{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:N4QWXHCFRJOODYM3M7PJ552HG4","short_pith_number":"pith:N4QWXHCF","canonical_record":{"source":{"id":"0912.0478","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-12-02T17:49:29Z","cross_cats_sorted":[],"title_canon_sha256":"1cac8fd2ff023b7f99b6778b3369ebf74437cdcce5541154968edb6cfe9c6fea","abstract_canon_sha256":"8feebf11b43be2dee354d5c1b6b44a24d88127de79325701123b4237ee7cb316"},"schema_version":"1.0"},"canonical_sha256":"6f216b9c458a5ce1e19b67de9ef747372fbabb8cdee0858263d937fa602f7282","source":{"kind":"arxiv","id":"0912.0478","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0478","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0478v1","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0478","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"pith_short_12","alias_value":"N4QWXHCFRJOO","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"N4QWXHCFRJOODYM3","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"N4QWXHCF","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:N4QWXHCFRJOODYM3M7PJ552HG4","target":"record","payload":{"canonical_record":{"source":{"id":"0912.0478","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-12-02T17:49:29Z","cross_cats_sorted":[],"title_canon_sha256":"1cac8fd2ff023b7f99b6778b3369ebf74437cdcce5541154968edb6cfe9c6fea","abstract_canon_sha256":"8feebf11b43be2dee354d5c1b6b44a24d88127de79325701123b4237ee7cb316"},"schema_version":"1.0"},"canonical_sha256":"6f216b9c458a5ce1e19b67de9ef747372fbabb8cdee0858263d937fa602f7282","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:38.752574Z","signature_b64":"n5VLbufOU/im9FBgIKUKvZSVHhBwZ+OX+q1B0jEt6JDz2yoBDBIaCfhijEDLNejvr4TvghlHl9jumw532YmVCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f216b9c458a5ce1e19b67de9ef747372fbabb8cdee0858263d937fa602f7282","last_reissued_at":"2026-05-18T00:57:38.751970Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:38.751970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.0478","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":"2026-05-18T00:57:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Ut7sFlczyRvVD27zRdDsPtvyzDKScm1+x6lg3sQZmKWTLUCUegTdZVzTgLI/Zi2tptHnItu6QKhXGzZA/BfCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:27:08.167794Z"},"content_sha256":"e986256141076ad2e561b973a64efa59d5eed0883f356216a152efd8965daa2b","schema_version":"1.0","event_id":"sha256:e986256141076ad2e561b973a64efa59d5eed0883f356216a152efd8965daa2b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:N4QWXHCFRJOODYM3M7PJ552HG4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-commuting lattice polynomial functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Erkko Lehtonen, Miguel Couceiro","submitted_at":"2009-12-02T17:49:29Z","abstract_excerpt":"We provide sufficient conditions for a lattice polynomial function to be self-commuting. We explicitly describe self-commuting polynomial functions over chains."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0478","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":"2026-05-18T00:57:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2WktrOlYvirStHsjPMj9MpRKxhwIQlCSphQBquXTTe1Ez/tEllLbyaOEiouqg1jYVYmdTRsvlhlB3fDihX9RBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:27:08.168666Z"},"content_sha256":"a84dee1bf83ab6c8902a3c37be5601565ed8b55998c58510b20f822e3b5e4403","schema_version":"1.0","event_id":"sha256:a84dee1bf83ab6c8902a3c37be5601565ed8b55998c58510b20f822e3b5e4403"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N4QWXHCFRJOODYM3M7PJ552HG4/bundle.json","state_url":"https://pith.science/pith/N4QWXHCFRJOODYM3M7PJ552HG4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N4QWXHCFRJOODYM3M7PJ552HG4/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":"2026-05-27T13:27:08Z","links":{"resolver":"https://pith.science/pith/N4QWXHCFRJOODYM3M7PJ552HG4","bundle":"https://pith.science/pith/N4QWXHCFRJOODYM3M7PJ552HG4/bundle.json","state":"https://pith.science/pith/N4QWXHCFRJOODYM3M7PJ552HG4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N4QWXHCFRJOODYM3M7PJ552HG4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:N4QWXHCFRJOODYM3M7PJ552HG4","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":"8feebf11b43be2dee354d5c1b6b44a24d88127de79325701123b4237ee7cb316","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-12-02T17:49:29Z","title_canon_sha256":"1cac8fd2ff023b7f99b6778b3369ebf74437cdcce5541154968edb6cfe9c6fea"},"schema_version":"1.0","source":{"id":"0912.0478","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0478","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0478v1","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0478","created_at":"2026-05-18T00:57:38Z"},{"alias_kind":"pith_short_12","alias_value":"N4QWXHCFRJOO","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"N4QWXHCFRJOODYM3","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"N4QWXHCF","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:a84dee1bf83ab6c8902a3c37be5601565ed8b55998c58510b20f822e3b5e4403","target":"graph","created_at":"2026-05-18T00:57:38Z","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":"We provide sufficient conditions for a lattice polynomial function to be self-commuting. We explicitly describe self-commuting polynomial functions over chains.","authors_text":"Erkko Lehtonen, Miguel Couceiro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-12-02T17:49:29Z","title":"Self-commuting lattice polynomial functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0478","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:e986256141076ad2e561b973a64efa59d5eed0883f356216a152efd8965daa2b","target":"record","created_at":"2026-05-18T00:57:38Z","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":"8feebf11b43be2dee354d5c1b6b44a24d88127de79325701123b4237ee7cb316","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-12-02T17:49:29Z","title_canon_sha256":"1cac8fd2ff023b7f99b6778b3369ebf74437cdcce5541154968edb6cfe9c6fea"},"schema_version":"1.0","source":{"id":"0912.0478","kind":"arxiv","version":1}},"canonical_sha256":"6f216b9c458a5ce1e19b67de9ef747372fbabb8cdee0858263d937fa602f7282","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f216b9c458a5ce1e19b67de9ef747372fbabb8cdee0858263d937fa602f7282","first_computed_at":"2026-05-18T00:57:38.751970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:38.751970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n5VLbufOU/im9FBgIKUKvZSVHhBwZ+OX+q1B0jEt6JDz2yoBDBIaCfhijEDLNejvr4TvghlHl9jumw532YmVCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:38.752574Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.0478","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e986256141076ad2e561b973a64efa59d5eed0883f356216a152efd8965daa2b","sha256:a84dee1bf83ab6c8902a3c37be5601565ed8b55998c58510b20f822e3b5e4403"],"state_sha256":"675db36ef7916cc30681b87a606994d518d45c239798658e787ce2c665e40fbc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IEQenyf+LfBPLRMYZKNPQjecrOf/81ks1zqa/XEuC01VX3JhhV79sjvcSEgLNKmQvC5UYnIyuiBcwv8Kv265CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T13:27:08.172231Z","bundle_sha256":"b6ad868c99eebc6a92ecbad9a5b1a6b7600502a14dd1f6494a28a4d848574dab"}}