{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:YIAD6OWWFQVQMDZXKJBV5OHSO5","short_pith_number":"pith:YIAD6OWW","canonical_record":{"source":{"id":"0811.0441","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-11-04T07:54:13Z","cross_cats_sorted":[],"title_canon_sha256":"6735e4973b6c39a74aa90cf02e1647b6894e98ed64c33a3ffb93b07ff24a7f79","abstract_canon_sha256":"bc20675aa2f932500f5383241aa118824edfca44d57f8cc3a7e69850cf4ff849"},"schema_version":"1.0"},"canonical_sha256":"c2003f3ad62c2b060f3752435eb8f2775cdda5b8a41a5ab518fbcfd9c49b3bd9","source":{"kind":"arxiv","id":"0811.0441","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.0441","created_at":"2026-07-04T15:15:43Z"},{"alias_kind":"arxiv_version","alias_value":"0811.0441v1","created_at":"2026-07-04T15:15:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.0441","created_at":"2026-07-04T15:15:43Z"},{"alias_kind":"pith_short_12","alias_value":"YIAD6OWWFQVQ","created_at":"2026-07-04T15:15:43Z"},{"alias_kind":"pith_short_16","alias_value":"YIAD6OWWFQVQMDZX","created_at":"2026-07-04T15:15:43Z"},{"alias_kind":"pith_short_8","alias_value":"YIAD6OWW","created_at":"2026-07-04T15:15:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:YIAD6OWWFQVQMDZXKJBV5OHSO5","target":"record","payload":{"canonical_record":{"source":{"id":"0811.0441","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-11-04T07:54:13Z","cross_cats_sorted":[],"title_canon_sha256":"6735e4973b6c39a74aa90cf02e1647b6894e98ed64c33a3ffb93b07ff24a7f79","abstract_canon_sha256":"bc20675aa2f932500f5383241aa118824edfca44d57f8cc3a7e69850cf4ff849"},"schema_version":"1.0"},"canonical_sha256":"c2003f3ad62c2b060f3752435eb8f2775cdda5b8a41a5ab518fbcfd9c49b3bd9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:15:43.902029Z","signature_b64":"fvEAcahAwTWGLtmq9A4h7zBPgA8lwKsGowz8SZjLUJhkUPWD4ZBt1Ys84+hW+fWTQsDtW7xwh8Nhxz7V8S5ACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2003f3ad62c2b060f3752435eb8f2775cdda5b8a41a5ab518fbcfd9c49b3bd9","last_reissued_at":"2026-07-04T15:15:43.901575Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:15:43.901575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0811.0441","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":"2026-07-04T15:15:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pvi15FEsPOAYq5ZjF9Kq/sk8JCsVKe/3JfQNjsnUrr7MlAowKInmxazPqWizzEX/sjI0m/Jatzd9TloGng8yDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T18:36:56.519390Z"},"content_sha256":"428134c16751a916489aa9c8bc27a9696c3ce95f33ea66ac6d646c6b1f71ab57","schema_version":"1.0","event_id":"sha256:428134c16751a916489aa9c8bc27a9696c3ce95f33ea66ac6d646c6b1f71ab57"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:YIAD6OWWFQVQMDZXKJBV5OHSO5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Introduction to Gravitational Microlensing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"Shude Mao","submitted_at":"2008-11-04T07:54:13Z","abstract_excerpt":"The basic concepts of gravitational microlensing are introduced. We start with the lens equation, and then derive the image positions and magnifications. The statistical quantities of optical depth and event rate are then described. We finish with a summary and a list of challenges and open questions. A problem set is given for students to practice."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.0441","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/0811.0441/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":"2026-07-04T15:15:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UG8GuVASTKtTY6oevHrhyDg7iVw6ht/fcyokeN0c1Y2vhJ4eLkeDzm9Ve5gwss9IPu5qxbNFSBgS9L+Zx7YgCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T18:36:56.519893Z"},"content_sha256":"9b3508498ad03e2e75cecb1fb59a665448d700ab328755ebb6fb81f5293f97fc","schema_version":"1.0","event_id":"sha256:9b3508498ad03e2e75cecb1fb59a665448d700ab328755ebb6fb81f5293f97fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YIAD6OWWFQVQMDZXKJBV5OHSO5/bundle.json","state_url":"https://pith.science/pith