{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:OPTPFOXTRJ75ALQ7FSSLJJ7LLT","short_pith_number":"pith:OPTPFOXT","canonical_record":{"source":{"id":"1203.2136","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-03-09T17:04:00Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"3a2ef79f1dafdce7f11c902c89e56bc3122e4cf61da5ab9ff5f3d87f68b8ccb3","abstract_canon_sha256":"877ab1bb61936ac60a6e408ae107ef009cbad749e4e0dab77e99641817e77e61"},"schema_version":"1.0"},"canonical_sha256":"73e6f2baf38a7fd02e1f2ca4b4a7eb5ceb12248129b6e2f15eddea112e343cb0","source":{"kind":"arxiv","id":"1203.2136","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2136","created_at":"2026-05-18T02:55:39Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2136v1","created_at":"2026-05-18T02:55:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2136","created_at":"2026-05-18T02:55:39Z"},{"alias_kind":"pith_short_12","alias_value":"OPTPFOXTRJ75","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OPTPFOXTRJ75ALQ7","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OPTPFOXT","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:OPTPFOXTRJ75ALQ7FSSLJJ7LLT","target":"record","payload":{"canonical_record":{"source":{"id":"1203.2136","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-03-09T17:04:00Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"3a2ef79f1dafdce7f11c902c89e56bc3122e4cf61da5ab9ff5f3d87f68b8ccb3","abstract_canon_sha256":"877ab1bb61936ac60a6e408ae107ef009cbad749e4e0dab77e99641817e77e61"},"schema_version":"1.0"},"canonical_sha256":"73e6f2baf38a7fd02e1f2ca4b4a7eb5ceb12248129b6e2f15eddea112e343cb0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:39.460870Z","signature_b64":"Y8kbRyTd+WfjNyvJgDl8/wRPcR89qai/YElB3GDui9FQEbMH+9PUwZl9RKsYfIqi+HUykP0zAIuk8oUE5fRSBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73e6f2baf38a7fd02e1f2ca4b4a7eb5ceb12248129b6e2f15eddea112e343cb0","last_reissued_at":"2026-05-18T02:55:39.460157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:39.460157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.2136","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":"2026-05-18T02:55:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pbqtDq8o7667B//GtxAlhNLuRxv5rFZpvp7OlwVitxT1chugBqspXCRhgtOte/Nc7SbivqPkP0pDhU3GFXyiBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T05:35:29.868130Z"},"content_sha256":"001acddfcaea24c84f8c960d62550ee086ebd78078825be2defcf64a6a1f319c","schema_version":"1.0","event_id":"sha256:001acddfcaea24c84f8c960d62550ee086ebd78078825be2defcf64a6a1f319c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:OPTPFOXTRJ75ALQ7FSSLJJ7LLT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Information completeness in Nelson algebras of rough sets induced by quasiorders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.RA","authors_text":"Jouni J\\\"arvinen, Piero Pagliani, S\\'andor Radeleczki","submitted_at":"2012-03-09T17:04:00Z","abstract_excerpt":"In this paper, we give an algebraic completeness theorem for constructive logic with strong negation in terms of finite rough set-based Nelson algebras determined by quasiorders. We show how for a quasiorder $R$, its rough set-based Nelson algebra can be obtained by applying the well-known construction by Sendlewski. We prove that if the set of all $R$-closed elements, which may be viewed as the set of completely defined objects, is cofinal, then the rough set-based Nelson algebra determined by a quasiorder forms an effective lattice, that is, an algebraic model of the logic $E_0$, which is ch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2136","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":"2026-05-18T02:55:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+OOozlbrcwAFfqtaWDMjQDvKH/8Rt7OrhQjPKNYObmqNF6OnxvNKVMBXjUfLtMZpIbDAp6x0n2ci3rwLv6vJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T05:35:29.868743Z"},"content_sha256":"7f0224ba17bb0cee0a815866d423e1a8ddd78fdf690481b34460f6b5addb9ff2","schema_version":"1.0","event_id":"sha256:7f0224ba17bb0cee0a815866d423e1a8ddd78fdf690481b34460f6b5addb9ff2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OPTPFOXTRJ75ALQ7FSSLJJ7LLT/bundle.json","state_url