{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1996:QZ5YJZI2WKXY2EPOU4JZWJJ75B","short_pith_number":"pith:QZ5YJZI2","canonical_record":{"source":{"id":"astro-ph/9610121","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"1996-10-16T06:19:29Z","cross_cats_sorted":[],"title_canon_sha256":"0a269b899693e7851aa8427ae249d393bb31e4858547030f0eb02f2ac9827062","abstract_canon_sha256":"1e33f3803d16722f1f44ebf526226609b14500dc5d502b89c29240537a7d38f7"},"schema_version":"1.0"},"canonical_sha256":"867b84e51ab2af8d11eea7139b253fe879edcb6634f248981a7c2be12f8b548d","source":{"kind":"arxiv","id":"astro-ph/9610121","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/9610121","created_at":"2026-07-04T16:00:16Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/9610121v1","created_at":"2026-07-04T16:00:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/9610121","created_at":"2026-07-04T16:00:16Z"},{"alias_kind":"pith_short_12","alias_value":"QZ5YJZI2WKXY","created_at":"2026-07-04T16:00:16Z"},{"alias_kind":"pith_short_16","alias_value":"QZ5YJZI2WKXY2EPO","created_at":"2026-07-04T16:00:16Z"},{"alias_kind":"pith_short_8","alias_value":"QZ5YJZI2","created_at":"2026-07-04T16:00:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1996:QZ5YJZI2WKXY2EPOU4JZWJJ75B","target":"record","payload":{"canonical_record":{"source":{"id":"astro-ph/9610121","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"1996-10-16T06:19:29Z","cross_cats_sorted":[],"title_canon_sha256":"0a269b899693e7851aa8427ae249d393bb31e4858547030f0eb02f2ac9827062","abstract_canon_sha256":"1e33f3803d16722f1f44ebf526226609b14500dc5d502b89c29240537a7d38f7"},"schema_version":"1.0"},"canonical_sha256":"867b84e51ab2af8d11eea7139b253fe879edcb6634f248981a7c2be12f8b548d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:00:16.734459Z","signature_b64":"dP7rLH6Sksj6VGhgyQuDtf1uebK7P7kkLxVAqjLpRcpeExaPdCK+91pCMCEHIOSe3HAuH7bnPaZ8tqob8MqWAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"867b84e51ab2af8d11eea7139b253fe879edcb6634f248981a7c2be12f8b548d","last_reissued_at":"2026-07-04T16:00:16.734059Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:00:16.734059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"astro-ph/9610121","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":"2026-07-04T16:00:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eYxjDe9tuj4tOfz6FHVFmERizGpZe8TEZ55trYn+6A5GbvNpH5pfG//8nog9YTpIF2p8BOGkIiHQV4NRtdShCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T00:34:16.135145Z"},"content_sha256":"ca21895cb7f0774ab92b76286441d38d27221a56fc6cf6b8346aa29881c61638","schema_version":"1.0","event_id":"sha256:ca21895cb7f0774ab92b76286441d38d27221a56fc6cf6b8346aa29881c61638"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1996:QZ5YJZI2WKXY2EPOU4JZWJJ75B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Minimum Total Mass of MACHOs and Halo Models of the Galaxy","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"R. Nishi, T. Nakamura, Y. Kan-ya","submitted_at":"1996-10-16T06:19:29Z","abstract_excerpt":"If the density distribution \\rho (r) of MACHOs is spherically symmetric with respect to the Galactic center, it is shown that the minimal total mass M_{min}^{{ MACHO}} of the MACHOs is 1.7\\times 10^{10}\\sol \\tau_{-6.7}^{{ LMC}} where \\tau_{-6.7}^{{ LMC}} is the optical depth (\\tau^{{ LMC}}) toward the Large Magellanic Cloud (LMC) in the unit of 2\\times 10^{-7}. If \\rho (r) is a decreasing function of r, it is proved that M_{min}^{{ MACHO}} is 5.6\\times 10^{10}\\sol \\tau_{-6.7}^{{ LMC}}. Several spherical and axially symmetric halo models of the Galaxy with a few free parameters are also