{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:63MS3JY6D4JVRU7VLD2EYH3QZG","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":"5b3c270fd01ae5716159cd0d14d06539aab8495d681ea3b5411851ca05614dd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-03-16T16:07:18Z","title_canon_sha256":"dc4bf3cd89d86c94c886c3c6dab22ef43d197f7001a6194ce6a61bcd53334be5"},"schema_version":"1.0","source":{"id":"1903.06951","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.06951","created_at":"2026-05-17T23:43:02Z"},{"alias_kind":"arxiv_version","alias_value":"1903.06951v1","created_at":"2026-05-17T23:43:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06951","created_at":"2026-05-17T23:43:02Z"},{"alias_kind":"pith_short_12","alias_value":"63MS3JY6D4JV","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"63MS3JY6D4JVRU7V","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"63MS3JY6","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:4725abd42dab2badc035769cd8770b7ab75dfa4909ca0e695ce7adcc00302914","target":"graph","created_at":"2026-05-17T23:43:02Z","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 study the weak-field deflection of light by mass distributions described by two-power-law densities $\\rho(R)=\\rho_0 R^{-\\alpha}(R+1)^{\\beta-\\alpha}$, where $\\alpha$ and $\\beta$ are non-negative integers. New analytic expressions of deflection angles are obtained via the application of the Gauss-Bonnet theorem to a chosen surface on the optical manifold. Some of the well-known models of this two-power law form are the Navarro-Frenk-White (NFW) model $(\\alpha,\\beta)=(1,3)$, Hernquist $(1,4)$, Jaffe $(2,4)$, and the singular isothermal sphere $(2,2)$. The calculated deflection angles for Hernq","authors_text":"Ian Vega, Karlo de Leon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-03-16T16:07:18Z","title":"Weak gravitational lensing by two-power-law densities using the Gauss-Bonnet theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06951","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":"sha256:8ef48ef4bedb081d57ddc9048c10e1b165a73f9d8e1079670a39bb93ba5f4370","target":"record","created_at":"2026-05-17T23:43:02Z","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":"5b3c270fd01ae5716159cd0d14d06539aab8495d681ea3b5411851ca05614dd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2019-03-16T16:07:18Z","title_canon_sha256":"dc4bf3cd89d86c94c886c3c6dab22ef43d197f7001a6194ce6a61bcd53334be5"},"schema_version":"1.0","source":{"id":"1903.06951","kind":"arxiv","version":1}},"canonical_sha256":"f6d92da71e1f1358d3f558f44c1f70c9934b17be67a80600dd5be97290aae8f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6d92da71e1f1358d3f558f44c1f70c9934b17be67a80600dd5be97290aae8f5","first_computed_at":"2026-05-17T23:43:02.927583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:02.927583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LK4SAuH9m2/7G0Ayc8hY5dFug0COZFCd580hTO5iQXkLB09GC0CYJKT72aEYTF4aDKBCXzKrvhuV4KFfdz33Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:02.928114Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.06951","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ef48ef4bedb081d57ddc9048c10e1b165a73f9d8e1079670a39bb93ba5f4370","sha256:4725abd42dab2badc035769cd8770b7ab75dfa4909ca0e695ce7adcc00302914"],"state_sha256":"0823caa42fa32a8f3b2876a39f85b7670df5b7a5dc8f82530abf00a74437019f"}