{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:BHCAVRVOETVKHPD6EDKHXK5NX3","short_pith_number":"pith:BHCAVRVO","schema_version":"1.0","canonical_sha256":"09c40ac6ae24eaa3bc7e20d47babadbed71d4fc49c756cb0c2ff2a98e4175bf4","source":{"kind":"arxiv","id":"1908.01742","version":1},"attestation_state":"computed","paper":{"title":"Rendering Non-Euclidean Geometry in Real-Time Using Spherical and Hyperbolic Trigonometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"cs.GR","authors_text":"Christopher Child, Daniil Osudin, Yang-Hui He","submitted_at":"2019-08-05T17:33:45Z","abstract_excerpt":"This paper introduces a method of calculating and rendering shapes in a non-Euclidean 2D space. In order to achieve this, we developed a physics and graphics engine that uses hyperbolic trigonometry to calculate and subsequently render the shapes in a 2D space of constant negative or positive curvature in real-time. We have chosen to use polar coordinates to record the parameters of the objects as well as an azimuthal equidistant projection to render the space onto the screen because of the multiple useful properties they have. For example, polar coordinate system works well with trigonometric"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1908.01742","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2019-08-05T17:33:45Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"b92ed78a25129ab82767aaec19a894716b320b14adb43c9219073af1f713cf74","abstract_canon_sha256":"ca51dcb726f4d30a3c3ab3cd9f1beafb0fcd147c5b4bfafe2302d781ea0de380"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:52:42.068481Z","signature_b64":"m2cwYVH5+HlzNuihc+rLx05QI7BRVmIGEjV7kX5mGsZpXes2FkkBlgjYzdGRrlWQSpyVIQQuWtLJO1DjjoctBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09c40ac6ae24eaa3bc7e20d47babadbed71d4fc49c756cb0c2ff2a98e4175bf4","last_reissued_at":"2026-07-04T23:52:42.067959Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:52:42.067959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rendering Non-Euclidean Geometry in Real-Time Using Spherical and Hyperbolic Trigonometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"cs.GR","authors_text":"Christopher Child, Daniil Osudin, Yang-Hui He","submitted_at":"2019-08-05T17:33:45Z","abstract_excerpt":"This paper introduces a method of calculating and rendering shapes in a non-Euclidean 2D space. In order to achieve this, we developed a physics and graphics engine that uses hyperbolic trigonometry to calculate and subsequently render the shapes in a 2D space of constant negative or positive curvature in real-time. We have chosen to use polar coordinates to record the parameters of the objects as well as an azimuthal equidistant projection to render the space onto the screen because of the multiple useful properties they have. For example, polar coordinate system works well with trigonometric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01742","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.01742/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1908.01742","created_at":"2026-07-04T23:52:42.068013+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.01742v1","created_at":"2026-07-04T23:52:42.068013+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01742","created_at":"2026-07-04T23:52:42.068013+00:00"},{"alias_kind":"pith_short_12","alias_value":"BHCAVRVOETVK","created_at":"2026-07-04T23:52:42.068013+00:00"},{"alias_kind":"pith_short_16","alias_value":"BHCAVRVOETVKHPD6","created_at":"2026-07-04T23:52:42.068013+00:00"},{"alias_kind":"pith_short_8","alias_value":"BHCAVRVO","created_at":"2026-07-04T23:52:42.068013+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BHCAVRVOETVKHPD6EDKHXK5NX3","json":"https://pith.science/pith/BHCAVRVOETVKHPD6EDKHXK5NX3.json","graph_json":"https://pith.science/api/pith-number/BHCAVRVOETVKHPD6EDKHXK5NX3/graph.json","events_json":"https://pith.science/api/pith-number/BHCAVRVOETVKHPD6EDKHXK5NX3/events.json","paper":"https://pith.science/paper/BHCAVRVO"},"agent_actions":{"view_html":"https://pith.science/pith/BHCAVRVOETVKHPD6EDKHXK5NX3","download_json":"https://pith.science/pith/BHCAVRVOETVKHPD6EDKHXK5NX3.json","view_paper":"https://pith.science/paper/BHCAVRVO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.01742&json=true","fetch_graph":"https://pith.science/api/pith-number/BHCAVRVOETVKHPD6EDKHXK5NX3/graph.json","fetch_events":"https://pith.science/api/pith-number/BHCAVRVOETVKHPD6EDKHXK5NX3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BHCAVRVOETVKHPD6EDKHXK5NX3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BHCAVRVOETVKHPD6EDKHXK5NX3/action/storage_attestation","attest_author":"https://pith.science/pith/BHCAVRVOETVKHPD6EDKHXK5NX3/action/author_attestation","sign_citation":"https://pith.science/pith/BHCAVRVOETVKHPD6EDKHXK5NX3/action/citation_signature","submit_replication":"https://pith.science/pith/BHCAVRVOETVKHPD6EDKHXK5NX3/action/replication_record"}},"created_at":"2026-07-04T23:52:42.068013+00:00","updated_at":"2026-07-04T23:52:42.068013+00:00"}