{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HY2RHRNCETEJACKQHEDS7EXKDB","short_pith_number":"pith:HY2RHRNC","canonical_record":{"source":{"id":"1809.06210","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-09-09T21:16:14Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"2be1390d15bbb77406ecf906d4968cf8d2faf13328d9e7085324cfe0834cf7e7","abstract_canon_sha256":"3115e1f9e281cb4b68591c8e65f411ea129984e524f61b09e68b3390c091113e"},"schema_version":"1.0"},"canonical_sha256":"3e3513c5a224c890095039072f92ea185396807643139ec5ee8ca2110af68e2f","source":{"kind":"arxiv","id":"1809.06210","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.06210","created_at":"2026-05-18T00:05:35Z"},{"alias_kind":"arxiv_version","alias_value":"1809.06210v1","created_at":"2026-05-18T00:05:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06210","created_at":"2026-05-18T00:05:35Z"},{"alias_kind":"pith_short_12","alias_value":"HY2RHRNCETEJ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HY2RHRNCETEJACKQ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HY2RHRNC","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HY2RHRNCETEJACKQHEDS7EXKDB","target":"record","payload":{"canonical_record":{"source":{"id":"1809.06210","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-09-09T21:16:14Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"2be1390d15bbb77406ecf906d4968cf8d2faf13328d9e7085324cfe0834cf7e7","abstract_canon_sha256":"3115e1f9e281cb4b68591c8e65f411ea129984e524f61b09e68b3390c091113e"},"schema_version":"1.0"},"canonical_sha256":"3e3513c5a224c890095039072f92ea185396807643139ec5ee8ca2110af68e2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:35.336632Z","signature_b64":"IOK+YU28ElqyA0q5Buk2IIsoiZjVTl+xkPY5Y4dDjGUIF3igYnV7SMdn+d9n6yFXPbeUwdCfVcbn5uYAr8IrCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e3513c5a224c890095039072f92ea185396807643139ec5ee8ca2110af68e2f","last_reissued_at":"2026-05-18T00:05:35.336205Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:35.336205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.06210","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":"2026-05-18T00:05:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"agNquROfY/CFFrJaBXWvTCc0PvgDuGk228NGJhRdQfNPfd9GxJFYHQ8OVAwhT9FAQxYlsSDu33Tly/+SSjlkDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:44:25.299653Z"},"content_sha256":"c5903f996dd94852ad038e9bc4a325f82ebde2c4b055408e52acd878ad0a10b9","schema_version":"1.0","event_id":"sha256:c5903f996dd94852ad038e9bc4a325f82ebde2c4b055408e52acd878ad0a10b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HY2RHRNCETEJACKQHEDS7EXKDB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Filters on some classes of quantum B-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.LO","authors_text":"Jan Paseka, Michal Botur","submitted_at":"2018-09-09T21:16:14Z","abstract_excerpt":"In this paper, we continue the study of quantum B-algebras with emphasis on filters on integral quantum B-algebras. We then study filters in the setting of pseudo-hoops. First, we establish an embedding of a cartesion product of polars of a pseudo-hoop into itself. Second, we give sufficient conditions for a pseudohoop to be subdirectly reducible. We also extend the result of Kondo and Turunen to the setting of noncommutative residuated $\\vee$-semilattices that, if prime filters and $\\vee$-prime filters of a residuated $\\vee$-semilattice $A$ coincide, then $A$ must be a pseudo MTL-algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06210","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":"2026-05-18T00:05:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eNna7+EBUH6d2ISJeBPmdPr5zxLdGfdeiECYfvMEPK4Dg1n+JjVYaPbT51dp2TTUXqL/DxbmK6EH3VLYc7QbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T11:44:25.300378Z"},"content_sha256":"c83ff37260ad4992a9be67d7681e5d833553c45c1c253718783a76f093e5edab","schema_version":"1.0","event_id":"sha256:c83ff37260ad4992a9be67d7681e5d833553c45c1c253718783a76f093e5edab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HY2RHRNCETEJACKQHEDS7EXKDB/bundle.json","state_url":"