{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:C75OYD75IFUWROSOFVM2WGXO2H","short_pith_number":"pith:C75OYD75","canonical_record":{"source":{"id":"1809.07646","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-09-20T14:19:34Z","cross_cats_sorted":[],"title_canon_sha256":"df16e0a2cf2e53e181b3df9050d1d763560f81e290b35892a64238d884c24670","abstract_canon_sha256":"983f49b90aae4d01248cd8f35cdcb9efc51a96f29b07268aa175a01ba05fb13b"},"schema_version":"1.0"},"canonical_sha256":"17faec0ffd416968ba4e2d59ab1aeed1e0e418de85b7313cbc99e93004e9750e","source":{"kind":"arxiv","id":"1809.07646","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07646","created_at":"2026-05-18T00:05:15Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07646v1","created_at":"2026-05-18T00:05:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07646","created_at":"2026-05-18T00:05:15Z"},{"alias_kind":"pith_short_12","alias_value":"C75OYD75IFUW","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"C75OYD75IFUWROSO","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"C75OYD75","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:C75OYD75IFUWROSOFVM2WGXO2H","target":"record","payload":{"canonical_record":{"source":{"id":"1809.07646","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-09-20T14:19:34Z","cross_cats_sorted":[],"title_canon_sha256":"df16e0a2cf2e53e181b3df9050d1d763560f81e290b35892a64238d884c24670","abstract_canon_sha256":"983f49b90aae4d01248cd8f35cdcb9efc51a96f29b07268aa175a01ba05fb13b"},"schema_version":"1.0"},"canonical_sha256":"17faec0ffd416968ba4e2d59ab1aeed1e0e418de85b7313cbc99e93004e9750e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:15.624677Z","signature_b64":"WAaj3yZD3eADZravaSo6UXIUrfcH7aVxa5zP0h5aup9J+P71pRECB5MSTqqQYvFTmJEJIDHM0xqMdNNyFIyECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17faec0ffd416968ba4e2d59ab1aeed1e0e418de85b7313cbc99e93004e9750e","last_reissued_at":"2026-05-18T00:05:15.624160Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:15.624160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.07646","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":"2026-05-18T00:05:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w02pwI9KO9R6abb8u7wK4NX+1Lpo9BfrtZy57BCKUH5lLCmouXPZ8aSVOcugbESa4lwxF2Pz2ZO8cj6ihg4oBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:38:59.618088Z"},"content_sha256":"430511366e9f2731df71e6f288d64379d6eaa78fbd2fda052be5d4d0b2744bac","schema_version":"1.0","event_id":"sha256:430511366e9f2731df71e6f288d64379d6eaa78fbd2fda052be5d4d0b2744bac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:C75OYD75IFUWROSOFVM2WGXO2H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"When does a semiring become a residuated lattice?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Helmut L\\\"anger, Ivan Chajda","submitted_at":"2018-09-20T14:19:34Z","abstract_excerpt":"It is an easy observation that every residuated lattice is in fact a semiring because multiplication distributes over join and the other axioms of a semiring are satisfied trivially. This semiring is commutative, idempotent and simple. The natural question arises if the converse assertion is also true. We show that the conversion is possible provided the given semiring is, moreover, completely distributive. We characterize semirings associated to complete residuated lattices satisfying the double negation law where the assumption of complete distributivity can be omitted. A similar result is o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07646","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":"2026-05-18T00:05:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XTsgnZ6NqVbFJaNmLMj7h74AOhIOjzcHgEJVLX0B/s2uFBvxUHJqhZrYvFZKL3Jxna2PIxsubtoT0DHmrePkCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:38:59.618452Z"},"content_sha256":"b63bc295164cae9a72ab722862c0ff242c35fd40cffcafd1cd395e884855633b","schema_version":"1.0","event_id":"sha256:b63bc295164cae9a72ab722862c0ff242c35fd40cffcafd1cd395e884855633b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C75OYD75IFUWROSOFVM2WGXO2H/bundle.json","state_url":"https://pith.science/pith/C75OYD75IFUWROSOFVM2WGXO2H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C75OYD75IFUWROSOFVM2WGXO2H/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":"2026-06-22T12:38:59Z","links":{"resolver":"https://pith.science/pith/C75OYD75IFUWROSOFVM2WGXO2H","bundle":"https://pith.science/pith/C75OYD75IFUWROSOFVM2WGXO2H/bundle.json","state":"https://pith.science/pith/C75OYD75IFUWROSOFVM2WGXO2H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C75OYD75IFUWROSOFVM2WGXO2H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:C75OYD75IFUWROSOFVM2WGXO2H","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":"983f49b90aae4d01248cd8f35cdcb9efc51a96f29b07268aa175a01ba05fb13b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-09-20T14:19:34Z","title_canon_sha256":"df16e0a2cf2e53e181b3df9050d1d763560f81e290b35892a64238d884c24670"},"schema_version":"1.0","source":{"id":"1809.07646","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07646","created_at":"2026-05-18T00:05:15Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07646v1","created_at":"2026-05-18T00:05:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07646","created_at":"2026-05-18T00:05:15Z"},{"alias_kind":"pith_short_12","alias_value":"C75OYD75IFUW","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"C75OYD75IFUWROSO","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"C75OYD75","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:b63bc295164cae9a72ab722862c0ff242c35fd40cffcafd1cd395e884855633b","target":"graph","created_at":"2026-05-18T00:05:15Z","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":"It is an easy observation that every residuated lattice is in fact a semiring because multiplication distributes over join and the other axioms of a semiring are satisfied trivially. This semiring is commutative, idempotent and simple. The natural question arises if the converse assertion is also true. We show that the conversion is possible provided the given semiring is, moreover, completely distributive. We characterize semirings associated to complete residuated lattices satisfying the double negation law where the assumption of complete distributivity can be omitted. A similar result is o","authors_text":"Helmut L\\\"anger, Ivan Chajda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-09-20T14:19:34Z","title":"When does a semiring become a residuated lattice?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07646","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":"sha256:430511366e9f2731df71e6f288d64379d6eaa78fbd2fda052be5d4d0b2744bac","target":"record","created_at":"2026-05-18T00:05:15Z","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":"983f49b90aae4d01248cd8f35cdcb9efc51a96f29b07268aa175a01ba05fb13b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-09-20T14:19:34Z","title_canon_sha256":"df16e0a2cf2e53e181b3df9050d1d763560f81e290b35892a64238d884c24670"},"schema_version":"1.0","source":{"id":"1809.07646","kind":"arxiv","version":1}},"canonical_sha256":"17faec0ffd416968ba4e2d59ab1aeed1e0e418de85b7313cbc99e93004e9750e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17faec0ffd416968ba4e2d59ab1aeed1e0e418de85b7313cbc99e93004e9750e","first_computed_at":"2026-05-18T00:05:15.624160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:15.624160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WAaj3yZD3eADZravaSo6UXIUrfcH7aVxa5zP0h5aup9J+P71pRECB5MSTqqQYvFTmJEJIDHM0xqMdNNyFIyECw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:15.624677Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.07646","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:430511366e9f2731df71e6f288d64379d6eaa78fbd2fda052be5d4d0b2744bac","sha256:b63bc295164cae9a72ab722862c0ff242c35fd40cffcafd1cd395e884855633b"],"state_sha256":"fd1f513214e379224d2c7bdb1bfffda20bed2eaaf44210932bbf2b9c91b4ef0a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3/gHq79LN3ii8VTXWC0OpGDMRFBmHF61eRwmVETroY/oWrNh5cpBHUGqLD5iu+gt2UhSYhIR1dtTexbpWErcAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T12:38:59.620393Z","bundle_sha256":"d5b5409b0442edf4027bf5d3c96c571d5933820b167c777d5332796d6cf84b8d"}}