{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:QJXZ5YQKA2TOCA6UTV3ZFEJZGB","short_pith_number":"pith:QJXZ5YQK","canonical_record":{"source":{"id":"1101.2580","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-01-13T15:16:34Z","cross_cats_sorted":["math-ph","math.MP","math.QA"],"title_canon_sha256":"b611a808a42ab92f8bd8483abdc5f5c781d45ab68b4f58c6d47e633a2b1b6a1c","abstract_canon_sha256":"0d0611ee24315be6768f303aa9929d4fc3b823d692c6e93aadc0c7ad181ab9fa"},"schema_version":"1.0"},"canonical_sha256":"826f9ee20a06a6e103d49d77929139304f6015f11de830953700a426d5c0fe10","source":{"kind":"arxiv","id":"1101.2580","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2580","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2580v1","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2580","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"pith_short_12","alias_value":"QJXZ5YQKA2TO","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QJXZ5YQKA2TOCA6U","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QJXZ5YQK","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:QJXZ5YQKA2TOCA6UTV3ZFEJZGB","target":"record","payload":{"canonical_record":{"source":{"id":"1101.2580","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-01-13T15:16:34Z","cross_cats_sorted":["math-ph","math.MP","math.QA"],"title_canon_sha256":"b611a808a42ab92f8bd8483abdc5f5c781d45ab68b4f58c6d47e633a2b1b6a1c","abstract_canon_sha256":"0d0611ee24315be6768f303aa9929d4fc3b823d692c6e93aadc0c7ad181ab9fa"},"schema_version":"1.0"},"canonical_sha256":"826f9ee20a06a6e103d49d77929139304f6015f11de830953700a426d5c0fe10","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:41.826278Z","signature_b64":"8VRfH4xyYSd3XZoeTcl9kKR/vXLRHVBKZtAITgDmAak+xFNvxw+4QsJn+Ej1hZ7SQ4/hOBxMsrNisZRHBox7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"826f9ee20a06a6e103d49d77929139304f6015f11de830953700a426d5c0fe10","last_reissued_at":"2026-05-18T04:31:41.825853Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:41.825853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.2580","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":"2026-05-18T04:31:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VBoHfw2Jin6mQQI1ThRlkzPcwjm6aYNgs3GIPWf2tnKWzmyfM0FB94hpO3vlWKjZt2sMWBMkqUU+EWyXohErAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:53:28.515552Z"},"content_sha256":"01ee818310e16c2d5e17ebf574f537ec7e1d5ce3776371192b0a23f22e5a2e14","schema_version":"1.0","event_id":"sha256:01ee818310e16c2d5e17ebf574f537ec7e1d5ce3776371192b0a23f22e5a2e14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:QJXZ5YQKA2TOCA6UTV3ZFEJZGB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"More about sharp and meager elements in Archimedean atomic lattice effect algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"math.LO","authors_text":"Jan Paseka, Josef Niederle","submitted_at":"2011-01-13T15:16:34Z","abstract_excerpt":"The aim of our paper is twofold. First, we thoroughly study the set of meager elements M(E), the center C(E) and the compatibility center B(E)in the setting of atomic Archimedean lattice effect algebras E. The main result is that in this case the center C(E) is bifull (atomic) iff the compatibility center B(E) is bifull (atomic) whenever E is sharply dominating. As a by-product, we give a new descriciption of the smallest sharp element over x in E via the basic decomposition of x. Second, we prove the Triple Representation Theorem for sharply dominating atomic Archimedean lattice effect algebr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2580","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":"2026-05-18T04:31:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qOOhgrstU8J/VxAUQUdn0S34dLRfbHszi53MF7iPEoeBDdCFTyBR51ozTHA8KYlmi7LC0GlgXKMMB4K9ZnykBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:53:28.516333Z"},"content_sha256":"9c6fdbaa1a49fe22eafa38ff45e1016f7e4a8be590aba510f20e64b9f3da9864","schema_version":"1.0","event_id":"sha256:9c6fdbaa1a49fe22eafa38ff45e1016f7e4a8be590aba510f20e64b9f3da9864"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QJXZ5YQKA2TOCA6UTV3ZFEJZGB/bundle.json","state