{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WRJZIWWDJWMPL4UZXGFRC2NN32","short_pith_number":"pith:WRJZIWWD","canonical_record":{"source":{"id":"1304.6776","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-25T00:10:36Z","cross_cats_sorted":[],"title_canon_sha256":"5beef0503883514212ad21f709fef2fb926b110c461ee06ec54accdb299c12af","abstract_canon_sha256":"9a9552271643127551f482563fd8e8e27e24bf2a14f2bd4f2087849f5395f472"},"schema_version":"1.0"},"canonical_sha256":"b453945ac34d98f5f299b98b1169addea8f89815d53e06278b63ff85053473a2","source":{"kind":"arxiv","id":"1304.6776","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6776","created_at":"2026-05-18T03:25:58Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6776v2","created_at":"2026-05-18T03:25:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6776","created_at":"2026-05-18T03:25:58Z"},{"alias_kind":"pith_short_12","alias_value":"WRJZIWWDJWMP","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WRJZIWWDJWMPL4UZ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WRJZIWWD","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WRJZIWWDJWMPL4UZXGFRC2NN32","target":"record","payload":{"canonical_record":{"source":{"id":"1304.6776","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-25T00:10:36Z","cross_cats_sorted":[],"title_canon_sha256":"5beef0503883514212ad21f709fef2fb926b110c461ee06ec54accdb299c12af","abstract_canon_sha256":"9a9552271643127551f482563fd8e8e27e24bf2a14f2bd4f2087849f5395f472"},"schema_version":"1.0"},"canonical_sha256":"b453945ac34d98f5f299b98b1169addea8f89815d53e06278b63ff85053473a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:58.098427Z","signature_b64":"Pc2MeUzsin26NhH/QOWvqas2SgSgoUCcMRMWVF/iN9V5mo8UqyFHwQn7oBzV31GMc6x21od05JjtNMnFtAN9Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b453945ac34d98f5f299b98b1169addea8f89815d53e06278b63ff85053473a2","last_reissued_at":"2026-05-18T03:25:58.097618Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:58.097618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.6776","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:25:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MLcUOetao2E1J8DeC4E4d1uAzszrBOChVprbsKQJmrCX1qkt8D6XWljXrKzQHYIUyYquzM3/R3skI6mNqF/qDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T16:33:27.264149Z"},"content_sha256":"8522d11c73ca74403a12a79ef0c17bdd8c988d7c9a224b9f2ee818e2c1bd455e","schema_version":"1.0","event_id":"sha256:8522d11c73ca74403a12a79ef0c17bdd8c988d7c9a224b9f2ee818e2c1bd455e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WRJZIWWDJWMPL4UZXGFRC2NN32","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Several characterizations of the 4--valued modal algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Aldo V. Figallo, Paolo Landini","submitted_at":"2013-04-25T00:10:36Z","abstract_excerpt":"A. Monteiro, in 1978, defined the algebras he named tetravalent modal algebras, will be called 4--valued modal algebras in this work. These algebras constitute a generalization of the 3--valued Lukasiewicz algebras defined by Moisil.\n  The theory of the 4--valued modal algebras has been widely developed by I. Loureiro in [6,7,8,9,10,11,12] and by A. V. Figallo in [2,3,4,5].\n  J. Font and M. Rius indicated, in the introduction to the important work [1], a brief but detailed review on the $4-$valued modal algebras.\n  In this work varied characterizations are presented that show the \"closeness\" t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6776","kind":"arxiv","version":2},"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":"2026-05-18T03:25:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jSrkOPNT6EKBDxUicZwM9JDibxh8oTPvCFI0uUF8a4+YlGiOYSnZbx0Z6AYzTrhmCO32i+SOX5B0wuVoh8ziDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T16:33:27.264517Z"},"content_sha256":"24a06485c0899751e0c1853da61d20980e45165b75dd456e8e34190cc6a00717","schema_version":"1.0","event_id":"sha256:24a06485c0899751e0c1853da61d20980e45165b75dd456e8e34190cc6a00717"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WRJZIWWDJWMPL4UZXGFRC2NN32/bundle.json","state_url":"https://pith.science/pith/WRJZIWWDJWMPL4UZXGFRC2NN32/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WRJZIWWDJWMPL4UZXGFRC2NN32/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":"2026-07-01T16:33:27Z","links":{"resolver":"https://pith.science/pith/WRJZIWWDJWMPL4UZXGFRC2NN32","bundle":"https://pith.science/pith/WRJZIWWDJWMPL4UZXGFRC2NN32/bundle.json","state":"https://pith.science/pith/WRJZIWWDJWMPL4UZXGFRC2NN32/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WRJZIWWDJWMPL4UZXGFRC2NN32/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WRJZIWWDJWMPL4UZXGFRC2NN32","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":"9a9552271643127551f482563fd8e8e27e24bf2a14f2bd4f2087849f5395f472","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-25T00:10:36Z","title_canon_sha256":"5beef0503883514212ad21f709fef2fb926b110c461ee06ec54accdb299c12af"},"schema_version":"1.0","source":{"id":"1304.6776","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6776","created_at":"2026-05-18T03:25:58Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6776v2","created_at":"2026-05-18T03:25:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6776","created_at":"2026-05-18T03:25:58Z"},{"alias_kind":"pith_short_12","alias_value":"WRJZIWWDJWMP","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WRJZIWWDJWMPL4UZ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WRJZIWWD","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:24a06485c0899751e0c1853da61d20980e45165b75dd456e8e34190cc6a00717","target":"graph","created_at":"2026-05-18T03:25:58Z","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":"A. Monteiro, in 1978, defined the algebras he named tetravalent modal algebras, will be called 4--valued modal algebras in this work. These algebras constitute a generalization of the 3--valued Lukasiewicz algebras defined by Moisil.\n  The theory of the 4--valued modal algebras has been widely developed by I. Loureiro in [6,7,8,9,10,11,12] and by A. V. Figallo in [2,3,4,5].\n  J. Font and M. Rius indicated, in the introduction to the important work [1], a brief but detailed review on the $4-$valued modal algebras.\n  In this work varied characterizations are presented that show the \"closeness\" t","authors_text":"Aldo V. Figallo, Paolo Landini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-25T00:10:36Z","title":"Several characterizations of the 4--valued modal algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6776","kind":"arxiv","version":2},"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":"sha256:8522d11c73ca74403a12a79ef0c17bdd8c988d7c9a224b9f2ee818e2c1bd455e","target":"record","created_at":"2026-05-18T03:25:58Z","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":"9a9552271643127551f482563fd8e8e27e24bf2a14f2bd4f2087849f5395f472","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-04-25T00:10:36Z","title_canon_sha256":"5beef0503883514212ad21f709fef2fb926b110c461ee06ec54accdb299c12af"},"schema_version":"1.0","source":{"id":"1304.6776","kind":"arxiv","version":2}},"canonical_sha256":"b453945ac34d98f5f299b98b1169addea8f89815d53e06278b63ff85053473a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b453945ac34d98f5f299b98b1169addea8f89815d53e06278b63ff85053473a2","first_computed_at":"2026-05-18T03:25:58.097618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:58.097618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pc2MeUzsin26NhH/QOWvqas2SgSgoUCcMRMWVF/iN9V5mo8UqyFHwQn7oBzV31GMc6x21od05JjtNMnFtAN9Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:58.098427Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.6776","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8522d11c73ca74403a12a79ef0c17bdd8c988d7c9a224b9f2ee818e2c1bd455e","sha256:24a06485c0899751e0c1853da61d20980e45165b75dd456e8e34190cc6a00717"],"state_sha256":"fd17c766b861f97fa74a06a2af80a246b51df455653d23d3828c5b3cc1144ef9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eNzIfUWIZskWx90Zu/j6Trr+gPl3kMjgZqiCEbc88XuloEWs+CUsjrxgUeBMghQb11yAK24QtCs9FtlWTKPmCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T16:33:27.266521Z","bundle_sha256":"bd26a1f5d8934af5f7232e844a2a4b49bcf5cd2ec02bbec0b298413640d51712"}}