{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:AYQGIW3ZKJ6QGSBQJLDCC5BLNK","short_pith_number":"pith:AYQGIW3Z","canonical_record":{"source":{"id":"0709.2831","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cs.CG","submitted_at":"2007-09-18T15:36:38Z","cross_cats_sorted":[],"title_canon_sha256":"3f73f24e698f9f93637440352c12e29957c26c921d0c975777a2e9c58cba6565","abstract_canon_sha256":"b0bab428dda26178eaaba9e3192eaa859a0d85ffbb1826a5787600499d69eea9"},"schema_version":"1.0"},"canonical_sha256":"0620645b79527d0348304ac621742b6aa71e840226aec08d2d830c827a6732a8","source":{"kind":"arxiv","id":"0709.2831","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0709.2831","created_at":"2026-05-18T04:09:14Z"},{"alias_kind":"arxiv_version","alias_value":"0709.2831v2","created_at":"2026-05-18T04:09:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.2831","created_at":"2026-05-18T04:09:14Z"},{"alias_kind":"pith_short_12","alias_value":"AYQGIW3ZKJ6Q","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"AYQGIW3ZKJ6QGSBQ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"AYQGIW3Z","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:AYQGIW3ZKJ6QGSBQJLDCC5BLNK","target":"record","payload":{"canonical_record":{"source":{"id":"0709.2831","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"cs.CG","submitted_at":"2007-09-18T15:36:38Z","cross_cats_sorted":[],"title_canon_sha256":"3f73f24e698f9f93637440352c12e29957c26c921d0c975777a2e9c58cba6565","abstract_canon_sha256":"b0bab428dda26178eaaba9e3192eaa859a0d85ffbb1826a5787600499d69eea9"},"schema_version":"1.0"},"canonical_sha256":"0620645b79527d0348304ac621742b6aa71e840226aec08d2d830c827a6732a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:14.483295Z","signature_b64":"H6DXYLEQ/KL4Ah286k9a3lBRzlfmM4zJMAcr+zCG+qdpYmmLuoRmMYMtBw4QB7vGPsOsM+NxZ9ZJdpOtI4PmBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0620645b79527d0348304ac621742b6aa71e840226aec08d2d830c827a6732a8","last_reissued_at":"2026-05-18T04:09:14.482617Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:14.482617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0709.2831","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:09:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PtbCOtmbkXujGRsBSs26fz+B0mu+k5+9GzUvhqOyNSmgrTEQ2XgZgVxXK31mJPvu1lhjtc/PkeRufO2XneCjAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:45:49.391847Z"},"content_sha256":"9ce365f3a1f556dc1ea7599da8d1bdbcd3f45184151acbc003fd66ac08e8869c","schema_version":"1.0","event_id":"sha256:9ce365f3a1f556dc1ea7599da8d1bdbcd3f45184151acbc003fd66ac08e8869c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:AYQGIW3ZKJ6QGSBQJLDCC5BLNK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Triangulating the Real Projective Plane","license":"","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Monique Teillaud (INRIA Sophia Antipolis), Mridul Aanjaneya","submitted_at":"2007-09-18T15:36:38Z","abstract_excerpt":"We consider the problem of computing a triangulation of the real projective plane P2, given a finite point set S={p1, p2,..., pn} as input. We prove that a triangulation of P2 always exists if at least six points in S are in general position, i.e., no three of them are collinear. We also design an algorithm for triangulating P2 if this necessary condition holds. As far as we know, this is the first computational result on the real projective plane."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.2831","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:09:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qdarf+ZF80GHowi40bxSUbFUa3rZJzVOr2x6dSw7D0SGTLdNzlWRhGjR4yPHNvXcH89s6MeNp/ba5awsdVGkBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:45:49.392188Z"},"content_sha256":"179f182cc12f28265c73f49fa7f969e5197eb9413611b560855a4e970669894e","schema_version":"1.0","event_id":"sha256:179f182cc12f28265c73f49fa7f969e5197eb9413611b560855a4e970669894e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AYQGIW3ZKJ6QGSBQJLDCC5BLNK/bundle.json","state_url":"https://pith.science/pith/AYQGIW3ZKJ6QGSBQJLDCC5BLNK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AYQGIW3ZKJ6QGSBQJLDCC5BLNK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T11:45:49Z","links":{"resolver":"https://pith.science/pith/AYQGIW3ZKJ6QGSBQJLDCC5BLNK","bundle":"https://pith.science/pith/AYQGIW3ZKJ6QGSBQJLDCC5BLNK/bundle.json","state":"https://pith.science/pith/AYQGIW3ZKJ6QGSBQJLDCC5BLNK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AYQGIW3ZKJ6QGSBQJLDCC5BLNK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:AYQGIW3ZKJ6QGSBQJLDCC5BLNK","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":"b0bab428dda26178eaaba9e3192eaa859a0d85ffbb1826a5787600499d69eea9","cross_cats_sorted":[],"license":"","primary_cat":"cs.CG","submitted_at":"2007-09-18T15:36:38Z","title_canon_sha256":"3f73f24e698f9f93637440352c12e29957c26c921d0c975777a2e9c58cba6565"},"schema_version":"1.0","source":{"id":"0709.2831","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0709.2831","created_at":"2026-05-18T04:09:14Z"},{"alias_kind":"arxiv_version","alias_value":"0709.2831v2","created_at":"2026-05-18T04:09:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.2831","created_at":"2026-05-18T04:09:14Z"},{"alias_kind":"pith_short_12","alias_value":"AYQGIW3ZKJ6Q","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"AYQGIW3ZKJ6QGSBQ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"AYQGIW3Z","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:179f182cc12f28265c73f49fa7f969e5197eb9413611b560855a4e970669894e","target":"graph","created_at":"2026-05-18T04:09:14Z","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":"We consider the problem of computing a triangulation of the real projective plane P2, given a finite point set S={p1, p2,..., pn} as input. We prove that a triangulation of P2 always exists if at least six points in S are in general position, i.e., no three of them are collinear. We also design an algorithm for triangulating P2 if this necessary condition holds. As far as we know, this is the first computational result on the real projective plane.","authors_text":"Monique Teillaud (INRIA Sophia Antipolis), Mridul Aanjaneya","cross_cats":[],"headline":"","license":"","primary_cat":"cs.CG","submitted_at":"2007-09-18T15:36:38Z","title":"Triangulating the Real Projective Plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.2831","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":"sha256:9ce365f3a1f556dc1ea7599da8d1bdbcd3f45184151acbc003fd66ac08e8869c","target":"record","created_at":"2026-05-18T04:09:14Z","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":"b0bab428dda26178eaaba9e3192eaa859a0d85ffbb1826a5787600499d69eea9","cross_cats_sorted":[],"license":"","primary_cat":"cs.CG","submitted_at":"2007-09-18T15:36:38Z","title_canon_sha256":"3f73f24e698f9f93637440352c12e29957c26c921d0c975777a2e9c58cba6565"},"schema_version":"1.0","source":{"id":"0709.2831","kind":"arxiv","version":2}},"canonical_sha256":"0620645b79527d0348304ac621742b6aa71e840226aec08d2d830c827a6732a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0620645b79527d0348304ac621742b6aa71e840226aec08d2d830c827a6732a8","first_computed_at":"2026-05-18T04:09:14.482617Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:14.482617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H6DXYLEQ/KL4Ah286k9a3lBRzlfmM4zJMAcr+zCG+qdpYmmLuoRmMYMtBw4QB7vGPsOsM+NxZ9ZJdpOtI4PmBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:14.483295Z","signed_message":"canonical_sha256_bytes"},"source_id":"0709.2831","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ce365f3a1f556dc1ea7599da8d1bdbcd3f45184151acbc003fd66ac08e8869c","sha256:179f182cc12f28265c73f49fa7f969e5197eb9413611b560855a4e970669894e"],"state_sha256":"9ad70ec9e0f2a2cef27f69d94a75bfcdc5912d7ff34ddc1e77491f78aa21f43c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ezQsixXoWtTmz1NDWocH8klVr3xFU9PJLswtnBEZv63z2AS91nWtd9OO19BNl80EJoXeq7C/DHXHK8h+CplbCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T11:45:49.394149Z","bundle_sha256":"7a4a7f9fb75f9fc4415f7d5c4782e80e5bf9923d59843b4f60e35e81e72b8527"}}