_url":"https://pith.science/pith/QJXZ5YQKA2TOCA6UTV3ZFEJZGB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QJXZ5YQKA2TOCA6UTV3ZFEJZGB/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":"2026-06-10T12:53:28Z","links":{"resolver":"https://pith.science/pith/QJXZ5YQKA2TOCA6UTV3ZFEJZGB","bundle":"https://pith.science/pith/QJXZ5YQKA2TOCA6UTV3ZFEJZGB/bundle.json","state":"https://pith.science/pith/QJXZ5YQKA2TOCA6UTV3ZFEJZGB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QJXZ5YQKA2TOCA6UTV3ZFEJZGB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QJXZ5YQKA2TOCA6UTV3ZFEJZGB","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":"0d0611ee24315be6768f303aa9929d4fc3b823d692c6e93aadc0c7ad181ab9fa","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-01-13T15:16:34Z","title_canon_sha256":"b611a808a42ab92f8bd8483abdc5f5c781d45ab68b4f58c6d47e633a2b1b6a1c"},"schema_version":"1.0","source":{"id":"1101.2580","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2580","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2580v1","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2580","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"pith_short_12","alias_value":"QJXZ5YQKA2TO","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QJXZ5YQKA2TOCA6U","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QJXZ5YQK","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:9c6fdbaa1a49fe22eafa38ff45e1016f7e4a8be590aba510f20e64b9f3da9864","target":"graph","created_at":"2026-05-18T04:31:41Z","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":"The aim of our paper is twofold. First, we thoroughly study the set of meager elements M(E), the center C(E) and the compatibility center B(E)in the setting of atomic Archimedean lattice effect algebras E. The main result is that in this case the center C(E) is bifull (atomic) iff the compatibility center B(E) is bifull (atomic) whenever E is sharply dominating. As a by-product, we give a new descriciption of the smallest sharp element over x in E via the basic decomposition of x. Second, we prove the Triple Representation Theorem for sharply dominating atomic Archimedean lattice effect algebr","authors_text":"Jan Paseka, Josef Niederle","cross_cats":["math-ph","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-01-13T15:16:34Z","title":"More about sharp and meager elements in Archimedean atomic lattice effect algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2580","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":"sha256:01ee818310e16c2d5e17ebf574f537ec7e1d5ce3776371192b0a23f22e5a2e14","target":"record","created_at":"2026-05-18T04:31:41Z","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":"0d0611ee24315be6768f303aa9929d4fc3b823d692c6e93aadc0c7ad181ab9fa","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-01-13T15:16:34Z","title_canon_sha256":"b611a808a42ab92f8bd8483abdc5f5c781d45ab68b4f58c6d47e633a2b1b6a1c"},"schema_version":"1.0","source":{"id":"1101.2580","kind":"arxiv","version":1}},"canonical_sha256":"826f9ee20a06a6e103d49d77929139304f6015f11de830953700a426d5c0fe10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"826f9ee20a06a6e103d49d77929139304f6015f11de830953700a426d5c0fe10","first_computed_at":"2026-05-18T04:31:41.825853Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:41.825853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8VRfH4xyYSd3XZoeTcl9kKR/vXLRHVBKZtAITgDmAak+xFNvxw+4QsJn+Ej1hZ7SQ4/hOBxMsrNisZRHBox7Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:41.826278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.2580","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01ee818310e16c2d5e17ebf574f537ec7e1d5ce3776371192b0a23f22e5a2e14","sha256:9c6fdbaa1a49fe22eafa38ff45e1016f7e4a8be590aba510f20e64b9f3da9864"],"state_sha256":"ee59941771d7dbbba492450f438aaa9f696a425514ccfade5ddefde6396349f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wYIIRqmutr3ObvJpVfZj1i6Hb89dAYmLDsjj8C63ijrXQ4nTeppySne2D15ppfSoOdqlOkWleI/y91hFLSSNBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T12:53:28.521051Z","bundle_sha256":"390b8c00a3f965166533248f9f5ae7823ffeba71a1bf042b68a63bdfaa02abe8"}}