{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:BBGDTBUMSC7773SHUCPHC22BR4","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":"33f7070a4cfcfe513deae90cea86689e012ffe92b5f231fd4626eecda8457b35","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2007-12-14T23:06:14Z","title_canon_sha256":"8cdf78f7bdbd90d1b81fbef5e6e58dbf6f3697ef1bbd5deae2124a3c598ebfc6"},"schema_version":"1.0","source":{"id":"0712.2809","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.2809","created_at":"2026-05-18T02:35:24Z"},{"alias_kind":"arxiv_version","alias_value":"0712.2809v1","created_at":"2026-05-18T02:35:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.2809","created_at":"2026-05-18T02:35:24Z"},{"alias_kind":"pith_short_12","alias_value":"BBGDTBUMSC77","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"BBGDTBUMSC7773SH","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"BBGDTBUM","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:9f9d41329bb4118e2c78e6499d45d5ce44dd6c72ca8fd3ef1bc351b540213d34","target":"graph","created_at":"2026-05-18T02:35:24Z","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":"Concordance cosmology points to a Universe of zero mean curvature, due to the inflation mechanism which occurred soon after the Big Bang, while along a relatively small number of lower redshift light paths where lensing events are observed, space is positively curved. How do we know that global geometry and topology are robust rather than in a state of chaos? The phenomenon of cosmic shear provides an effective way of mapping curvature fluctuations, because it affects {\\it any} light rays whether they intercept mass clumps or not. We discuss a range of astrophysical applications of the princip","authors_text":"Richard Lieu","cross_cats":[],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2007-12-14T23:06:14Z","title":"On the absence of shear from perfect Einstein rings and the stability of geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.2809","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":"sha256:68177a05fc7971c94fe835ce673cba5ef30ef45d3d37302ae99d759113cefdb9","target":"record","created_at":"2026-05-18T02:35:24Z","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":"33f7070a4cfcfe513deae90cea86689e012ffe92b5f231fd4626eecda8457b35","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2007-12-14T23:06:14Z","title_canon_sha256":"8cdf78f7bdbd90d1b81fbef5e6e58dbf6f3697ef1bbd5deae2124a3c598ebfc6"},"schema_version":"1.0","source":{"id":"0712.2809","kind":"arxiv","version":1}},"canonical_sha256":"084c39868c90bfffee47a09e716b418f293f28fa7564779e6b3a0812b1277d03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"084c39868c90bfffee47a09e716b418f293f28fa7564779e6b3a0812b1277d03","first_computed_at":"2026-05-18T02:35:24.055065Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:35:24.055065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vu3Xz/PAZesbXYr2m8MmpcIkbc2dgKiDjlIgVeifjtsiJECA1qMlJL1u9CzKhGb4d3Dmzgbs8gOqA4yn/5+uBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:35:24.055539Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.2809","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68177a05fc7971c94fe835ce673cba5ef30ef45d3d37302ae99d759113cefdb9","sha256:9f9d41329bb4118e2c78e6499d45d5ce44dd6c72ca8fd3ef1bc351b540213d34"],"state_sha256":"ba892fb89052bfb665a22c314d413c36bf1ef4ca3f16aa7133a24f1d8188e223"}