{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:LTQBUQ7BCBQ3C4QKJ7BTVVN2RX","short_pith_number":"pith:LTQBUQ7B","canonical_record":{"source":{"id":"2506.05824","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2025-06-06T07:42:16Z","cross_cats_sorted":[],"title_canon_sha256":"6e9d6e9dd9151447bc026b37418a84853b30533b0b6a26aa9d1281d4f6a38d8d","abstract_canon_sha256":"138ce1cba8d9eaa7bca611a9fcfb1a020793c23829e97248d72a54e033b9728d"},"schema_version":"1.0"},"canonical_sha256":"5ce01a43e11061b1720a4fc33ad5ba8dfd99a8c203c194680e0af23c239f74fb","source":{"kind":"arxiv","id":"2506.05824","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.05824","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"2506.05824v1","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.05824","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"LTQBUQ7BCBQ3","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"pith_short_16","alias_value":"LTQBUQ7BCBQ3C4QK","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"pith_short_8","alias_value":"LTQBUQ7B","created_at":"2026-07-05T11:17:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:LTQBUQ7BCBQ3C4QKJ7BTVVN2RX","target":"record","payload":{"canonical_record":{"source":{"id":"2506.05824","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2025-06-06T07:42:16Z","cross_cats_sorted":[],"title_canon_sha256":"6e9d6e9dd9151447bc026b37418a84853b30533b0b6a26aa9d1281d4f6a38d8d","abstract_canon_sha256":"138ce1cba8d9eaa7bca611a9fcfb1a020793c23829e97248d72a54e033b9728d"},"schema_version":"1.0"},"canonical_sha256":"5ce01a43e11061b1720a4fc33ad5ba8dfd99a8c203c194680e0af23c239f74fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:17:10.754570Z","signature_b64":"rMelLk4othIkH029GvhC9hvxNbj6PmH+4T8C1kVv9CV+d2ttsSMECyHNxRTPTu1/WILyHsJRKTY+XXDmh65CAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ce01a43e11061b1720a4fc33ad5ba8dfd99a8c203c194680e0af23c239f74fb","last_reissued_at":"2026-07-05T11:17:10.753981Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:17:10.753981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.05824","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":"2026-07-05T11:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DQZcoTf4oOljzywq9ejcmMdgM+MxdblKrfTZLIS8lE4Cf+b4C5fRq8tsGJvs0B1IIfNxfel1CpLlpZLeAiwtDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T09:10:14.454247Z"},"content_sha256":"95a102819ec29e6449a83f2a8c41c654723ef6843ddb72bcd07d5d0b0148a315","schema_version":"1.0","event_id":"sha256:95a102819ec29e6449a83f2a8c41c654723ef6843ddb72bcd07d5d0b0148a315"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:LTQBUQ7BCBQ3C4QKJ7BTVVN2RX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive Varieties of Lattice Languages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Yuji Komatsu, Yusuke Inoue","submitted_at":"2025-06-06T07:42:16Z","abstract_excerpt":"While a language assigns a value of either `yes' or `no' to each word, a lattice language assigns an element of a given lattice to each word. An advantage of lattice languages is that joins and meets of languages can be defined as generalizations of unions and intersections. This fact also allows for the definition of positive varieties -- classes closed under joins, meets, quotients, and inverse homomorphisms -- of lattice languages. In this paper, we extend Pin's positive variety theorem, proving a one-to-one correspondence between positive varieties of regular lattice languages and pseudo-v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05824","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.05824/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v7z0rt+K16otYBMWpdjn/pgGz7nRWArUt2St/PApsASkm9aT/SqPLjW1okhlo1UYSlYyVMBkrpoQrtMaM1XPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T09:10:14.455426Z"},"content_sha256":"ee55faa76525d90a39c9434289fa324192698f73f0c47ba9f18d1bfcab1febc6","schema_version":"1.0","event_id":"sha256:ee55faa76525d90a39c9434289fa324192698f73f0c47ba9f18d1bfcab1febc6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LTQBUQ7BCBQ3C4QKJ7BTVVN2RX/bundle.json","state_url":"https://pith.science/pith/LTQBUQ7BCBQ3C4QKJ7BTVVN2RX