/YIAD6OWWFQVQMDZXKJBV5OHSO5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YIAD6OWWFQVQMDZXKJBV5OHSO5/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":"2026-08-07T18:36:56Z","links":{"resolver":"https://pith.science/pith/YIAD6OWWFQVQMDZXKJBV5OHSO5","bundle":"https://pith.science/pith/YIAD6OWWFQVQMDZXKJBV5OHSO5/bundle.json","state":"https://pith.science/pith/YIAD6OWWFQVQMDZXKJBV5OHSO5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YIAD6OWWFQVQMDZXKJBV5OHSO5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:YIAD6OWWFQVQMDZXKJBV5OHSO5","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":"bc20675aa2f932500f5383241aa118824edfca44d57f8cc3a7e69850cf4ff849","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-11-04T07:54:13Z","title_canon_sha256":"6735e4973b6c39a74aa90cf02e1647b6894e98ed64c33a3ffb93b07ff24a7f79"},"schema_version":"1.0","source":{"id":"0811.0441","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.0441","created_at":"2026-07-04T15:15:43Z"},{"alias_kind":"arxiv_version","alias_value":"0811.0441v1","created_at":"2026-07-04T15:15:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.0441","created_at":"2026-07-04T15:15:43Z"},{"alias_kind":"pith_short_12","alias_value":"YIAD6OWWFQVQ","created_at":"2026-07-04T15:15:43Z"},{"alias_kind":"pith_short_16","alias_value":"YIAD6OWWFQVQMDZX","created_at":"2026-07-04T15:15:43Z"},{"alias_kind":"pith_short_8","alias_value":"YIAD6OWW","created_at":"2026-07-04T15:15:43Z"}],"graph_snapshots":[{"event_id":"sha256:9b3508498ad03e2e75cecb1fb59a665448d700ab328755ebb6fb81f5293f97fc","target":"graph","created_at":"2026-07-04T15:15:43Z","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/0811.0441/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The basic concepts of gravitational microlensing are introduced. We start with the lens equation, and then derive the image positions and magnifications. The statistical quantities of optical depth and event rate are then described. We finish with a summary and a list of challenges and open questions. A problem set is given for students to practice.","authors_text":"Shude Mao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-11-04T07:54:13Z","title":"Introduction to Gravitational Microlensing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.0441","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":"sha256:428134c16751a916489aa9c8bc27a9696c3ce95f33ea66ac6d646c6b1f71ab57","target":"record","created_at":"2026-07-04T15:15:43Z","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":"bc20675aa2f932500f5383241aa118824edfca44d57f8cc3a7e69850cf4ff849","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph","submitted_at":"2008-11-04T07:54:13Z","title_canon_sha256":"6735e4973b6c39a74aa90cf02e1647b6894e98ed64c33a3ffb93b07ff24a7f79"},"schema_version":"1.0","source":{"id":"0811.0441","kind":"arxiv","version":1}},"canonical_sha256":"c2003f3ad62c2b060f3752435eb8f2775cdda5b8a41a5ab518fbcfd9c49b3bd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2003f3ad62c2b060f3752435eb8f2775cdda5b8a41a5ab518fbcfd9c49b3bd9","first_computed_at":"2026-07-04T15:15:43.901575Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:15:43.901575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fvEAcahAwTWGLtmq9A4h7zBPgA8lwKsGowz8SZjLUJhkUPWD4ZBt1Ys84+hW+fWTQsDtW7xwh8Nhxz7V8S5ACA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:15:43.902029Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.0441","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:428134c16751a916489aa9c8bc27a9696c3ce95f33ea66ac6d646c6b1f71ab57","sha256:9b3508498ad03e2e75cecb1fb59a665448d700ab328755ebb6fb81f5293f97fc"],"state_sha256":"c316c6d3d21022f55f51fb08cdf09f3689c6139d071ec1e1f623947aa183a8b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IvxhiZdpWDehkP65P0zWzh5N3lfd0t484DJFDBNdDIdNIrJluKLoLloKGcjrNzaQi3GD3B2INJ6Y9FIzZg7YAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T18:36:56.524252Z","bundle_sha256":"68f072b35c7499b7c7b0c752acf5ac0ca187ada6c41d2f67a2803c70d3e034fe"}}