{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IOMIAE5GGI4BRVT6SFBZMT6CJS","short_pith_number":"pith:IOMIAE5G","canonical_record":{"source":{"id":"1610.08654","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-27T08:21:45Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"faffe77946c52da0bebfd00aca375f91712718c13c50938a599f60e3ab47ef3e","abstract_canon_sha256":"2ad7e157b30e91d4d66d39e09fe620825685cb3f3270abc1592682c49eabcfe9"},"schema_version":"1.0"},"canonical_sha256":"43988013a6323818d67e9143964fc24c95af1d01bfb1f625d8ec95a6b2973343","source":{"kind":"arxiv","id":"1610.08654","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08654","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08654v1","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08654","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"pith_short_12","alias_value":"IOMIAE5GGI4B","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IOMIAE5GGI4BRVT6","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IOMIAE5G","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IOMIAE5GGI4BRVT6SFBZMT6CJS","target":"record","payload":{"canonical_record":{"source":{"id":"1610.08654","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-27T08:21:45Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"faffe77946c52da0bebfd00aca375f91712718c13c50938a599f60e3ab47ef3e","abstract_canon_sha256":"2ad7e157b30e91d4d66d39e09fe620825685cb3f3270abc1592682c49eabcfe9"},"schema_version":"1.0"},"canonical_sha256":"43988013a6323818d67e9143964fc24c95af1d01bfb1f625d8ec95a6b2973343","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:08.644750Z","signature_b64":"n/H7JUUsSAJWssj13aamCzD/QKlPQEynxToTRxs9NxmBSEt4kuDdOUuPHAwxAZAm0iFjt8XkFFJYqSRf9kyoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43988013a6323818d67e9143964fc24c95af1d01bfb1f625d8ec95a6b2973343","last_reissued_at":"2026-05-17T23:52:08.644363Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:08.644363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.08654","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tP629eHgZMuqs3BaO4mw8Siu2rOz2ThrnJa19wzk68aaoAb00d+cNkrad2xVzjYV6bmrDY9ZkfI/0eCcdneADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:15:49.021072Z"},"content_sha256":"468003cb8451ff35d506bb0601ec04c8d2e04042271a8fa875a6016dabf33311","schema_version":"1.0","event_id":"sha256:468003cb8451ff35d506bb0601ec04c8d2e04042271a8fa875a6016dabf33311"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IOMIAE5GGI4BRVT6SFBZMT6CJS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Four-Body Convex Central Configuration with Perpendicular Diagonals Is Necessarily a Kite","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Gareth E. Roberts, Josep M. Cors, Montserrat Corbera","submitted_at":"2016-10-27T08:21:45Z","abstract_excerpt":"We prove that any four-body convex central configuration with perpendicular diagonals must be a kite configuration. The result extends to general power-law potential functions, including the planar four-vortex problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08654","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":""},"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":"2026-05-17T23:52:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WaKCs0PCaaeIF7KuHdn64XXA0WyzlDJH3uRZLH3B3Qwc3vCouEl+G6PtJPpIuVburO6jpQRqPOvn5aq/C5/wCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:15:49.021941Z"},"content_sha256":"78a6f8b125f2e61eeeba09ef3b6e6daa3dedfd9f72583a8bab5a1d62ad1fb137","schema_version":"1.0","event_id":"sha256:78a6f8b125f2e61eeeba09ef3b6e6daa3dedfd9f72583a8bab5a1d62ad1fb137"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IOMIAE5GGI4BRVT6SFBZMT6CJS/bundle.json","state_url":"https://pith.science/pith/IOMIAE5GGI4BRVT6SFBZMT6CJS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IOMIAE5GGI4BRVT6SFBZMT6CJS/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":"2026-05-31T17:15:49Z","links":{"resolver":"https://pith.science/pith/IOMIAE5GGI4BRVT6SFBZMT6CJS","bundle":"https://pith.science/pith/IOMIAE5GGI4BRVT6SFBZMT6CJS/bundle.json","state":"https://pith.science/pith/IOMIAE5GGI4BRVT6SFBZMT6CJS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IOMIAE5GGI4BRVT6SFBZMT6CJS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IOMIAE5GGI4BRVT6SFBZMT6CJS","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":"2ad7e157b30e91d4d66d39e09fe620825685cb3f3270abc1592682c49eabcfe9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-27T08:21:45Z","title_canon_sha256":"faffe77946c52da0bebfd00aca375f91712718c13c50938a599f60e3ab47ef3e"},"schema_version":"1.0","source":{"id":"1610.08654","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08654","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08654v1","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08654","created_at":"2026-05-17T23:52:08Z"},{"alias_kind":"pith_short_12","alias_value":"IOMIAE5GGI4B","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IOMIAE5GGI4BRVT6","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IOMIAE5G","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:78a6f8b125f2e61eeeba09ef3b6e6daa3dedfd9f72583a8bab5a1d62ad1fb137","target":"graph","created_at":"2026-05-17T23:52:08Z","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 prove that any four-body convex central configuration with perpendicular diagonals must be a kite configuration. The result extends to general power-law potential functions, including the planar four-vortex problem.","authors_text":"Gareth E. Roberts, Josep M. Cors, Montserrat Corbera","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-27T08:21:45Z","title":"A Four-Body Convex Central Configuration with Perpendicular Diagonals Is Necessarily a Kite"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08654","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":"sha256:468003cb8451ff35d506bb0601ec04c8d2e04042271a8fa875a6016dabf33311","target":"record","created_at":"2026-05-17T23:52:08Z","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":"2ad7e157b30e91d4d66d39e09fe620825685cb3f3270abc1592682c49eabcfe9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-10-27T08:21:45Z","title_canon_sha256":"faffe77946c52da0bebfd00aca375f91712718c13c50938a599f60e3ab47ef3e"},"schema_version":"1.0","source":{"id":"1610.08654","kind":"arxiv","version":1}},"canonical_sha256":"43988013a6323818d67e9143964fc24c95af1d01bfb1f625d8ec95a6b2973343","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43988013a6323818d67e9143964fc24c95af1d01bfb1f625d8ec95a6b2973343","first_computed_at":"2026-05-17T23:52:08.644363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:08.644363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n/H7JUUsSAJWssj13aamCzD/QKlPQEynxToTRxs9NxmBSEt4kuDdOUuPHAwxAZAm0iFjt8XkFFJYqSRf9kyoBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:08.644750Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08654","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:468003cb8451ff35d506bb0601ec04c8d2e04042271a8fa875a6016dabf33311","sha256:78a6f8b125f2e61eeeba09ef3b6e6daa3dedfd9f72583a8bab5a1d62ad1fb137"],"state_sha256":"c9b9bce1f549bac36e651fca0b2cc1265ad932ff17b9ee23372d6f584dfb79ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BfPv6mlZITRVT2D1sGDwYs3ypc7D9tjrfGi/Q9nzME+wupBUjndHDsaV2rOXVVI23Mk8DJ58sTn5w2FH8fajCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T17:15:49.025604Z","bundle_sha256":"09651b947be5efc34fca1c722a2c7067fb9f6e1386e0359ccfc320bf19337ce5"}}