{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:OMGNI327WOE2UQUYX2YVU3533A","short_pith_number":"pith:OMGNI327","canonical_record":{"source":{"id":"0809.3234","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-09-18T19:52:48Z","cross_cats_sorted":[],"title_canon_sha256":"7331c5111d626b1e92397c653f8b776e408d60f429820a77e2a843f3959d337d","abstract_canon_sha256":"4ae2c3043b3921a147b90991b140052f68051d029fa058d3d69126e471bbf803"},"schema_version":"1.0"},"canonical_sha256":"730cd46f5fb389aa4298beb15a6fbbd83bc5ce014815cc0f5637dbdd8e5040a3","source":{"kind":"arxiv","id":"0809.3234","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.3234","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"arxiv_version","alias_value":"0809.3234v2","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.3234","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"pith_short_12","alias_value":"OMGNI327WOE2","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"OMGNI327WOE2UQUY","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"OMGNI327","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:OMGNI327WOE2UQUYX2YVU3533A","target":"record","payload":{"canonical_record":{"source":{"id":"0809.3234","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-09-18T19:52:48Z","cross_cats_sorted":[],"title_canon_sha256":"7331c5111d626b1e92397c653f8b776e408d60f429820a77e2a843f3959d337d","abstract_canon_sha256":"4ae2c3043b3921a147b90991b140052f68051d029fa058d3d69126e471bbf803"},"schema_version":"1.0"},"canonical_sha256":"730cd46f5fb389aa4298beb15a6fbbd83bc5ce014815cc0f5637dbdd8e5040a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:53.772498Z","signature_b64":"JHKDHuSs8DzrrWAyYsKvwmedIJkI/zCYK/q0UzG/TYxIM/DKy2EUHbzMAs0J0hzt5u79Xx22GajLvrqIiPIzDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"730cd46f5fb389aa4298beb15a6fbbd83bc5ce014815cc0f5637dbdd8e5040a3","last_reissued_at":"2026-05-18T01:14:53.771764Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:53.771764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0809.3234","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":"2026-05-18T01:14:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uuZ93H84SRm2pOlaB41k7wOMCH9wXpcM0ZzKIfxHlUabdd1u3tO+lqLph+RaTWlmuhS3vWbjBqX0T8+8XDSpBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T07:22:59.972072Z"},"content_sha256":"a237c978d399a2cdffe46e833d594eef2ab9a179e4b4ceb9dddeb5c1aff5ead9","schema_version":"1.0","event_id":"sha256:a237c978d399a2cdffe46e833d594eef2ab9a179e4b4ceb9dddeb5c1aff5ead9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:OMGNI327WOE2UQUYX2YVU3533A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on minors determined by clones of semilattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Erkko Lehtonen","submitted_at":"2008-09-18T19:52:48Z","abstract_excerpt":"The C-minor partial orders determined by the clones generated by a semilattice operation (and possibly the constant operations corresponding to its identity or zero elements) are shown to satisfy the descending chain condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.3234","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":"2026-05-18T01:14:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YUyZ5JYWbmPUPqGUL1BX9Bh44IKFXyzclHNJdLsKsg1BHsMlGMpZ9U0RHOKWJtAxOIaFtvviVFwSIurfUuX8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T07:22:59.972442Z"},"content_sha256":"6286bb543e25a71ee8b2a5e41066cc59e5aa979c3d606bb4083bb81bd8462cd1","schema_version":"1.0","event_id":"sha256:6286bb543e25a71ee8b2a5e41066cc59e5aa979c3d606bb4083bb81bd8462cd1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OMGNI327WOE2UQUYX2YVU3533A/bundle.json","state_url":"https://pith.science/pith/OMGNI327WOE2UQUYX2YVU3533A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OMGNI327WOE2UQUYX2YVU3533A/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":"2026-06-29T07:22:59Z","links":{"resolver":"https://pith.science/pith/OMGNI327WOE2UQUYX2YVU3533A","bundle":"https://pith.science/pith/OMGNI327WOE2UQUYX2YVU3533A/bundle.json","state":"https://pith.science/pith/OMGNI327WOE2UQUYX2YVU3533A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OMGNI327WOE2UQUYX2YVU3533A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:OMGNI327WOE2UQUYX2YVU3533A","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":"4ae2c3043b3921a147b90991b140052f68051d029fa058d3d69126e471bbf803","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-09-18T19:52:48Z","title_canon_sha256":"7331c5111d626b1e92397c653f8b776e408d60f429820a77e2a843f3959d337d"},"schema_version":"1.0","source":{"id":"0809.3234","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.3234","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"arxiv_version","alias_value":"0809.3234v2","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.3234","created_at":"2026-05-18T01:14:53Z"},{"alias_kind":"pith_short_12","alias_value":"OMGNI327WOE2","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"OMGNI327WOE2UQUY","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"OMGNI327","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:6286bb543e25a71ee8b2a5e41066cc59e5aa979c3d606bb4083bb81bd8462cd1","target":"graph","created_at":"2026-05-18T01:14:53Z","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":"The C-minor partial orders determined by the clones generated by a semilattice operation (and possibly the constant operations corresponding to its identity or zero elements) are shown to satisfy the descending chain condition.","authors_text":"Erkko Lehtonen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-09-18T19:52:48Z","title":"A note on minors determined by clones of semilattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.3234","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:a237c978d399a2cdffe46e833d594eef2ab9a179e4b4ceb9dddeb5c1aff5ead9","target":"record","created_at":"2026-05-18T01:14:53Z","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":"4ae2c3043b3921a147b90991b140052f68051d029fa058d3d69126e471bbf803","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2008-09-18T19:52:48Z","title_canon_sha256":"7331c5111d626b1e92397c653f8b776e408d60f429820a77e2a843f3959d337d"},"schema_version":"1.0","source":{"id":"0809.3234","kind":"arxiv","version":2}},"canonical_sha256":"730cd46f5fb389aa4298beb15a6fbbd83bc5ce014815cc0f5637dbdd8e5040a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"730cd46f5fb389aa4298beb15a6fbbd83bc5ce014815cc0f5637dbdd8e5040a3","first_computed_at":"2026-05-18T01:14:53.771764Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:53.771764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JHKDHuSs8DzrrWAyYsKvwmedIJkI/zCYK/q0UzG/TYxIM/DKy2EUHbzMAs0J0hzt5u79Xx22GajLvrqIiPIzDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:53.772498Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.3234","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a237c978d399a2cdffe46e833d594eef2ab9a179e4b4ceb9dddeb5c1aff5ead9","sha256:6286bb543e25a71ee8b2a5e41066cc59e5aa979c3d606bb4083bb81bd8462cd1"],"state_sha256":"8bcfd0de42d51a61f9e37933b5c707561e9ebac4f2cc23479fcf0c8af8ac114b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2K4sfDwEXX20oXbpsg9cWEXW5inYCTA8dkvAo3yTCE8OwepaBLgqnMhHJLQPRpECQtVbxuu37A2wgzdz7QI5Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T07:22:59.974718Z","bundle_sha256":"2cb0cbd68546d8d9f54583dd50ae621206db68305dcb140fbefc81ca5274e63c"}}