{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HXOAYQKUJP4JS27LMCH5HHTQNU","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":"c8280149b10d83e9eea2950707f345c06a68fefa6b5285682e5d216b327ef305","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-09-24T19:34:55Z","title_canon_sha256":"4247ff9344a6073c4a073549b3f6066b3c91cab8d32e06f37025520e93d80696"},"schema_version":"1.0","source":{"id":"1209.5372","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.5372","created_at":"2026-05-18T03:44:58Z"},{"alias_kind":"arxiv_version","alias_value":"1209.5372v1","created_at":"2026-05-18T03:44:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.5372","created_at":"2026-05-18T03:44:58Z"},{"alias_kind":"pith_short_12","alias_value":"HXOAYQKUJP4J","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HXOAYQKUJP4JS27L","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HXOAYQKU","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:803edc4ea16e263160b0adbcb53c969af97100e28da59abe14a92ffe79f854ce","target":"graph","created_at":"2026-05-18T03:44:58Z","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 prove a simplicity criterion for certain twin tree lattices. It applies to all rank two Kac-Moody groups over finite fields with non-trivial commutation relations, thereby yielding examples of simple non-uniform lattices in the product of two trees.","authors_text":"Bertrand Remy (ICJ), Pierre-Emmanuel Caprace","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-09-24T19:34:55Z","title":"Simplicity of twin tree lattices with non-trivial commutation relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.5372","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":"sha256:78556a646a40fa21819a8038fefb27562ca849c48633d36be2b3a92b0b2aebf8","target":"record","created_at":"2026-05-18T03:44:58Z","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":"c8280149b10d83e9eea2950707f345c06a68fefa6b5285682e5d216b327ef305","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-09-24T19:34:55Z","title_canon_sha256":"4247ff9344a6073c4a073549b3f6066b3c91cab8d32e06f37025520e93d80696"},"schema_version":"1.0","source":{"id":"1209.5372","kind":"arxiv","version":1}},"canonical_sha256":"3ddc0c41544bf8996beb608fd39e706d19177e08f83d96b75d054a87a6b2ede4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ddc0c41544bf8996beb608fd39e706d19177e08f83d96b75d054a87a6b2ede4","first_computed_at":"2026-05-18T03:44:58.320028Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:58.320028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J9KLluUdE0XNrKhSRsz7dR22+D/a7tvBbjCNBrl+jOMKPC2qbzrB+9GA2CHURr/Mt+hoZ9yKNl0cD/D31iITBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:58.320613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.5372","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78556a646a40fa21819a8038fefb27562ca849c48633d36be2b3a92b0b2aebf8","sha256:803edc4ea16e263160b0adbcb53c969af97100e28da59abe14a92ffe79f854ce"],"state_sha256":"be7175f1049ad2f4afb734bee41d9f140721372775ab834be8a3acdc3c91f048"}