":"https://pith.science/pith/OPTPFOXTRJ75ALQ7FSSLJJ7LLT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OPTPFOXTRJ75ALQ7FSSLJJ7LLT/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":"2026-06-05T05:35:29Z","links":{"resolver":"https://pith.science/pith/OPTPFOXTRJ75ALQ7FSSLJJ7LLT","bundle":"https://pith.science/pith/OPTPFOXTRJ75ALQ7FSSLJJ7LLT/bundle.json","state":"https://pith.science/pith/OPTPFOXTRJ75ALQ7FSSLJJ7LLT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OPTPFOXTRJ75ALQ7FSSLJJ7LLT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OPTPFOXTRJ75ALQ7FSSLJJ7LLT","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":"877ab1bb61936ac60a6e408ae107ef009cbad749e4e0dab77e99641817e77e61","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-03-09T17:04:00Z","title_canon_sha256":"3a2ef79f1dafdce7f11c902c89e56bc3122e4cf61da5ab9ff5f3d87f68b8ccb3"},"schema_version":"1.0","source":{"id":"1203.2136","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2136","created_at":"2026-05-18T02:55:39Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2136v1","created_at":"2026-05-18T02:55:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2136","created_at":"2026-05-18T02:55:39Z"},{"alias_kind":"pith_short_12","alias_value":"OPTPFOXTRJ75","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OPTPFOXTRJ75ALQ7","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OPTPFOXT","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:7f0224ba17bb0cee0a815866d423e1a8ddd78fdf690481b34460f6b5addb9ff2","target":"graph","created_at":"2026-05-18T02:55:39Z","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 give an algebraic completeness theorem for constructive logic with strong negation in terms of finite rough set-based Nelson algebras determined by quasiorders. We show how for a quasiorder $R$, its rough set-based Nelson algebra can be obtained by applying the well-known construction by Sendlewski. We prove that if the set of all $R$-closed elements, which may be viewed as the set of completely defined objects, is cofinal, then the rough set-based Nelson algebra determined by a quasiorder forms an effective lattice, that is, an algebraic model of the logic $E_0$, which is ch","authors_text":"Jouni J\\\"arvinen, Piero Pagliani, S\\'andor Radeleczki","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-03-09T17:04:00Z","title":"Information completeness in Nelson algebras of rough sets induced by quasiorders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2136","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":"sha256:001acddfcaea24c84f8c960d62550ee086ebd78078825be2defcf64a6a1f319c","target":"record","created_at":"2026-05-18T02:55:39Z","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":"877ab1bb61936ac60a6e408ae107ef009cbad749e4e0dab77e99641817e77e61","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-03-09T17:04:00Z","title_canon_sha256":"3a2ef79f1dafdce7f11c902c89e56bc3122e4cf61da5ab9ff5f3d87f68b8ccb3"},"schema_version":"1.0","source":{"id":"1203.2136","kind":"arxiv","version":1}},"canonical_sha256":"73e6f2baf38a7fd02e1f2ca4b4a7eb5ceb12248129b6e2f15eddea112e343cb0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73e6f2baf38a7fd02e1f2ca4b4a7eb5ceb12248129b6e2f15eddea112e343cb0","first_computed_at":"2026-05-18T02:55:39.460157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:39.460157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y8kbRyTd+WfjNyvJgDl8/wRPcR89qai/YElB3GDui9FQEbMH+9PUwZl9RKsYfIqi+HUykP0zAIuk8oUE5fRSBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:39.460870Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2136","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:001acddfcaea24c84f8c960d62550ee086ebd78078825be2defcf64a6a1f319c","sha256:7f0224ba17bb0cee0a815866d423e1a8ddd78fdf690481b34460f6b5addb9ff2"],"state_sha256":"4a140d74fc91abf3bb5a1805532ecccd17990082b0d0a2cb5dbbb201560205f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FRNvx/RsxfGG1QHd1ettrtLyi1++/cY24lmlw5b+3KoVfg+9Mfk9GIuZRtffIiWeiX5WzZO3aG7FqFhQS3yCDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T05:35:29.871896Z","bundle_sha256":"7ead5c9048572429450bf0100ec8df10a18f545176d4768e519dc4d73bb0437a"}}