{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HPU7GROWS7BHYRQ5YRGGBL5BHN","short_pith_number":"pith:HPU7GROW","canonical_record":{"source":{"id":"1604.06037","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-04-20T17:12:03Z","cross_cats_sorted":[],"title_canon_sha256":"1fab4d05fbb01c4d2ac592dbb87b1be42cd4dc4858cdf2e30bf2ab6a230d1b47","abstract_canon_sha256":"c564b0564910663877396bf1d89254a7728c06a4fe6a48d8a792e7bfc09d21d7"},"schema_version":"1.0"},"canonical_sha256":"3be9f345d697c27c461dc44c60afa13b5e81b22441bebfb8a1eeeaaa979f2633","source":{"kind":"arxiv","id":"1604.06037","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06037","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06037v1","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06037","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"pith_short_12","alias_value":"HPU7GROWS7BH","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HPU7GROWS7BHYRQ5","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HPU7GROW","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HPU7GROWS7BHYRQ5YRGGBL5BHN","target":"record","payload":{"canonical_record":{"source":{"id":"1604.06037","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-04-20T17:12:03Z","cross_cats_sorted":[],"title_canon_sha256":"1fab4d05fbb01c4d2ac592dbb87b1be42cd4dc4858cdf2e30bf2ab6a230d1b47","abstract_canon_sha256":"c564b0564910663877396bf1d89254a7728c06a4fe6a48d8a792e7bfc09d21d7"},"schema_version":"1.0"},"canonical_sha256":"3be9f345d697c27c461dc44c60afa13b5e81b22441bebfb8a1eeeaaa979f2633","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:33.910543Z","signature_b64":"WMt25rfH0/Qa/V0zNvbVLhFyPBsobeoGOb33KOZsusIv4gGZB+PoslwaLOCWmg+O/OMkU2xF0JywIymSnBkoCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3be9f345d697c27c461dc44c60afa13b5e81b22441bebfb8a1eeeaaa979f2633","last_reissued_at":"2026-05-18T01:16:33.909604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:33.909604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.06037","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":"2026-05-18T01:16:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K53T4PtDpQbZkchsKru59Q11Oq6hjzYsgthQJC3or0Cmaf8bqtdp+fvV0IqHI1RilDtshAoUYvoGm1hKmm9AAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T07:21:29.837010Z"},"content_sha256":"577ce35dd27ac21a10256f652879735296916643952a34ddabd4a467b3630422","schema_version":"1.0","event_id":"sha256:577ce35dd27ac21a10256f652879735296916643952a34ddabd4a467b3630422"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HPU7GROWS7BHYRQ5YRGGBL5BHN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Commutative pseudo equality algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Lavinia Corina Ciungu","submitted_at":"2016-04-20T17:12:03Z","abstract_excerpt":"Pseudo equality algebras were initially introduced by Jenei and $\\rm K\\acute{o}r\\acute{o}di$ as a possible algebraic semantic for fuzzy type theory, and they have been revised by Dvure\\v{c}enskij and Zahiri under the name of JK-algebras. In this paper we define and study the commutative pseudo equality algebras. We give a characterization of commutative pseudo equality algebras and we prove that an invariant pseudo equality algebra is commutative if and only if its corresponding pseudo BCK(pC)-meet-semilattice is commutative. Other results consist of proving that every commutative pseudo equal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06037","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":"2026-05-18T01:16:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vkHb923zKFEqFEeENS3/cCytVgZ4x9vDik9N4U5PmB3Puqu7CvqtlCaaRXfM7IZTGaoW6KRBQIrAsG6VO1nMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T07:21:29.837382Z"},"content_sha256":"ddd2b507adf52d8b067a50b3b2e78d6c437f85c82aba11de4513d71f644b5733","schema_version":"1.0","event_id":"sha256:ddd2b507adf52d8b067a50b3b2e78d6c437f85c82aba11de4513d71f644b5733"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HPU7GROWS7BHYRQ5YRGGBL5BHN/bundle.json","state_url":"https://pith.science