{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2NRL7IR6GCQHUADVMCEVHOBGUH","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":"3f90def7d71cccfe398a2cd04981f8363eaecb8ac3408913f13847319f65db2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-04-18T09:26:05Z","title_canon_sha256":"89526bf5c367d0f701e94d7512458e51336dc16cfdf991bd60950caa30aa16ae"},"schema_version":"1.0","source":{"id":"1604.05581","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.05581","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"arxiv_version","alias_value":"1604.05581v3","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05581","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"pith_short_12","alias_value":"2NRL7IR6GCQH","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2NRL7IR6GCQHUADV","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2NRL7IR6","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:95f59b2fb294a8be3962a73b655c2ff9a09ab8acdf742163d31d58b988cd8af6","target":"graph","created_at":"2026-05-18T01:13:30Z","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 give a non-Paschian plane based on the property of betweenness which cannot be derived from an ordering of the points of a line. In this model there is no possibility to define the congruence of segments but we can define angle, triangle and angle measure, respectively. With respect to our definitions the plane has an elliptic character, meaning that the sum of the angles of a triangle is greater than $\\pi$.","authors_text":"\\'Akos G.Horv\\'ath","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-04-18T09:26:05Z","title":"On the non-Paschian ordered planes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05581","kind":"arxiv","version":3},"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":"sha256:73117184b0e444cfefd5db67a1c74521b09e3de5608f80b5dac79b632e22011e","target":"record","created_at":"2026-05-18T01:13:30Z","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":"3f90def7d71cccfe398a2cd04981f8363eaecb8ac3408913f13847319f65db2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2016-04-18T09:26:05Z","title_canon_sha256":"89526bf5c367d0f701e94d7512458e51336dc16cfdf991bd60950caa30aa16ae"},"schema_version":"1.0","source":{"id":"1604.05581","kind":"arxiv","version":3}},"canonical_sha256":"d362bfa23e30a07a0075608953b826a1c0d91b55d3dd5ca00bacf6dccc9618fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d362bfa23e30a07a0075608953b826a1c0d91b55d3dd5ca00bacf6dccc9618fb","first_computed_at":"2026-05-18T01:13:30.232285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:30.232285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lZShkZm3+ty0hy8W+fYbHRaXBYDZQL2s17sW5aVNL5HCdBfSgCDjz+GNdVZZCH4xhvICuaUfdVLajjXZL4mOAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:30.232953Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.05581","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73117184b0e444cfefd5db67a1c74521b09e3de5608f80b5dac79b632e22011e","sha256:95f59b2fb294a8be3962a73b655c2ff9a09ab8acdf742163d31d58b988cd8af6"],"state_sha256":"a85b859b3cd0abf0192e3b99fe8d2d663e819dbb9defe84f745a2bb2ca50f972"}