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LTQBUQ7BCBQ3C4QKJ7BTVVN2RX/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":"2026-08-10T09:10:14Z","links":{"resolver":"https://pith.science/pith/LTQBUQ7BCBQ3C4QKJ7BTVVN2RX","bundle":"https://pith.science/pith/LTQBUQ7BCBQ3C4QKJ7BTVVN2RX/bundle.json","state":"https://pith.science/pith/LTQBUQ7BCBQ3C4QKJ7BTVVN2RX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LTQBUQ7BCBQ3C4QKJ7BTVVN2RX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:LTQBUQ7BCBQ3C4QKJ7BTVVN2RX","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":"138ce1cba8d9eaa7bca611a9fcfb1a020793c23829e97248d72a54e033b9728d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2025-06-06T07:42:16Z","title_canon_sha256":"6e9d6e9dd9151447bc026b37418a84853b30533b0b6a26aa9d1281d4f6a38d8d"},"schema_version":"1.0","source":{"id":"2506.05824","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.05824","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"2506.05824v1","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.05824","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"LTQBUQ7BCBQ3","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"pith_short_16","alias_value":"LTQBUQ7BCBQ3C4QK","created_at":"2026-07-05T11:17:10Z"},{"alias_kind":"pith_short_8","alias_value":"LTQBUQ7B","created_at":"2026-07-05T11:17:10Z"}],"graph_snapshots":[{"event_id":"sha256:ee55faa76525d90a39c9434289fa324192698f73f0c47ba9f18d1bfcab1febc6","target":"graph","created_at":"2026-07-05T11:17:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.05824/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"While a language assigns a value of either `yes' or `no' to each word, a lattice language assigns an element of a given lattice to each word. An advantage of lattice languages is that joins and meets of languages can be defined as generalizations of unions and intersections. This fact also allows for the definition of positive varieties -- classes closed under joins, meets, quotients, and inverse homomorphisms -- of lattice languages. In this paper, we extend Pin's positive variety theorem, proving a one-to-one correspondence between positive varieties of regular lattice languages and pseudo-v","authors_text":"Yuji Komatsu, Yusuke Inoue","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2025-06-06T07:42:16Z","title":"Positive Varieties of Lattice Languages"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05824","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":"sha256:95a102819ec29e6449a83f2a8c41c654723ef6843ddb72bcd07d5d0b0148a315","target":"record","created_at":"2026-07-05T11:17:10Z","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":"138ce1cba8d9eaa7bca611a9fcfb1a020793c23829e97248d72a54e033b9728d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.FL","submitted_at":"2025-06-06T07:42:16Z","title_canon_sha256":"6e9d6e9dd9151447bc026b37418a84853b30533b0b6a26aa9d1281d4f6a38d8d"},"schema_version":"1.0","source":{"id":"2506.05824","kind":"arxiv","version":1}},"canonical_sha256":"5ce01a43e11061b1720a4fc33ad5ba8dfd99a8c203c194680e0af23c239f74fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ce01a43e11061b1720a4fc33ad5ba8dfd99a8c203c194680e0af23c239f74fb","first_computed_at":"2026-07-05T11:17:10.753981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:17:10.753981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rMelLk4othIkH029GvhC9hvxNbj6PmH+4T8C1kVv9CV+d2ttsSMECyHNxRTPTu1/WILyHsJRKTY+XXDmh65CAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:17:10.754570Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.05824","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95a102819ec29e6449a83f2a8c41c654723ef6843ddb72bcd07d5d0b0148a315","sha256:ee55faa76525d90a39c9434289fa324192698f73f0c47ba9f18d1bfcab1febc6"],"state_sha256":"75713c7cf08a2f6244e3c6c5cea3a709ac60ca6166e7eed51200e5986b13d632"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AUW4kTQAt26I28rJClMLEuH3mCO27P5sWDtPeACdd+qdGr1y5IzeLEuCJN7HfCL9d01mhZITo8Yzo3Wu2laqCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T09:10:14.463456Z","bundle_sha256":"50d9402af730d71ca88c5ae405bbd2cb349f4d97fe9f5362548dc6d0d2e48cf8"}}