{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LNSENQUTH4S4RIWBNWC2HANZ32","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":"9a5b35040a312fc18fb10fe448aa6a7efb861424b9c7255cca7857d6f927e4d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-06-15T13:19:13Z","title_canon_sha256":"c17432726ab7e3f2d6c6de72c4330e912782e14b7dab2261f8db35ac5da87eba"},"schema_version":"1.0","source":{"id":"1706.04858","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04858","created_at":"2026-05-18T00:42:19Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04858v1","created_at":"2026-05-18T00:42:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04858","created_at":"2026-05-18T00:42:19Z"},{"alias_kind":"pith_short_12","alias_value":"LNSENQUTH4S4","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LNSENQUTH4S4RIWB","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LNSENQUT","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:548c1a83ce1d85f5de115778daea9365c17cab98ab2a65f21b38d910b98bb84b","target":"graph","created_at":"2026-05-18T00:42:19Z","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":"All known Moufang sets arise, in some way or another, from an algebraic structure which can be called `division' in some way. In this PhD dissertation, I made an attempt to develop a theory of local Moufang sets, which generalize Moufang sets in a way to allow constructing using the corresponding local algebraic structures. In the first of the two major parts of the dissertation, I develop the theory of local Moufang sets, while in the second part, some examples are constructed. The most general example constructed arises from a local Jordan pair (which corresponds to a local Jordan algebra), ","authors_text":"Erik Rijcken","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-06-15T13:19:13Z","title":"Local Moufang sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04858","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:b14f66a434fcf9174cdd8b8902762af32df1c002956774f28a169604ef60d5f9","target":"record","created_at":"2026-05-18T00:42:19Z","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":"9a5b35040a312fc18fb10fe448aa6a7efb861424b9c7255cca7857d6f927e4d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-06-15T13:19:13Z","title_canon_sha256":"c17432726ab7e3f2d6c6de72c4330e912782e14b7dab2261f8db35ac5da87eba"},"schema_version":"1.0","source":{"id":"1706.04858","kind":"arxiv","version":1}},"canonical_sha256":"5b6446c2933f25c8a2c16d85a381b9dea91846bcd225e2fa730dcbbc8f0bfa8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b6446c2933f25c8a2c16d85a381b9dea91846bcd225e2fa730dcbbc8f0bfa8d","first_computed_at":"2026-05-18T00:42:19.037940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:19.037940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CCqvjkJLuciOnGhOrOrjAHzIZjTMkGDO1thhCmvePjEl8hR+JrHlwf4dd6Um81f/s2DYb1RglRNFADOD7jYvDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:19.038688Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.04858","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b14f66a434fcf9174cdd8b8902762af32df1c002956774f28a169604ef60d5f9","sha256:548c1a83ce1d85f5de115778daea9365c17cab98ab2a65f21b38d910b98bb84b"],"state_sha256":"b2597c2b103810cb89a51a565119365fd5c6a6dc27142f57e7b59f1a20df3028"}