{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:4FHOYYYKUOPBMKGZMYRMXOOM6D","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":"90d225c0f3acba764d634d9c958b4fa1f7ac89b07945ec1e90328d3c62aa4b89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-03-21T14:20:11Z","title_canon_sha256":"3648f52e3e45e9c29d65ab56b2ffef84d1e2a5e8a920149fc40d30b389fe21fc"},"schema_version":"1.0","source":{"id":"2003.09668","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.09668","created_at":"2026-07-05T00:49:45Z"},{"alias_kind":"arxiv_version","alias_value":"2003.09668v1","created_at":"2026-07-05T00:49:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.09668","created_at":"2026-07-05T00:49:45Z"},{"alias_kind":"pith_short_12","alias_value":"4FHOYYYKUOPB","created_at":"2026-07-05T00:49:45Z"},{"alias_kind":"pith_short_16","alias_value":"4FHOYYYKUOPBMKGZ","created_at":"2026-07-05T00:49:45Z"},{"alias_kind":"pith_short_8","alias_value":"4FHOYYYK","created_at":"2026-07-05T00:49:45Z"}],"graph_snapshots":[{"event_id":"sha256:537484ca8c69ffa592b341957f8081a4b48d52644647153bcd2375342caa7605","target":"graph","created_at":"2026-07-05T00:49:45Z","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/2003.09668/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Around 2001 we classified the Leonard systems up to isomorphism. The proof was lengthy and involved considerable computation. In this paper we give a proof that is shorter and involves minimal computation. We also give a comprehensive descriptionof the intersection numbers of a Leonard system.","authors_text":"Paul Terwilliger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-03-21T14:20:11Z","title":"Notes on the Leonard system classification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.09668","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":"sha256:12d053e2222e6e792d5b8ba4ea88d069557c32c841cc47ee9ba06af7089c3b0a","target":"record","created_at":"2026-07-05T00:49:45Z","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":"90d225c0f3acba764d634d9c958b4fa1f7ac89b07945ec1e90328d3c62aa4b89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-03-21T14:20:11Z","title_canon_sha256":"3648f52e3e45e9c29d65ab56b2ffef84d1e2a5e8a920149fc40d30b389fe21fc"},"schema_version":"1.0","source":{"id":"2003.09668","kind":"arxiv","version":1}},"canonical_sha256":"e14eec630aa39e1628d96622cbb9ccf0c813a1d80783c81aeeb3b1f5599706dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e14eec630aa39e1628d96622cbb9ccf0c813a1d80783c81aeeb3b1f5599706dc","first_computed_at":"2026-07-05T00:49:45.933001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:49:45.933001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VNnhbmBuMnuwoAEOE0tFlLDlJZ2w4enWf5l4XnzDLLd1lpIvuDYSu/uUW6dIzvLIse0bUvq+uJiIcgDz8xsXAw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:49:45.933373Z","signed_message":"canonical_sha256_bytes"},"source_id":"2003.09668","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12d053e2222e6e792d5b8ba4ea88d069557c32c841cc47ee9ba06af7089c3b0a","sha256:537484ca8c69ffa592b341957f8081a4b48d52644647153bcd2375342caa7605"],"state_sha256":"2c2ddcb7454f9c0f83eea01dbed8f909c5566505037137ec2b9c76d1fa0d1777"}