{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DY6DZDFY3HV4PTZNJXKZBWKSSY","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":"01e3ee405f8da82ba2e58ae998d48f40fa0c8b08e5e33d9081687e88c90e487e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-07-13T23:41:14Z","title_canon_sha256":"8a4e575891c3ec05daa1da5f0f6e05db77de3b60d7bdf9ecba71e449af8991e6"},"schema_version":"1.0","source":{"id":"1407.4398","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.4398","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"arxiv_version","alias_value":"1407.4398v2","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4398","created_at":"2026-05-18T01:28:14Z"},{"alias_kind":"pith_short_12","alias_value":"DY6DZDFY3HV4","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DY6DZDFY3HV4PTZN","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DY6DZDFY","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:3ae68057241a78abdc0d6be60f7aaf48ba24ebb95ac31cb6f70f0f1c2a1b6b88","target":"graph","created_at":"2026-05-18T01:28:14Z","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":"Euclidean geometry consists of straightedge-and-compass constructions and reasoning about the results of those constructions. We show that Euclidean geometry can be developed using only intuitionistic logic. We consider three versions of Euclid's parallel postulate: Euclid's own formulation in his Postulate 5; Playfair's 1795 version, and a new version we call the strong parallel postulate. These differ in that Euclid's version and the new version both assert the existence of a point where two lines meet, while Playfair's version makes no existence assertion. Classically, the models of Euclide","authors_text":"Michael Beeson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-07-13T23:41:14Z","title":"Constructive Geometry and the Parallel Postulate"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4398","kind":"arxiv","version":2},"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":"sha256:6141c4deaf660b2fc1b2d33665865de5a3a12b387036a18ab0c666d4039f6052","target":"record","created_at":"2026-05-18T01:28:14Z","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":"01e3ee405f8da82ba2e58ae998d48f40fa0c8b08e5e33d9081687e88c90e487e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-07-13T23:41:14Z","title_canon_sha256":"8a4e575891c3ec05daa1da5f0f6e05db77de3b60d7bdf9ecba71e449af8991e6"},"schema_version":"1.0","source":{"id":"1407.4398","kind":"arxiv","version":2}},"canonical_sha256":"1e3c3c8cb8d9ebc7cf2d4dd590d952962f934f9e8d8ea3c655ed41ecc6080791","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e3c3c8cb8d9ebc7cf2d4dd590d952962f934f9e8d8ea3c655ed41ecc6080791","first_computed_at":"2026-05-18T01:28:14.907305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:14.907305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lPcRh5ddxQfbhtBOtKGpsLrVRCwVcuveaWIqPKMyyuPi2CqgVv5ndSDcGLEvS4C8v9phRqYMkc/oEwOlaXdTCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:14.907967Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.4398","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6141c4deaf660b2fc1b2d33665865de5a3a12b387036a18ab0c666d4039f6052","sha256:3ae68057241a78abdc0d6be60f7aaf48ba24ebb95ac31cb6f70f0f1c2a1b6b88"],"state_sha256":"4c587f64c78cf65230f3e3139790364acd812026b355a18691992f0c055cd8d2"}