https://pith.science/pith/HY2RHRNCETEJACKQHEDS7EXKDB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HY2RHRNCETEJACKQHEDS7EXKDB/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":"2026-06-10T11:44:25Z","links":{"resolver":"https://pith.science/pith/HY2RHRNCETEJACKQHEDS7EXKDB","bundle":"https://pith.science/pith/HY2RHRNCETEJACKQHEDS7EXKDB/bundle.json","state":"https://pith.science/pith/HY2RHRNCETEJACKQHEDS7EXKDB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HY2RHRNCETEJACKQHEDS7EXKDB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HY2RHRNCETEJACKQHEDS7EXKDB","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":"3115e1f9e281cb4b68591c8e65f411ea129984e524f61b09e68b3390c091113e","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-09-09T21:16:14Z","title_canon_sha256":"2be1390d15bbb77406ecf906d4968cf8d2faf13328d9e7085324cfe0834cf7e7"},"schema_version":"1.0","source":{"id":"1809.06210","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.06210","created_at":"2026-05-18T00:05:35Z"},{"alias_kind":"arxiv_version","alias_value":"1809.06210v1","created_at":"2026-05-18T00:05:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06210","created_at":"2026-05-18T00:05:35Z"},{"alias_kind":"pith_short_12","alias_value":"HY2RHRNCETEJ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HY2RHRNCETEJACKQ","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HY2RHRNC","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:c83ff37260ad4992a9be67d7681e5d833553c45c1c253718783a76f093e5edab","target":"graph","created_at":"2026-05-18T00:05:35Z","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, we continue the study of quantum B-algebras with emphasis on filters on integral quantum B-algebras. We then study filters in the setting of pseudo-hoops. First, we establish an embedding of a cartesion product of polars of a pseudo-hoop into itself. Second, we give sufficient conditions for a pseudohoop to be subdirectly reducible. We also extend the result of Kondo and Turunen to the setting of noncommutative residuated $\\vee$-semilattices that, if prime filters and $\\vee$-prime filters of a residuated $\\vee$-semilattice $A$ coincide, then $A$ must be a pseudo MTL-algebra.","authors_text":"Jan Paseka, Michal Botur","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-09-09T21:16:14Z","title":"Filters on some classes of quantum B-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06210","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:c5903f996dd94852ad038e9bc4a325f82ebde2c4b055408e52acd878ad0a10b9","target":"record","created_at":"2026-05-18T00:05:35Z","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":"3115e1f9e281cb4b68591c8e65f411ea129984e524f61b09e68b3390c091113e","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-09-09T21:16:14Z","title_canon_sha256":"2be1390d15bbb77406ecf906d4968cf8d2faf13328d9e7085324cfe0834cf7e7"},"schema_version":"1.0","source":{"id":"1809.06210","kind":"arxiv","version":1}},"canonical_sha256":"3e3513c5a224c890095039072f92ea185396807643139ec5ee8ca2110af68e2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e3513c5a224c890095039072f92ea185396807643139ec5ee8ca2110af68e2f","first_computed_at":"2026-05-18T00:05:35.336205Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:35.336205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IOK+YU28ElqyA0q5Buk2IIsoiZjVTl+xkPY5Y4dDjGUIF3igYnV7SMdn+d9n6yFXPbeUwdCfVcbn5uYAr8IrCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:35.336632Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.06210","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5903f996dd94852ad038e9bc4a325f82ebde2c4b055408e52acd878ad0a10b9","sha256:c83ff37260ad4992a9be67d7681e5d833553c45c1c253718783a76f093e5edab"],"state_sha256":"bb7d5cafc3dfb49bf1b261ddbf7515dabed0ce3ba601db5e9351222ec895bb67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F2RnuvolQlOE8P3ip/Kwv+67SdR1KqDks2OwD2zw/6fIrFpaN8/7IYVVQGNXYnGj82ALpVGSOyRhUFvUcswhBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T11:44:25.304554Z","bundle_sha256":"5af458c7014385f429b38981cdd44ea6c2f6bc9cd16d2c83c6772e74edec1216"}}