{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Z2SDTZ7DYKJEBYFDVNYT6ZW4WH","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":"a5b9b7618e2b439f64b7fd6738699681b2e48db3c7cfd681e360aad6dba4c12d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-04-02T11:33:39Z","title_canon_sha256":"09f8ac36af7c5fb05108ebd8b4305eb83cd7506ca7d3400df66616294481ec72"},"schema_version":"1.0","source":{"id":"1204.0372","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0372","created_at":"2026-05-18T03:58:49Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0372v1","created_at":"2026-05-18T03:58:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0372","created_at":"2026-05-18T03:58:49Z"},{"alias_kind":"pith_short_12","alias_value":"Z2SDTZ7DYKJE","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"Z2SDTZ7DYKJEBYFD","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"Z2SDTZ7D","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:da4b56eb2f3f6113a27079557a92d3e108d90ea6e6c03dd8741a43482c2b4543","target":"graph","created_at":"2026-05-18T03:58:49Z","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 investigate how observations of strong lensing can be used to infer cosmological parameters, in particular the equation of state of dark energy. We focus on the growth of the critical lines of lensing clusters with the source redshift as this behaviour depends on the distance-redshift relation and is therefore cosmologically sensitive. Purely analytical approaches are generally insufficient because they rely on axisymmetric mass distributions and thus cannot take irregular critical curves into account. We devise a numerical method based on the Metropolis-Hastings algorithm: an elliptical ge","authors_text":"Britta Zieser, Matthias Bartelmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-04-02T11:33:39Z","title":"Constraints on Cosmological Parameters from Strong Gravitational Lensing by Galaxy Clusters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0372","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":"sha256:4a8a837b784405d66baf96c980c0845b1c65f34b5c1e804052404d8629eae04e","target":"record","created_at":"2026-05-18T03:58:49Z","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":"a5b9b7618e2b439f64b7fd6738699681b2e48db3c7cfd681e360aad6dba4c12d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-04-02T11:33:39Z","title_canon_sha256":"09f8ac36af7c5fb05108ebd8b4305eb83cd7506ca7d3400df66616294481ec72"},"schema_version":"1.0","source":{"id":"1204.0372","kind":"arxiv","version":1}},"canonical_sha256":"cea439e7e3c29240e0a3ab713f66dcb1f16729282a31a284655a2dd51e4389ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cea439e7e3c29240e0a3ab713f66dcb1f16729282a31a284655a2dd51e4389ff","first_computed_at":"2026-05-18T03:58:49.473738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:49.473738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y+qt+GhacW1impYKsJauPEqVTG/7F27goGu/eN37kHINozQyOBb7CuTF74XrmHVxTLYFRsuE3IRVYGaN8JqwBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:49.474610Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.0372","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a8a837b784405d66baf96c980c0845b1c65f34b5c1e804052404d8629eae04e","sha256:da4b56eb2f3f6113a27079557a92d3e108d90ea6e6c03dd8741a43482c2b4543"],"state_sha256":"93d137831a0fcd534f97a37478473a6450c002e22f677a8adb2db864c7f660b0"}