/pith/HPU7GROWS7BHYRQ5YRGGBL5BHN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HPU7GROWS7BHYRQ5YRGGBL5BHN/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":"2026-06-25T07:21:29Z","links":{"resolver":"https://pith.science/pith/HPU7GROWS7BHYRQ5YRGGBL5BHN","bundle":"https://pith.science/pith/HPU7GROWS7BHYRQ5YRGGBL5BHN/bundle.json","state":"https://pith.science/pith/HPU7GROWS7BHYRQ5YRGGBL5BHN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HPU7GROWS7BHYRQ5YRGGBL5BHN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HPU7GROWS7BHYRQ5YRGGBL5BHN","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":"c564b0564910663877396bf1d89254a7728c06a4fe6a48d8a792e7bfc09d21d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-04-20T17:12:03Z","title_canon_sha256":"1fab4d05fbb01c4d2ac592dbb87b1be42cd4dc4858cdf2e30bf2ab6a230d1b47"},"schema_version":"1.0","source":{"id":"1604.06037","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06037","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06037v1","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06037","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"pith_short_12","alias_value":"HPU7GROWS7BH","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HPU7GROWS7BHYRQ5","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HPU7GROW","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:ddd2b507adf52d8b067a50b3b2e78d6c437f85c82aba11de4513d71f644b5733","target":"graph","created_at":"2026-05-18T01:16:33Z","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":"Pseudo equality algebras were initially introduced by Jenei and $\\rm K\\acute{o}r\\acute{o}di$ as a possible algebraic semantic for fuzzy type theory, and they have been revised by Dvure\\v{c}enskij and Zahiri under the name of JK-algebras. In this paper we define and study the commutative pseudo equality algebras. We give a characterization of commutative pseudo equality algebras and we prove that an invariant pseudo equality algebra is commutative if and only if its corresponding pseudo BCK(pC)-meet-semilattice is commutative. Other results consist of proving that every commutative pseudo equal","authors_text":"Lavinia Corina Ciungu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-04-20T17:12:03Z","title":"Commutative pseudo equality algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06037","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":"sha256:577ce35dd27ac21a10256f652879735296916643952a34ddabd4a467b3630422","target":"record","created_at":"2026-05-18T01:16:33Z","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":"c564b0564910663877396bf1d89254a7728c06a4fe6a48d8a792e7bfc09d21d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-04-20T17:12:03Z","title_canon_sha256":"1fab4d05fbb01c4d2ac592dbb87b1be42cd4dc4858cdf2e30bf2ab6a230d1b47"},"schema_version":"1.0","source":{"id":"1604.06037","kind":"arxiv","version":1}},"canonical_sha256":"3be9f345d697c27c461dc44c60afa13b5e81b22441bebfb8a1eeeaaa979f2633","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3be9f345d697c27c461dc44c60afa13b5e81b22441bebfb8a1eeeaaa979f2633","first_computed_at":"2026-05-18T01:16:33.909604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:33.909604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WMt25rfH0/Qa/V0zNvbVLhFyPBsobeoGOb33KOZsusIv4gGZB+PoslwaLOCWmg+O/OMkU2xF0JywIymSnBkoCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:33.910543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06037","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:577ce35dd27ac21a10256f652879735296916643952a34ddabd4a467b3630422","sha256:ddd2b507adf52d8b067a50b3b2e78d6c437f85c82aba11de4513d71f644b5733"],"state_sha256":"8c32643448729cb48c50110e56b4f2ed7999c347f20c71e3431e2ea7c10aed43"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dmTVOSjOZ79GeQM5WCz8VhsXiPz/GKTXS2e5Sy4htWPPrARtgEGrdE3gMUSGfZ/cn+4tn7E2z6KNstitIGKXCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T07:21:29.839374Z","bundle_sha256":"0936aaff46f5fab46696293afe924204c75b027db0183779be614a557962b88a"}}