{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:X2RGSCLO55LTNOF3ZPRJEJQBSW","short_pith_number":"pith:X2RGSCLO","canonical_record":{"source":{"id":"0901.1630","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2009-01-12T18:13:36Z","cross_cats_sorted":[],"title_canon_sha256":"83fe02da178a2930c0ef8be3076fb0d9d189505ebb2315a61b4829e11a536d6f","abstract_canon_sha256":"31afad0d69115ff2146c64b8f91f0f2d0955d7c5b944bc21bb8431c7ebfcfb4b"},"schema_version":"1.0"},"canonical_sha256":"bea269096eef5736b8bbcbe292260195a3ff5382af9daeb5567960b4a8de47ee","source":{"kind":"arxiv","id":"0901.1630","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.1630","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"arxiv_version","alias_value":"0901.1630v1","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.1630","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"pith_short_12","alias_value":"X2RGSCLO55LT","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"X2RGSCLO55LTNOF3","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"X2RGSCLO","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:X2RGSCLO55LTNOF3ZPRJEJQBSW","target":"record","payload":{"canonical_record":{"source":{"id":"0901.1630","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2009-01-12T18:13:36Z","cross_cats_sorted":[],"title_canon_sha256":"83fe02da178a2930c0ef8be3076fb0d9d189505ebb2315a61b4829e11a536d6f","abstract_canon_sha256":"31afad0d69115ff2146c64b8f91f0f2d0955d7c5b944bc21bb8431c7ebfcfb4b"},"schema_version":"1.0"},"canonical_sha256":"bea269096eef5736b8bbcbe292260195a3ff5382af9daeb5567960b4a8de47ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:12.456852Z","signature_b64":"vPGbBbaLQiSEC/EztddSC37OKu7ZjHBeNceNb70w8RNR4HXipKyX/QX5tBvpc4+7JthDTYsnJYNJ4CcSIwbBBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bea269096eef5736b8bbcbe292260195a3ff5382af9daeb5567960b4a8de47ee","last_reissued_at":"2026-05-18T02:28:12.456414Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:12.456414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0901.1630","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":"2026-05-18T02:28:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aohqErRr6fl399UvVZR2n2DERspCruk+UK9Lb2senZYmlKhIAaUkskPRQlcrAE628vLhCxO/z+M09rxIkUWPAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T22:35:04.782032Z"},"content_sha256":"fc132cda0bc3b05352663c75a5f9b70df1459e700982c0c9317a16d8d5dfefa9","schema_version":"1.0","event_id":"sha256:fc132cda0bc3b05352663c75a5f9b70df1459e700982c0c9317a16d8d5dfefa9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:X2RGSCLO55LTNOF3ZPRJEJQBSW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dense Elements and Classes of Residuated Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Claudia Mure\\c{s}an","submitted_at":"2009-01-12T18:13:36Z","abstract_excerpt":"In this paper we study the dense elements and the radical of a residuated lattice, residuated lattices with lifting Boolean center, simple, local, semilocal and quasi-local residuated lattices. BL-algebras have lifting Boolean center; moreover, Glivenko residuated lattices which fulfill a certain equation (that is satisfied by BL-algebras) have lifting Boolean center."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1630","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":"2026-05-18T02:28:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AevYtpuH9jz1yPzD1RA6EZXTdjnbvj3K0FT87t0VV/d2hAYwRn20TI7gAmUPo4izZRjPj7EPPTNotcZ/jmOkDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T22:35:04.782398Z"},"content_sha256":"652aa4d7b7e7341e3d845b4e8dd0f8fcd47e0588cb4ba305e5b99e434c58b7ae","schema_version":"1.0","event_id":"sha256:652aa4d7b7e7341e3d845b4e8dd0f8fcd47e0588cb4ba305e5b99e434c58b7ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X2RGSCLO55LTNOF3ZPRJEJQBSW/bundle.json","state_url":"https://pith.science/pith/X2RGSCLO55LTNOF3ZPRJEJQBSW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X2RGSCLO55LTNOF3ZPRJEJQBSW/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":"2026-06-30T22:35:04Z","links":{"resolver":"https://pith.science/pith/X2RGSCLO55LTNOF3ZPRJEJQBSW","bundle":"https://pith.science/pith/X2RGSCLO55LTNOF3ZPRJEJQBSW/bundle.json","state":"https://pith.science/pith/X2RGSCLO55LTNOF3ZPRJEJQBSW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X2RGSCLO55LTNOF3ZPRJEJQBSW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:X2RGSCLO55LTNOF3ZPRJEJQBSW","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":"31afad0d69115ff2146c64b8f91f0f2d0955d7c5b944bc21bb8431c7ebfcfb4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2009-01-12T18:13:36Z","title_canon_sha256":"83fe02da178a2930c0ef8be3076fb0d9d189505ebb2315a61b4829e11a536d6f"},"schema_version":"1.0","source":{"id":"0901.1630","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.1630","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"arxiv_version","alias_value":"0901.1630v1","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.1630","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"pith_short_12","alias_value":"X2RGSCLO55LT","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"X2RGSCLO55LTNOF3","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"X2RGSCLO","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:652aa4d7b7e7341e3d845b4e8dd0f8fcd47e0588cb4ba305e5b99e434c58b7ae","target":"graph","created_at":"2026-05-18T02:28:12Z","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 study the dense elements and the radical of a residuated lattice, residuated lattices with lifting Boolean center, simple, local, semilocal and quasi-local residuated lattices. BL-algebras have lifting Boolean center; moreover, Glivenko residuated lattices which fulfill a certain equation (that is satisfied by BL-algebras) have lifting Boolean center.","authors_text":"Claudia Mure\\c{s}an","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2009-01-12T18:13:36Z","title":"Dense Elements and Classes of Residuated Lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1630","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:fc132cda0bc3b05352663c75a5f9b70df1459e700982c0c9317a16d8d5dfefa9","target":"record","created_at":"2026-05-18T02:28:12Z","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":"31afad0d69115ff2146c64b8f91f0f2d0955d7c5b944bc21bb8431c7ebfcfb4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2009-01-12T18:13:36Z","title_canon_sha256":"83fe02da178a2930c0ef8be3076fb0d9d189505ebb2315a61b4829e11a536d6f"},"schema_version":"1.0","source":{"id":"0901.1630","kind":"arxiv","version":1}},"canonical_sha256":"bea269096eef5736b8bbcbe292260195a3ff5382af9daeb5567960b4a8de47ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bea269096eef5736b8bbcbe292260195a3ff5382af9daeb5567960b4a8de47ee","first_computed_at":"2026-05-18T02:28:12.456414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:12.456414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vPGbBbaLQiSEC/EztddSC37OKu7ZjHBeNceNb70w8RNR4HXipKyX/QX5tBvpc4+7JthDTYsnJYNJ4CcSIwbBBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:12.456852Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.1630","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc132cda0bc3b05352663c75a5f9b70df1459e700982c0c9317a16d8d5dfefa9","sha256:652aa4d7b7e7341e3d845b4e8dd0f8fcd47e0588cb4ba305e5b99e434c58b7ae"],"state_sha256":"7bfd09f7731faa249c6e1bba87badb7138ce51cf772ee6d5ac2532f0ed0384e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tlcUIglG8rSbRl2y4GgCKnUn2CkcPTyI5kpg5G1SUYdatB3lMGid5V03yYtDuksXIn0KqDVys4bybPmfDylZBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T22:35:04.784448Z","bundle_sha256":"f0d8f8a94f5d0074ee400cbd2fbbefc3b7a616389e957d540cde0cf3b634865d"}}