{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:LDB7TZXZRXVIU2P2KNS6IDD444","short_pith_number":"pith:LDB7TZXZ","canonical_record":{"source":{"id":"0812.4546","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2008-12-24T16:14:47Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"bdb7f4f7698e105a0886ac40684e285e72b7c66d590793f093c36f8c59f289a2","abstract_canon_sha256":"1d2897827600204798ba90404820df655c4c6e0dda094b95ebdaf8a9f07bf8d1"},"schema_version":"1.0"},"canonical_sha256":"58c3f9e6f98dea8a69fa5365e40c7ce734ef0fc61716f1975e311fa5bcaa5a34","source":{"kind":"arxiv","id":"0812.4546","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.4546","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"arxiv_version","alias_value":"0812.4546v1","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.4546","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"pith_short_12","alias_value":"LDB7TZXZRXVI","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"LDB7TZXZRXVIU2P2","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"LDB7TZXZ","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:LDB7TZXZRXVIU2P2KNS6IDD444","target":"record","payload":{"canonical_record":{"source":{"id":"0812.4546","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2008-12-24T16:14:47Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"bdb7f4f7698e105a0886ac40684e285e72b7c66d590793f093c36f8c59f289a2","abstract_canon_sha256":"1d2897827600204798ba90404820df655c4c6e0dda094b95ebdaf8a9f07bf8d1"},"schema_version":"1.0"},"canonical_sha256":"58c3f9e6f98dea8a69fa5365e40c7ce734ef0fc61716f1975e311fa5bcaa5a34","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:12.464626Z","signature_b64":"mUIPwCPGwSmeNXZUMD3ggUNPBCSTbpPgJQyoBH0dIl9EtuUC+0Jf0djcFymT1DkSZYPG2AH2jO+RXlERjEJjDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58c3f9e6f98dea8a69fa5365e40c7ce734ef0fc61716f1975e311fa5bcaa5a34","last_reissued_at":"2026-05-18T02:28:12.464167Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:12.464167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0812.4546","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":"jKhqqJ0ttjq86aXyXMDGBZ7x/ZvShj29j9EbFwXQ6mPq0Fo/WIQi9dl0rTURWMWW3BP+FvlubkWm7ydj1SLqDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:11:56.869970Z"},"content_sha256":"939d49f0b830c8078472c05e3c81b42239e9d5783e4de1568e4ea98a5986c1aa","schema_version":"1.0","event_id":"sha256:939d49f0b830c8078472c05e3c81b42239e9d5783e4de1568e4ea98a5986c1aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:LDB7TZXZRXVIU2P2KNS6IDD444","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximal residuated lattices with lifting Boolean center","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.LO","authors_text":"Claudia Mure\\c{s}an, George Georgescu, Lauren\\c{t}iu Leu\\c{s}tean","submitted_at":"2008-12-24T16:14:47Z","abstract_excerpt":"In this paper we define, inspired by ring theory, the class of maximal residuated lattices with lifting Boolean center and prove a structure theorem for them: any maximal residuated lattice with lifting Boolean center is isomorphic to a finite direct product of local residuated lattices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.4546","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":"Lz5c6QCWTVQeNlM7EsAL89y9OGjKaJsV3tNSQbisohfjactIka709BOm8sK6CZPKO4HFZAsfSDJZPU6qKqIZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:11:56.870313Z"},"content_sha256":"eee53fe8748d0a08f0e8eafa34193e650050d723301699b741dc6f542a6ee0a6","schema_version":"1.0","event_id":"sha256:eee53fe8748d0a08f0e8eafa34193e650050d723301699b741dc6f542a6ee0a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LDB7TZXZRXVIU2P2KNS6IDD444/bundle.json","state_url":"https://pith.science/pith/LDB7TZXZRXVIU2P2KNS6IDD444/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LDB7TZXZRXVIU2P2KNS6IDD444/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":"2026-06-30T23:11:56Z","links":{"resolver":"https://pith.science/pith/LDB7TZXZRXVIU2P2KNS6IDD444","bundle":"https://pith.science/pith/LDB7TZXZRXVIU2P2KNS6IDD444/bundle.json","state":"https://pith.science/pith/LDB7TZXZRXVIU2P2KNS6IDD444/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LDB7TZXZRXVIU2P2KNS6IDD444/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:LDB7TZXZRXVIU2P2KNS6IDD444","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":"1d2897827600204798ba90404820df655c4c6e0dda094b95ebdaf8a9f07bf8d1","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2008-12-24T16:14:47Z","title_canon_sha256":"bdb7f4f7698e105a0886ac40684e285e72b7c66d590793f093c36f8c59f289a2"},"schema_version":"1.0","source":{"id":"0812.4546","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.4546","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"arxiv_version","alias_value":"0812.4546v1","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.4546","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"pith_short_12","alias_value":"LDB7TZXZRXVI","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"LDB7TZXZRXVIU2P2","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"LDB7TZXZ","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:eee53fe8748d0a08f0e8eafa34193e650050d723301699b741dc6f542a6ee0a6","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 define, inspired by ring theory, the class of maximal residuated lattices with lifting Boolean center and prove a structure theorem for them: any maximal residuated lattice with lifting Boolean center is isomorphic to a finite direct product of local residuated lattices.","authors_text":"Claudia Mure\\c{s}an, George Georgescu, Lauren\\c{t}iu Leu\\c{s}tean","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2008-12-24T16:14:47Z","title":"Maximal residuated lattices with lifting Boolean center"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.4546","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":"sha256:939d49f0b830c8078472c05e3c81b42239e9d5783e4de1568e4ea98a5986c1aa","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":"1d2897827600204798ba90404820df655c4c6e0dda094b95ebdaf8a9f07bf8d1","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2008-12-24T16:14:47Z","title_canon_sha256":"bdb7f4f7698e105a0886ac40684e285e72b7c66d590793f093c36f8c59f289a2"},"schema_version":"1.0","source":{"id":"0812.4546","kind":"arxiv","version":1}},"canonical_sha256":"58c3f9e6f98dea8a69fa5365e40c7ce734ef0fc61716f1975e311fa5bcaa5a34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58c3f9e6f98dea8a69fa5365e40c7ce734ef0fc61716f1975e311fa5bcaa5a34","first_computed_at":"2026-05-18T02:28:12.464167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:12.464167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mUIPwCPGwSmeNXZUMD3ggUNPBCSTbpPgJQyoBH0dIl9EtuUC+0Jf0djcFymT1DkSZYPG2AH2jO+RXlERjEJjDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:12.464626Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.4546","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:939d49f0b830c8078472c05e3c81b42239e9d5783e4de1568e4ea98a5986c1aa","sha256:eee53fe8748d0a08f0e8eafa34193e650050d723301699b741dc6f542a6ee0a6"],"state_sha256":"445f488ff159507aba01ab1ddab2e6a005675eef3398645ab739370f0ac0478b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MW97B132+QLJMw9TB2jOGzmPD2VYThpEeDXTBUnn6f9ac0ysdRocsXV6+rK4raIiO/hFOs5TQu51E02vOpVrBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T23:11:56.872265Z","bundle_sha256":"a5392d3bd0b181a223c58f04f1bc894199c51df0ad7998052c9f0c0091b3c659"}}