{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:K74SHL7NWV37XQDF33ZNOKEQUI","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":"10c0d4b4f423949ee57c19bc2b74e9812f0890b436402cbfc82462a47492d280","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-02T00:17:30Z","title_canon_sha256":"72390b744d55333667877b012de282210613379113c62c1cb87a523a43548fdc"},"schema_version":"1.0","source":{"id":"1107.0346","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0346","created_at":"2026-05-18T04:18:54Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0346v1","created_at":"2026-05-18T04:18:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0346","created_at":"2026-05-18T04:18:54Z"},{"alias_kind":"pith_short_12","alias_value":"K74SHL7NWV37","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"K74SHL7NWV37XQDF","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"K74SHL7N","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:961c19de6d0434b55cf5270ae288dd663299046a601140dad28ec94fa1050b97","target":"graph","created_at":"2026-05-18T04:18:54Z","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":"These lecture notes are based on [arXiv: math/0702714, 0907.4469, 0907.4470]. We introduce and study basic aspects of non-Euclidean geometries from a coordinate-free viewpoint.","authors_text":"Carlos H. Grossi, Sasha Anan'in","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-02T00:17:30Z","title":"Basic coordinate-free non-Euclidean geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0346","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":"sha256:73b0c502eb96c11e4ac49bd9bd587bea6b7891fecdcb9bf22ad81de2923cd947","target":"record","created_at":"2026-05-18T04:18:54Z","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":"10c0d4b4f423949ee57c19bc2b74e9812f0890b436402cbfc82462a47492d280","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-02T00:17:30Z","title_canon_sha256":"72390b744d55333667877b012de282210613379113c62c1cb87a523a43548fdc"},"schema_version":"1.0","source":{"id":"1107.0346","kind":"arxiv","version":1}},"canonical_sha256":"57f923afedb577fbc065def2d72890a21c4b56db17d28b3c63386f342af66930","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57f923afedb577fbc065def2d72890a21c4b56db17d28b3c63386f342af66930","first_computed_at":"2026-05-18T04:18:54.146001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:54.146001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i8OW7P+J+2e13ox9Qe5ocwXDo2BN4ETQ5btZ6Ks+eBdlFmA0zicflP5vkFEyv6ULPp7cYGcH6XmvXN1AAGmtDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:54.146484Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0346","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73b0c502eb96c11e4ac49bd9bd587bea6b7891fecdcb9bf22ad81de2923cd947","sha256:961c19de6d0434b55cf5270ae288dd663299046a601140dad28ec94fa1050b97"],"state_sha256":"424b66f5ba9e09d59dfb7334f4c81099e32bd598742a220dc82264d9dfd1af49"}