{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RJCXAXFGE4FQC2FIEYJKS3TA4L","short_pith_number":"pith:RJCXAXFG","canonical_record":{"source":{"id":"1302.5352","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-21T17:46:39Z","cross_cats_sorted":[],"title_canon_sha256":"2b700836e8f062993c6f223296ca8eb2215ffc64996f95e424fce2c88f27f2fa","abstract_canon_sha256":"b439fc3e6622cd8b6fda267169bea04c8d9b557dc3dd954c7ab741cbb59fb62b"},"schema_version":"1.0"},"canonical_sha256":"8a45705ca6270b0168a82612a96e60e2dab84267c45ec1baf00cb2a1c8b80251","source":{"kind":"arxiv","id":"1302.5352","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5352","created_at":"2026-05-18T01:19:18Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5352v2","created_at":"2026-05-18T01:19:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5352","created_at":"2026-05-18T01:19:18Z"},{"alias_kind":"pith_short_12","alias_value":"RJCXAXFGE4FQ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RJCXAXFGE4FQC2FI","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RJCXAXFG","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RJCXAXFGE4FQC2FIEYJKS3TA4L","target":"record","payload":{"canonical_record":{"source":{"id":"1302.5352","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-21T17:46:39Z","cross_cats_sorted":[],"title_canon_sha256":"2b700836e8f062993c6f223296ca8eb2215ffc64996f95e424fce2c88f27f2fa","abstract_canon_sha256":"b439fc3e6622cd8b6fda267169bea04c8d9b557dc3dd954c7ab741cbb59fb62b"},"schema_version":"1.0"},"canonical_sha256":"8a45705ca6270b0168a82612a96e60e2dab84267c45ec1baf00cb2a1c8b80251","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:18.914891Z","signature_b64":"RDJ0e+b/qk8wTF/fyZ0qcu/+Hw/BunsZIqwWfcBRdmRJ8AL1DmK7uYGgYT4E8ommgnzA9E3zx9wktIblJG9EBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a45705ca6270b0168a82612a96e60e2dab84267c45ec1baf00cb2a1c8b80251","last_reissued_at":"2026-05-18T01:19:18.914444Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:18.914444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.5352","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":"2026-05-18T01:19:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qx6Jm2rQrT1CUjqNJZi0mOWEwkhcYueWT7fWJ5Goq8xFh7LhaZMHvM46aGrLI2nEZleMwwK3hrdUybDqN6PeCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:18:04.654810Z"},"content_sha256":"28504a43a55a1d1f125fc45be99ec6ae443f183b253a35c4a21e7a7bee37aff3","schema_version":"1.0","event_id":"sha256:28504a43a55a1d1f125fc45be99ec6ae443f183b253a35c4a21e7a7bee37aff3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RJCXAXFGE4FQC2FIEYJKS3TA4L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rectangular orbits of the curved 4-body problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Brendan Thorn, Florin Diacu","submitted_at":"2013-02-21T17:46:39Z","abstract_excerpt":"We consider the 4-body problem in spaces of constant curvature and study the existence of spherical and hyperbolic rectangular solutions, i.e. equiangular quadrilateral motions on spheres and hyperbolic spheres. We focus on relative equilibria (orbits that maintain constant mutual distances) and rotopulsators (configurations that rotate and change size, but preserve equiangularity). We prove that when such orbits exist, they are necessarily spherical or hyperbolic squares, i.e. equiangular equilateral quadrilaterals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5352","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":"2026-05-18T01:19:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S7yaP92Y+8wVg6Q3COkSR4jAoXpHME3KjGbI9RI0yEmxqfQQL7Xe/5blz8U1ihoMu/eO/eiWNTOCfzUMHp0eCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:18:04.655530Z"},"content_sha256":"d66242d9feb69a0eb1a6fd923e0eb9ca577a361769a3202daf91e81876482ec9","schema_version":"1.0","event_id":"sha256:d66242d9feb69a0eb1a6fd923e0eb9ca577a361769a3202daf91e81876482ec9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RJCXAXFGE4FQC2FIEYJKS3TA4L/bundle.json","state_url":"https://pith.