{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2U5C2GSKABGO77ZZRJRIWTFFP4","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":"b8cc6f3c06bd0a5fd880f24d786da217cea86d9c6c6594cabed32a7985df3854","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-27T22:53:25Z","title_canon_sha256":"9fd0fa70ee8f86fde84dfd29cf72b9bd044e82b494bb49ebd29e79ee4362d7e0"},"schema_version":"1.0","source":{"id":"1604.08262","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.08262","created_at":"2026-05-18T01:16:04Z"},{"alias_kind":"arxiv_version","alias_value":"1604.08262v1","created_at":"2026-05-18T01:16:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08262","created_at":"2026-05-18T01:16:04Z"},{"alias_kind":"pith_short_12","alias_value":"2U5C2GSKABGO","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2U5C2GSKABGO77ZZ","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2U5C2GSK","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:c2b2d870385d55aea672ccb395b5afae450d5dd142d37b1c1c35e02967174963","target":"graph","created_at":"2026-05-18T01:16:04Z","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":"This paper is a study of the so-called `ricochet configuration' (or $R$-configuration) which arises in the context of Pascal's theorem. We give a geometric proof of the fact that a specific pair of Pascal lines is coincident for a sextuple in $R$-configuration. We calculate the symmetry group of a generic $R$-configuration, as well as the degree of the subvariety ${\\mathcal R} \\subseteq {\\mathbb P}^6$ of all such configurations. We also determine the $SL(2)$-equivariant defining equations for ${\\mathcal R}$, and show that it is an ideal-theoretic complete intersection of two invariant hypersur","authors_text":"Jaydeep Chipalkatti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-27T22:53:25Z","title":"On the geometry of the ricochet locus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08262","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:db19d8e4f585a61f695747a67fd9204f80a686933e7f922e5def14591aae0a96","target":"record","created_at":"2026-05-18T01:16:04Z","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":"b8cc6f3c06bd0a5fd880f24d786da217cea86d9c6c6594cabed32a7985df3854","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-27T22:53:25Z","title_canon_sha256":"9fd0fa70ee8f86fde84dfd29cf72b9bd044e82b494bb49ebd29e79ee4362d7e0"},"schema_version":"1.0","source":{"id":"1604.08262","kind":"arxiv","version":1}},"canonical_sha256":"d53a2d1a4a004cefff398a628b4ca57f2a3dbe253fc64545038d608433632725","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d53a2d1a4a004cefff398a628b4ca57f2a3dbe253fc64545038d608433632725","first_computed_at":"2026-05-18T01:16:04.429157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:04.429157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ho6jN/GsykLrESYp1hHyqfUqR6t9DYzFZQL20LI8bd9lcfVDto4ghkbDK3L5aHGyak2rPgKUZSySYD+AfGdABA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:04.429835Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.08262","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db19d8e4f585a61f695747a67fd9204f80a686933e7f922e5def14591aae0a96","sha256:c2b2d870385d55aea672ccb395b5afae450d5dd142d37b1c1c35e02967174963"],"state_sha256":"714d0b9e49317c3fae8587833999dd09d2e340597582b637b1d8a215ee6f76cd"}