{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZZXHFG5RWXT5XBZ27TAGT7KHIS","short_pith_number":"pith:ZZXHFG5R","canonical_record":{"source":{"id":"1510.03688","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-13T14:14:55Z","cross_cats_sorted":[],"title_canon_sha256":"f4aaa85f2ad37d4eb0034a8796f516fd2270c27d5e428e1d853890c7d769815e","abstract_canon_sha256":"30cd3f9f3e348525c63f01a33314d9ddcc75e7f2a0dce1c83cf1df6f37cbf5ae"},"schema_version":"1.0"},"canonical_sha256":"ce6e729bb1b5e7db873afcc069fd4744b29c6a20f7ead071e8dd5ceaf1e7771d","source":{"kind":"arxiv","id":"1510.03688","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03688","created_at":"2026-05-18T00:48:43Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03688v4","created_at":"2026-05-18T00:48:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03688","created_at":"2026-05-18T00:48:43Z"},{"alias_kind":"pith_short_12","alias_value":"ZZXHFG5RWXT5","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZZXHFG5RWXT5XBZ2","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZZXHFG5R","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZZXHFG5RWXT5XBZ27TAGT7KHIS","target":"record","payload":{"canonical_record":{"source":{"id":"1510.03688","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-13T14:14:55Z","cross_cats_sorted":[],"title_canon_sha256":"f4aaa85f2ad37d4eb0034a8796f516fd2270c27d5e428e1d853890c7d769815e","abstract_canon_sha256":"30cd3f9f3e348525c63f01a33314d9ddcc75e7f2a0dce1c83cf1df6f37cbf5ae"},"schema_version":"1.0"},"canonical_sha256":"ce6e729bb1b5e7db873afcc069fd4744b29c6a20f7ead071e8dd5ceaf1e7771d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:43.123220Z","signature_b64":"regt/zrPgbchQSeQKonRJGmgGlh+bEyMdBMQzL7GiAP9QQcRN/CZZ1t7GW7cdTCt+N7RLoKig5ItwPJDyZUMBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce6e729bb1b5e7db873afcc069fd4744b29c6a20f7ead071e8dd5ceaf1e7771d","last_reissued_at":"2026-05-18T00:48:43.122704Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:43.122704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.03688","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QKe75LIoainRM5K5/PoHMrmqcRWWna47Nx1lxlocugA6fbirH1I4+04qGj8edYbiDU+v3EB2K3ZdHbFl8YOCCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T13:59:33.459623Z"},"content_sha256":"18dfdc52e0c8401a3a5aef2bda29268e2faeaed7667e5d2066f49acdf823a9a0","schema_version":"1.0","event_id":"sha256:18dfdc52e0c8401a3a5aef2bda29268e2faeaed7667e5d2066f49acdf823a9a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZZXHFG5RWXT5XBZ27TAGT7KHIS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local Moufang sets and PSL_2 over a local ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Erik Rijcken, Tom De Medts","submitted_at":"2015-10-13T14:14:55Z","abstract_excerpt":"We introduce local Moufang sets as a generalization of Moufang sets. We present a method to construct local Moufang sets from only one root group and one permutation. We use this to describe $\\mathsf{PSL}_2$ over a local ring as a local Moufang set, and give necessary and sufficient conditions for a local Moufang set to be of this form."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03688","kind":"arxiv","version":4},"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":"2026-05-18T00:48:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ogsqBikxt0Q+sKRhdaW0BW/NAJsbBHqrMDw0dNqoDp6HLWzV/5pgx231Gc7lFa1Emzgcmh2uoaCEvYLQqxxoAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T13:59:33.460265Z"},"content_sha256":"4d46cac7cbbc6ef1ae03dd6354a14ad7155cc1b7694e9ae5ec5f172a87d3aef9","schema_version":"1.0","event_id":"sha256:4d46cac7cbbc6ef1ae03dd6354a14ad7155cc1b7694e9ae5ec5f172a87d3aef9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZZXHFG5RWXT5XBZ27TAGT7KHIS/bundle.json","state_url":"https://pith.science/pith/ZZXHFG5RWXT5XBZ27TAGT7KHIS