{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:Y2KYCSN4W2C6PCPAQKPEP53NTI","short_pith_number":"pith:Y2KYCSN4","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"},"canonical_sha256":"c6958149bcb685e789e0829e47f76d9a0966871b9e8f357bb4bc93f4e8c7af31","source":{"kind":"arxiv","id":"1707.08617","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.08617","created_at":"2026-05-17T23:46:42Z"},{"alias_kind":"arxiv_version","alias_value":"1707.08617v1","created_at":"2026-05-17T23:46:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.08617","created_at":"2026-05-17T23:46:42Z"},{"alias_kind":"pith_short_12","alias_value":"Y2KYCSN4W2C6","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"Y2KYCSN4W2C6PCPA","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"Y2KYCSN4","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:Y2KYCSN4W2C6PCPAQKPEP53NTI","target":"record","payload":{"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"},"canonical_sha256":"c6958149bcb685e789e0829e47f76d9a0966871b9e8f357bb4bc93f4e8c7af31","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"},"source_kind":"arxiv","source_id":"1707.08617","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":"2026-05-17T23:46:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wdRkoKs3uOdL1BXqkmpdNpPaPh9Rxt5jFxeFx73PSAAuEdTFqdyAYjSv4p7FbqDZugL3zZvHskVTvkZ2S50FCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T07:39:16.299239Z"},"content_sha256":"ca229f475e06a6e8f13879175023438da1f6d40b319cc46c98f1c75de5553b7f","schema_version":"1.0","event_id":"sha256:ca229f475e06a6e8f13879175023438da1f6d40b319cc46c98f1c75de5553b7f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:Y2KYCSN4W2C6PCPAQKPEP53NTI","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OaqYI4nd01wE6VtzfUYMHz9+wu7ztA1/FWskg26PbrAlfiXxTW9Vq30VwZjdspO9RHVEb3o1I7YMMWX48nYyCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T07:39:16.299589Z"},"content_sha256":"d42dc22815c1128cd7a7f0294b97b335ca9b5cea27658b9ca4f0936e715ba95d","schema_version":"1.0","event_id":"sha256:d42dc22815c1128cd7a7f0294b97b335ca9b5cea27658b9ca4f0936e715ba95d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y2KYCSN4W2C6PCPAQKPEP53NTI/bundle.json","state_url":"https://pith.science/pith/Y2KYCSN4W2C6PCPAQKPEP53NTI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y2KYCSN4W2C6PCPAQKPEP53NTI/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":"2026-06-27T07:39:16Z","links":{"resolver":"https://pith.science/pith/Y2KYCSN4W2C6PCPAQKPEP53NTI","bundle":"https://pith.science/pith/Y2KYCSN4W2C6PCPAQKPEP53NTI/bundle.json","state":"https://pith.science/pith/Y2KYCSN4W2C6PCPAQKPEP53NTI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y2KYCSN4W2C6PCPAQKPEP53NTI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Y2KYCSN4W2C6PCPAQKPEP53NTI","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":"4feeddbb8730d5378a810cbde9e848abe915fdabcf08ef0f3157027a9568b561","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-07-26T19:27:13Z","title_canon_sha256":"b43ff2dbd3362310a7e90f5bbad5753e2e3000afde059cd9ec59e6e95d3c3282"},"schema_version":"1.0","source":{"id":"1707.08617","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.08617","created_at":"2026-05-17T23:46:42Z"},{"alias_kind":"arxiv_version","alias_value":"1707.08617v1","created_at":"2026-05-17T23:46:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.08617","created_at":"2026-05-17T23:46:42Z"},{"alias_kind":"pith_short_12","alias_value":"Y2KYCSN4W2C6","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"Y2KYCSN4W2C6PCPA","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"Y2KYCSN4","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:d42dc22815c1128cd7a7f0294b97b335ca9b5cea27658b9ca4f0936e715ba95d","target":"graph","created_at":"2026-05-17T23:46:42Z","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":"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","authors_text":"Benjam\\'in Bedregal, Ivan Mezzomo, Renata Hax Sander Reiser","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-07-26T19:27:13Z","title":"n-Dimensional Fuzzy Negations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08617","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:ca229f475e06a6e8f13879175023438da1f6d40b319cc46c98f1c75de5553b7f","target":"record","created_at":"2026-05-17T23:46:42Z","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":"4feeddbb8730d5378a810cbde9e848abe915fdabcf08ef0f3157027a9568b561","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2017-07-26T19:27:13Z","title_canon_sha256":"b43ff2dbd3362310a7e90f5bbad5753e2e3000afde059cd9ec59e6e95d3c3282"},"schema_version":"1.0","source":{"id":"1707.08617","kind":"arxiv","version":1}},"canonical_sha256":"c6958149bcb685e789e0829e47f76d9a0966871b9e8f357bb4bc93f4e8c7af31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6958149bcb685e789e0829e47f76d9a0966871b9e8f357bb4bc93f4e8c7af31","first_computed_at":"2026-05-17T23:46:42.099273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:42.099273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BlzbcItXYiMLlJZpg5a9Sw+F/bmhd6yW6FkfxZ2Dkru2gFKccmFReNGRKStgr5LTkEuNcSOCkNuobuE+SsalCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:42.099981Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.08617","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca229f475e06a6e8f13879175023438da1f6d40b319cc46c98f1c75de5553b7f","sha256:d42dc22815c1128cd7a7f0294b97b335ca9b5cea27658b9ca4f0936e715ba95d"],"state_sha256":"bf538f6bebbed5e173e3c12924e00f423b7748794c8306800c981bc3d0ca453d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"09t69bk8Ar4E9rjD2Kv1mtlLLTNtTaGqsBZKMXcjSNGrHn4IiYVM4d6JzANHt7IAjdvbSyhhP3ZHQPNi+yoNDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T07:39:16.301564Z","bundle_sha256":"d2f4c37a13a599c4545aa7f3f88c996e8791063e08ad1b711673d2c73df2c9cf"}}