{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:TGRNMKDKUBZUDXWTCB5XU7JWX4","short_pith_number":"pith:TGRNMKDK","canonical_record":{"source":{"id":"astro-ph/9908213","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"1999-08-19T13:16:51Z","cross_cats_sorted":[],"title_canon_sha256":"dab93dad2c11bc52eff8a9d862ce4c1abaa0aa3cd36c6196e172863ff9e71a8a","abstract_canon_sha256":"56fd93d99a700a2189fbd7737ce4788532acf7219e29f22f5fecc278bb6c9ada"},"schema_version":"1.0"},"canonical_sha256":"99a2d6286aa07341ded3107b7a7d36bf204c3fe0a27610efc6ad37485d2a4040","source":{"kind":"arxiv","id":"astro-ph/9908213","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/9908213","created_at":"2026-07-04T14:17:03Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/9908213v1","created_at":"2026-07-04T14:17:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/9908213","created_at":"2026-07-04T14:17:03Z"},{"alias_kind":"pith_short_12","alias_value":"TGRNMKDKUBZU","created_at":"2026-07-04T14:17:03Z"},{"alias_kind":"pith_short_16","alias_value":"TGRNMKDKUBZUDXWT","created_at":"2026-07-04T14:17:03Z"},{"alias_kind":"pith_short_8","alias_value":"TGRNMKDK","created_at":"2026-07-04T14:17:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:TGRNMKDKUBZUDXWTCB5XU7JWX4","target":"record","payload":{"canonical_record":{"source":{"id":"astro-ph/9908213","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"1999-08-19T13:16:51Z","cross_cats_sorted":[],"title_canon_sha256":"dab93dad2c11bc52eff8a9d862ce4c1abaa0aa3cd36c6196e172863ff9e71a8a","abstract_canon_sha256":"56fd93d99a700a2189fbd7737ce4788532acf7219e29f22f5fecc278bb6c9ada"},"schema_version":"1.0"},"canonical_sha256":"99a2d6286aa07341ded3107b7a7d36bf204c3fe0a27610efc6ad37485d2a4040","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:17:03.227563Z","signature_b64":"yS2PccQOu3MBwGzC7JvGcFneMF5YFe3LJTJCi6kIiMzrlXKV9X/uJ0bmSO/SH95QGJoiobgN+/rbxUuYM4kTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99a2d6286aa07341ded3107b7a7d36bf204c3fe0a27610efc6ad37485d2a4040","last_reissued_at":"2026-07-04T14:17:03.227079Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:17:03.227079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"astro-ph/9908213","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":"2026-07-04T14:17:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U2mPG/8QZOEvMfr1I71Ibu+NSl9CdRGDUmiFvVh+dB9Y+cmVnNv/pKmrk1nIkVzMNSDvscHsE3Mm2/Pdw4HtCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T06:57:16.011480Z"},"content_sha256":"eccb89190a1d7ebf6a06c211180f625234d6b0c3fd8126041099e7a29c05a5f4","schema_version":"1.0","event_id":"sha256:eccb89190a1d7ebf6a06c211180f625234d6b0c3fd8126041099e7a29c05a5f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:TGRNMKDKUBZUDXWTCB5XU7JWX4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gravitational Lensing by NFW Halos","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"Candace Oaxaca Wright & Tereasa G. Brainerd","submitted_at":"1999-08-19T13:16:51Z","abstract_excerpt":"We investigate the gravitational lensing properties of dark matter halos with Navarro, Frenk & White (NFW) density profiles and derive an analytic expression for the radial dependence of the shear, $\\gamma(x)$, due to these objects. In addition, we derive an expression for the mean shear interior to a given radius, $\\bar{\\gamma}(x)$, and use this to quantify systematic errors that will arise in weak lensing mass estimates of astronomical objects in the case that the mass estimate is based on an a priori assumption that the underlying potential is that of a singular isothermal sphere when, in f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/9908213","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/astro-ph/9908213/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:17:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M13VNFeUdO3mA9yk4ULOT+b0MbowaJhtuTVxHbnVOTHaAIHJNVTbwHrSSpmbt7GnrmIYgl/Ff/91lz4VnMj6Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T06:57:16.012087Z"},"content_sha256":"2e2625dd606553fe74c1891ec17b667fca32cea0ae690ae5161005e9cc5b8976","schema_version":"1.0","event_id":"sha256:2e2625dd606553fe74c1891ec17b667fca32cea0ae690ae5161005e9cc5b8976"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TGRNMKDKUBZUDXWTCB5XU7JWX4/bundle.json","state_url":"https://pith