{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:EMTJI5LJ5OHJLSIAULPPJ2BQRN","short_pith_number":"pith:EMTJI5LJ","canonical_record":{"source":{"id":"astro-ph/0201198","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2002-01-12T20:33:41Z","cross_cats_sorted":[],"title_canon_sha256":"f912e720e370e76ab226120c93e4c51b1d272968a4c2c540f62f292c7109c45a","abstract_canon_sha256":"1786a7caf60f3d7c394e7effe92661ccbd5e265f161bcf7ad9863a8d1936c433"},"schema_version":"1.0"},"canonical_sha256":"2326947569eb8e95c900a2def4e8308b61a85cdf060a7b59532f907924ba2aa2","source":{"kind":"arxiv","id":"astro-ph/0201198","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0201198","created_at":"2026-07-04T16:29:14Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0201198v1","created_at":"2026-07-04T16:29:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0201198","created_at":"2026-07-04T16:29:14Z"},{"alias_kind":"pith_short_12","alias_value":"EMTJI5LJ5OHJ","created_at":"2026-07-04T16:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"EMTJI5LJ5OHJLSIA","created_at":"2026-07-04T16:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"EMTJI5LJ","created_at":"2026-07-04T16:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:EMTJI5LJ5OHJLSIAULPPJ2BQRN","target":"record","payload":{"canonical_record":{"source":{"id":"astro-ph/0201198","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2002-01-12T20:33:41Z","cross_cats_sorted":[],"title_canon_sha256":"f912e720e370e76ab226120c93e4c51b1d272968a4c2c540f62f292c7109c45a","abstract_canon_sha256":"1786a7caf60f3d7c394e7effe92661ccbd5e265f161bcf7ad9863a8d1936c433"},"schema_version":"1.0"},"canonical_sha256":"2326947569eb8e95c900a2def4e8308b61a85cdf060a7b59532f907924ba2aa2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:29:14.788169Z","signature_b64":"7zGAnvEpGCxA52eJyGThHX3jGB7p0savfNss8Ak4yKqu0jVRnR9CILYZpLHmQBTCZ3QgI/RKwMrnOcmA6Fj+CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2326947569eb8e95c900a2def4e8308b61a85cdf060a7b59532f907924ba2aa2","last_reissued_at":"2026-07-04T16:29:14.787801Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:29:14.787801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"astro-ph/0201198","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":"2026-07-04T16:29:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PxoUtC9Ezf95hFiJJ96OfIUfPuyozp+Uc55+Fe3VPdQF+t+gJSMr5ywNgNH/B7DXlCfIllq/fCM6C2/RaEv8Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T22:26:27.027343Z"},"content_sha256":"66d827149607ce2775c3a0a0cb148173b742013eb072d7b384cd679172e9e169","schema_version":"1.0","event_id":"sha256:66d827149607ce2775c3a0a0cb148173b742013eb072d7b384cd679172e9e169"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:EMTJI5LJ5OHJLSIAULPPJ2BQRN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Light Propagation in Inhomogeneous Universes. III. Distributions of Image Separations","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"Hugo Martel (University of Texas), Indonesia), Premana Premadi (Bandung Institute of Technology, Richard Matzner (University of Texas)","submitted_at":"2002-01-12T20:33:41Z","abstract_excerpt":"Using an analytical model, we compute the distribution of image separations resulting from gravitational lensing of distant sources, for 7 COBE-normalized CDM models with various combinations of Omega_0 and lambda_0. Our model assumes that multiple imaging results from strong lensing by individual galaxies. We model galaxies as nonsingular isothermal spheres, and take into account the finite angular size of the sources. Our model neglects the contribution of the background matter distribution, and assumes that lensing is entirely caused by galaxies. To test the validity of this assumption, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0201198","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/0201198/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":"2026-07-04T16:29:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eX8uJSnA6nHmz0MOUJBRgzileVjklTGRhbdWiROs7ZZ0CbQp7U7JdcucuykBQy3D+2cp28C/bDykH89fkqsjCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T22:26:27.027842Z"},"content_sha256":"b2aec93f2058dd5d52afc192d163a235f99b0a2ba32e219a8177eb211fc5a901","schema_version":"1.0","event_id":"sha256:b2aec93f2058dd5d52afc192d163a235f99b0a2ba32e219a8177eb211fc5a901"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EMTJI5LJ5OHJLSIAULPPJ2BQRN/bundle.json","state_url":"https://pith.science/pith