n-dimensional intervals. The set of n-dimensional intervals is denoted by Ln([0,1]). This paper aims to investigate a special extension from [0,1] - n-representable fuzzy negations on Ln([0,1]), summarizing the class of such functions which are continuous and monotone by part. The main properties of (strong) fuzzy negations on [0,1] are preserved by representable (strong) fuzzy negation on Ln([0,1]), mainly related to the analysis of de"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.08617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-07-26T19:27:13Z","cross_cats_sorted":[],"title_canon_sha256":"b43ff2dbd3362310a7e90f5bbad5753e2e3000afde059cd9ec59e6e95d3c3282","abstract_canon_sha256":"4feeddbb8730d5378a810cbde9e848abe915fdabcf08ef0f3157027a9568b561"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:42.099981Z","signature_b64":"BlzbcItXYiMLlJZpg5a9Sw+F/bmhd6yW6FkfxZ2Dkru2gFKccmFReNGRKStgr5LTkEuNcSOCkNuobuE+SsalCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6958149bcb685e789e0829e47f76d9a0966871b9e8f357bb4bc93f4e8c7af31","last_reissued_at":"2026-05-17T23:46:42.099273Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:42.099273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"n-Dimensional Fuzzy Negations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Benjam\\'in Bedregal, Ivan Mezzomo, Renata Hax Sander Reiser","submitted_at":"2017-07-26T19:27:13Z","abstract_excerpt":"n-Dimensional fuzzy sets is a fuzzy set extension where the membership values are n-tuples of real numbers in the unit interval [0,1] orderly increased, called n-dimensional intervals. The set of n-dimensional intervals is denoted by Ln([0,1]). This paper aims to investigate a special extension from [0,1] - n-representable fuzzy negations on Ln([0,1]), summarizing the class of such functions which are continuous and monotone by part. The main properties of (strong) fuzzy negations on [0,1] are preserved by representable (strong) fuzzy negation on Ln([0,1]), mainly related to the analysis of de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08617","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.08617","created_at":"2026-05-17T23:46:42.099419+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.08617v1","created_at":"2026-05-17T23:46:42.099419+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.08617","created_at":"2026-05-17T23:46:42.099419+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y2KYCSN4W2C6","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y2KYCSN4W2C6PCPA","created_at":"2026-05-18T12:31:56.362134+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y2KYCSN4","created_at":"2026-05-18T12:31:56.362134+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y2KYCSN4W2C6PCPAQKPEP53NTI","json":"https://pith.science/pith/Y2KYCSN4W2C6PCPAQKPEP53NTI.json","graph_json":"https://pith.science/api/pith-number/Y2KYCSN4W2C6PCPAQKPEP53NTI/graph.json","events_json":"https://pith.science/api/pith-number/Y2KYCSN4W2C6PCPAQKPEP53NTI/events.json","paper":"https://pith.science/paper/Y2KYCSN4"},"agent_actions":{"view_html":"https://pith.science/pith/Y2KYCSN4W2C6PCPAQKPEP53NTI","download_json":"https://pith.science/pith/Y2KYCSN4W2C6PCPAQKPEP53NTI.json","view_paper":"https://pith.science/paper/Y2KYCSN4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.08617&json=true","fetch_graph":"https://pith.science/api/pith-number/Y2KYCSN4W2C6PCPAQKPEP53NTI/graph.json","fetch_events":"https://pith.science/api/pith-number/Y2KYCSN4W2C6PCPAQKPEP53NTI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y2KYCSN4W2C6PCPAQKPEP53NTI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y2KYCSN4W2C6PCPAQKPEP53NTI/action/storage_attestation","attest_author":"https://pith.science/pith/Y2KYCSN4W2C6PCPAQKPEP53NTI/action/author_attestation","sign_citation":"https://pith.science/pith/Y2KYCSN4W2C6PCPAQKPEP53NTI/action/citation_signature","submit_replication":"https://pith.science/pith/Y2KYCSN4W2C6PCPAQKPEP53NTI/action/replication_record"}},"created_at":"2026-05-17T23:46:42.099419+00:00","updated_at":"2026-05-17T23:46:42.099419+00:00"}