.science/pith/TGRNMKDKUBZUDXWTCB5XU7JWX4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TGRNMKDKUBZUDXWTCB5XU7JWX4/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":"2026-08-04T06:57:16Z","links":{"resolver":"https://pith.science/pith/TGRNMKDKUBZUDXWTCB5XU7JWX4","bundle":"https://pith.science/pith/TGRNMKDKUBZUDXWTCB5XU7JWX4/bundle.json","state":"https://pith.science/pith/TGRNMKDKUBZUDXWTCB5XU7JWX4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TGRNMKDKUBZUDXWTCB5XU7JWX4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:TGRNMKDKUBZUDXWTCB5XU7JWX4","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":"56fd93d99a700a2189fbd7737ce4788532acf7219e29f22f5fecc278bb6c9ada","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"1999-08-19T13:16:51Z","title_canon_sha256":"dab93dad2c11bc52eff8a9d862ce4c1abaa0aa3cd36c6196e172863ff9e71a8a"},"schema_version":"1.0","source":{"id":"astro-ph/9908213","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/9908213","created_at":"2026-07-04T14:17:03Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/9908213v1","created_at":"2026-07-04T14:17:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/9908213","created_at":"2026-07-04T14:17:03Z"},{"alias_kind":"pith_short_12","alias_value":"TGRNMKDKUBZU","created_at":"2026-07-04T14:17:03Z"},{"alias_kind":"pith_short_16","alias_value":"TGRNMKDKUBZUDXWT","created_at":"2026-07-04T14:17:03Z"},{"alias_kind":"pith_short_8","alias_value":"TGRNMKDK","created_at":"2026-07-04T14:17:03Z"}],"graph_snapshots":[{"event_id":"sha256:2e2625dd606553fe74c1891ec17b667fca32cea0ae690ae5161005e9cc5b8976","target":"graph","created_at":"2026-07-04T14:17:03Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/astro-ph/9908213/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the gravitational lensing properties of dark matter halos with Navarro, Frenk & White (NFW) density profiles and derive an analytic expression for the radial dependence of the shear, $\\gamma(x)$, due to these objects. In addition, we derive an expression for the mean shear interior to a given radius, $\\bar{\\gamma}(x)$, and use this to quantify systematic errors that will arise in weak lensing mass estimates of astronomical objects in the case that the mass estimate is based on an a priori assumption that the underlying potential is that of a singular isothermal sphere when, in f","authors_text":"Candace Oaxaca Wright & Tereasa G. Brainerd","cross_cats":[],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"1999-08-19T13:16:51Z","title":"Gravitational Lensing by NFW Halos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/9908213","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:eccb89190a1d7ebf6a06c211180f625234d6b0c3fd8126041099e7a29c05a5f4","target":"record","created_at":"2026-07-04T14:17:03Z","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":"56fd93d99a700a2189fbd7737ce4788532acf7219e29f22f5fecc278bb6c9ada","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"1999-08-19T13:16:51Z","title_canon_sha256":"dab93dad2c11bc52eff8a9d862ce4c1abaa0aa3cd36c6196e172863ff9e71a8a"},"schema_version":"1.0","source":{"id":"astro-ph/9908213","kind":"arxiv","version":1}},"canonical_sha256":"99a2d6286aa07341ded3107b7a7d36bf204c3fe0a27610efc6ad37485d2a4040","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99a2d6286aa07341ded3107b7a7d36bf204c3fe0a27610efc6ad37485d2a4040","first_computed_at":"2026-07-04T14:17:03.227079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:17:03.227079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yS2PccQOu3MBwGzC7JvGcFneMF5YFe3LJTJCi6kIiMzrlXKV9X/uJ0bmSO/SH95QGJoiobgN+/rbxUuYM4kTDg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:17:03.227563Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/9908213","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eccb89190a1d7ebf6a06c211180f625234d6b0c3fd8126041099e7a29c05a5f4","sha256:2e2625dd606553fe74c1891ec17b667fca32cea0ae690ae5161005e9cc5b8976"],"state_sha256":"b98eb3ac3225044aab1b7d0911f9c2dbad23cdfb0821e46ebf045863712149e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ecnLfvUXYRVQjbPMWJ1IUR93rmh8jvxvBwJNVcMoqIHpsicmi8KldbB3/tXNksrVlTeXL4yUJShl+262wUFAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T06:57:16.017498Z","bundle_sha256":"df65858bdc2785c50f40d2a05c08e947eeb027b4fef27d6bb2029ae43b814505"}}