/EMTJI5LJ5OHJLSIAULPPJ2BQRN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EMTJI5LJ5OHJLSIAULPPJ2BQRN/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":"2026-08-08T22:26:27Z","links":{"resolver":"https://pith.science/pith/EMTJI5LJ5OHJLSIAULPPJ2BQRN","bundle":"https://pith.science/pith/EMTJI5LJ5OHJLSIAULPPJ2BQRN/bundle.json","state":"https://pith.science/pith/EMTJI5LJ5OHJLSIAULPPJ2BQRN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EMTJI5LJ5OHJLSIAULPPJ2BQRN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:EMTJI5LJ5OHJLSIAULPPJ2BQRN","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":"1786a7caf60f3d7c394e7effe92661ccbd5e265f161bcf7ad9863a8d1936c433","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2002-01-12T20:33:41Z","title_canon_sha256":"f912e720e370e76ab226120c93e4c51b1d272968a4c2c540f62f292c7109c45a"},"schema_version":"1.0","source":{"id":"astro-ph/0201198","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0201198","created_at":"2026-07-04T16:29:14Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0201198v1","created_at":"2026-07-04T16:29:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0201198","created_at":"2026-07-04T16:29:14Z"},{"alias_kind":"pith_short_12","alias_value":"EMTJI5LJ5OHJ","created_at":"2026-07-04T16:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"EMTJI5LJ5OHJLSIA","created_at":"2026-07-04T16:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"EMTJI5LJ","created_at":"2026-07-04T16:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:b2aec93f2058dd5d52afc192d163a235f99b0a2ba32e219a8177eb211fc5a901","target":"graph","created_at":"2026-07-04T16:29:14Z","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/0201198/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Using an analytical model, we compute the distribution of image separations resulting from gravitational lensing of distant sources, for 7 COBE-normalized CDM models with various combinations of Omega_0 and lambda_0. Our model assumes that multiple imaging results from strong lensing by individual galaxies. We model galaxies as nonsingular isothermal spheres, and take into account the finite angular size of the sources. Our model neglects the contribution of the background matter distribution, and assumes that lensing is entirely caused by galaxies. To test the validity of this assumption, we ","authors_text":"Hugo Martel (University of Texas), Indonesia), Premana Premadi (Bandung Institute of Technology, Richard Matzner (University of Texas)","cross_cats":[],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2002-01-12T20:33:41Z","title":"Light Propagation in Inhomogeneous Universes. III. Distributions of Image Separations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0201198","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":"sha256:66d827149607ce2775c3a0a0cb148173b742013eb072d7b384cd679172e9e169","target":"record","created_at":"2026-07-04T16:29:14Z","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":"1786a7caf60f3d7c394e7effe92661ccbd5e265f161bcf7ad9863a8d1936c433","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2002-01-12T20:33:41Z","title_canon_sha256":"f912e720e370e76ab226120c93e4c51b1d272968a4c2c540f62f292c7109c45a"},"schema_version":"1.0","source":{"id":"astro-ph/0201198","kind":"arxiv","version":1}},"canonical_sha256":"2326947569eb8e95c900a2def4e8308b61a85cdf060a7b59532f907924ba2aa2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2326947569eb8e95c900a2def4e8308b61a85cdf060a7b59532f907924ba2aa2","first_computed_at":"2026-07-04T16:29:14.787801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:29:14.787801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7zGAnvEpGCxA52eJyGThHX3jGB7p0savfNss8Ak4yKqu0jVRnR9CILYZpLHmQBTCZ3QgI/RKwMrnOcmA6Fj+CQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:29:14.788169Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/0201198","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66d827149607ce2775c3a0a0cb148173b742013eb072d7b384cd679172e9e169","sha256:b2aec93f2058dd5d52afc192d163a235f99b0a2ba32e219a8177eb211fc5a901"],"state_sha256":"9cb3e176ebdfabccc4f8e29d5ba3ed33381f75a3be532a4b76fd68d2e9771542"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"srxZFjXL62PIO+R+tY6XPYoioaQJhRarIDQHT67LP8CDOqN0uWv02qjgyz8nEIsG4R6Zaz4Idq0Crn6h1TOeAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T22:26:27.031099Z","bundle_sha256":"36cc844e92897ff9bf6223cd97e1d8529aca45d3af155070795e954fadc78589"}}