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZZXHFG5RWXT5XBZ27TAGT7KHIS/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":"2026-05-22T13:59:33Z","links":{"resolver":"https://pith.science/pith/ZZXHFG5RWXT5XBZ27TAGT7KHIS","bundle":"https://pith.science/pith/ZZXHFG5RWXT5XBZ27TAGT7KHIS/bundle.json","state":"https://pith.science/pith/ZZXHFG5RWXT5XBZ27TAGT7KHIS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZZXHFG5RWXT5XBZ27TAGT7KHIS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZZXHFG5RWXT5XBZ27TAGT7KHIS","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":"30cd3f9f3e348525c63f01a33314d9ddcc75e7f2a0dce1c83cf1df6f37cbf5ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-13T14:14:55Z","title_canon_sha256":"f4aaa85f2ad37d4eb0034a8796f516fd2270c27d5e428e1d853890c7d769815e"},"schema_version":"1.0","source":{"id":"1510.03688","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03688","created_at":"2026-05-18T00:48:43Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03688v4","created_at":"2026-05-18T00:48:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03688","created_at":"2026-05-18T00:48:43Z"},{"alias_kind":"pith_short_12","alias_value":"ZZXHFG5RWXT5","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZZXHFG5RWXT5XBZ2","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZZXHFG5R","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:4d46cac7cbbc6ef1ae03dd6354a14ad7155cc1b7694e9ae5ec5f172a87d3aef9","target":"graph","created_at":"2026-05-18T00:48:43Z","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 introduce local Moufang sets as a generalization of Moufang sets. We present a method to construct local Moufang sets from only one root group and one permutation. We use this to describe $\\mathsf{PSL}_2$ over a local ring as a local Moufang set, and give necessary and sufficient conditions for a local Moufang set to be of this form.","authors_text":"Erik Rijcken, Tom De Medts","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-13T14:14:55Z","title":"Local Moufang sets and PSL_2 over a local ring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03688","kind":"arxiv","version":4},"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":"sha256:18dfdc52e0c8401a3a5aef2bda29268e2faeaed7667e5d2066f49acdf823a9a0","target":"record","created_at":"2026-05-18T00:48:43Z","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":"30cd3f9f3e348525c63f01a33314d9ddcc75e7f2a0dce1c83cf1df6f37cbf5ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-13T14:14:55Z","title_canon_sha256":"f4aaa85f2ad37d4eb0034a8796f516fd2270c27d5e428e1d853890c7d769815e"},"schema_version":"1.0","source":{"id":"1510.03688","kind":"arxiv","version":4}},"canonical_sha256":"ce6e729bb1b5e7db873afcc069fd4744b29c6a20f7ead071e8dd5ceaf1e7771d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce6e729bb1b5e7db873afcc069fd4744b29c6a20f7ead071e8dd5ceaf1e7771d","first_computed_at":"2026-05-18T00:48:43.122704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:43.122704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"regt/zrPgbchQSeQKonRJGmgGlh+bEyMdBMQzL7GiAP9QQcRN/CZZ1t7GW7cdTCt+N7RLoKig5ItwPJDyZUMBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:43.123220Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03688","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18dfdc52e0c8401a3a5aef2bda29268e2faeaed7667e5d2066f49acdf823a9a0","sha256:4d46cac7cbbc6ef1ae03dd6354a14ad7155cc1b7694e9ae5ec5f172a87d3aef9"],"state_sha256":"d57b53d2208ced1aaa4bf6fa9f48cc317e69f62dc410b327224a55cc5f78586f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WppoSAcbI6ujzeggAlcJ0yT480qFBnejVRQ8t4cbhMlzvdD11X6j/6tY2LyDeecFFEJ6RgV2ddyU2tOors3wCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T13:59:33.463564Z","bundle_sha256":"090cc59ae6b4e1c7e46b4e4cec435cafad7e57cc497673f622c8c0f3c8f5a907"}}