science/pith/RJCXAXFGE4FQC2FIEYJKS3TA4L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RJCXAXFGE4FQC2FIEYJKS3TA4L/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":"2026-06-11T15:18:04Z","links":{"resolver":"https://pith.science/pith/RJCXAXFGE4FQC2FIEYJKS3TA4L","bundle":"https://pith.science/pith/RJCXAXFGE4FQC2FIEYJKS3TA4L/bundle.json","state":"https://pith.science/pith/RJCXAXFGE4FQC2FIEYJKS3TA4L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RJCXAXFGE4FQC2FIEYJKS3TA4L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RJCXAXFGE4FQC2FIEYJKS3TA4L","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":"b439fc3e6622cd8b6fda267169bea04c8d9b557dc3dd954c7ab741cbb59fb62b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-21T17:46:39Z","title_canon_sha256":"2b700836e8f062993c6f223296ca8eb2215ffc64996f95e424fce2c88f27f2fa"},"schema_version":"1.0","source":{"id":"1302.5352","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5352","created_at":"2026-05-18T01:19:18Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5352v2","created_at":"2026-05-18T01:19:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5352","created_at":"2026-05-18T01:19:18Z"},{"alias_kind":"pith_short_12","alias_value":"RJCXAXFGE4FQ","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RJCXAXFGE4FQC2FI","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RJCXAXFG","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:d66242d9feb69a0eb1a6fd923e0eb9ca577a361769a3202daf91e81876482ec9","target":"graph","created_at":"2026-05-18T01:19:18Z","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 4-body problem in spaces of constant curvature and study the existence of spherical and hyperbolic rectangular solutions, i.e. equiangular quadrilateral motions on spheres and hyperbolic spheres. We focus on relative equilibria (orbits that maintain constant mutual distances) and rotopulsators (configurations that rotate and change size, but preserve equiangularity). We prove that when such orbits exist, they are necessarily spherical or hyperbolic squares, i.e. equiangular equilateral quadrilaterals.","authors_text":"Brendan Thorn, Florin Diacu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-21T17:46:39Z","title":"Rectangular orbits of the curved 4-body problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5352","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":"sha256:28504a43a55a1d1f125fc45be99ec6ae443f183b253a35c4a21e7a7bee37aff3","target":"record","created_at":"2026-05-18T01:19:18Z","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":"b439fc3e6622cd8b6fda267169bea04c8d9b557dc3dd954c7ab741cbb59fb62b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-21T17:46:39Z","title_canon_sha256":"2b700836e8f062993c6f223296ca8eb2215ffc64996f95e424fce2c88f27f2fa"},"schema_version":"1.0","source":{"id":"1302.5352","kind":"arxiv","version":2}},"canonical_sha256":"8a45705ca6270b0168a82612a96e60e2dab84267c45ec1baf00cb2a1c8b80251","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a45705ca6270b0168a82612a96e60e2dab84267c45ec1baf00cb2a1c8b80251","first_computed_at":"2026-05-18T01:19:18.914444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:18.914444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RDJ0e+b/qk8wTF/fyZ0qcu/+Hw/BunsZIqwWfcBRdmRJ8AL1DmK7uYGgYT4E8ommgnzA9E3zx9wktIblJG9EBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:18.914891Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5352","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28504a43a55a1d1f125fc45be99ec6ae443f183b253a35c4a21e7a7bee37aff3","sha256:d66242d9feb69a0eb1a6fd923e0eb9ca577a361769a3202daf91e81876482ec9"],"state_sha256":"fbabb4a885a839867d7102d98a35d7dc31aee9dc3fe9c0cd8ee854f726fec08d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KSCPm6Czh1Fblbi75XkOGMmYK+oJXJr8BOZkeQqvyxt8H2wqplPu0QoRyomU8xN5QW50MHpQYW8jo1SLpqZvAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T15:18:04.659450Z","bundle_sha256":"72bdb898f272a7d03751042d44cab33418b80bb163edfe033484f2fa270c0c65"}}