conside"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/9610121","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/9610121/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":"2026-07-04T16:00:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iYYPMG3z6kGcv2Ox6NqXYPnSCTkmYUo8kItZjkgpLcfZzVw6LtGfnx+ILN4tJb6WwlKInTdp3w1yBZi0pNdTBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T00:34:16.135641Z"},"content_sha256":"9d17149dc9bda1c1d7d23b90b6631a8b5a5889e0444e5027742f50067614f49e","schema_version":"1.0","event_id":"sha256:9d17149dc9bda1c1d7d23b90b6631a8b5a5889e0444e5027742f50067614f49e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QZ5YJZI2WKXY2EPOU4JZWJJ75B/bundle.json","state_url":"https://pith.science/pith/QZ5YJZI2WKXY2EPOU4JZWJJ75B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QZ5YJZI2WKXY2EPOU4JZWJJ75B/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":"2026-08-05T00:34:16Z","links":{"resolver":"https://pith.science/pith/QZ5YJZI2WKXY2EPOU4JZWJJ75B","bundle":"https://pith.science/pith/QZ5YJZI2WKXY2EPOU4JZWJJ75B/bundle.json","state":"https://pith.science/pith/QZ5YJZI2WKXY2EPOU4JZWJJ75B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QZ5YJZI2WKXY2EPOU4JZWJJ75B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:QZ5YJZI2WKXY2EPOU4JZWJJ75B","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":"1e33f3803d16722f1f44ebf526226609b14500dc5d502b89c29240537a7d38f7","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"1996-10-16T06:19:29Z","title_canon_sha256":"0a269b899693e7851aa8427ae249d393bb31e4858547030f0eb02f2ac9827062"},"schema_version":"1.0","source":{"id":"astro-ph/9610121","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/9610121","created_at":"2026-07-04T16:00:16Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/9610121v1","created_at":"2026-07-04T16:00:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/9610121","created_at":"2026-07-04T16:00:16Z"},{"alias_kind":"pith_short_12","alias_value":"QZ5YJZI2WKXY","created_at":"2026-07-04T16:00:16Z"},{"alias_kind":"pith_short_16","alias_value":"QZ5YJZI2WKXY2EPO","created_at":"2026-07-04T16:00:16Z"},{"alias_kind":"pith_short_8","alias_value":"QZ5YJZI2","created_at":"2026-07-04T16:00:16Z"}],"graph_snapshots":[{"event_id":"sha256:9d17149dc9bda1c1d7d23b90b6631a8b5a5889e0444e5027742f50067614f49e","target":"graph","created_at":"2026-07-04T16:00:16Z","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/9610121/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"If the density distribution \\rho (r) of MACHOs is spherically symmetric with respect to the Galactic center, it is shown that the minimal total mass M_{min}^{{ MACHO}} of the MACHOs is 1.7\\times 10^{10}\\sol \\tau_{-6.7}^{{ LMC}} where \\tau_{-6.7}^{{ LMC}} is the optical depth (\\tau^{{ LMC}}) toward the Large Magellanic Cloud (LMC) in the unit of 2\\times 10^{-7}. If \\rho (r) is a decreasing function of r, it is proved that M_{min}^{{ MACHO}} is 5.6\\times 10^{10}\\sol \\tau_{-6.7}^{{ LMC}}. Several spherical and axially symmetric halo models of the Galaxy with a few free parameters are also conside","authors_text":"R. Nishi, T. Nakamura, Y. Kan-ya","cross_cats":[],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"1996-10-16T06:19:29Z","title":"The Minimum Total Mass of MACHOs and Halo Models of the Galaxy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/9610121","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:ca21895cb7f0774ab92b76286441d38d27221a56fc6cf6b8346aa29881c61638","target":"record","created_at":"2026-07-04T16:00:16Z","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":"1e33f3803d16722f1f44ebf526226609b14500dc5d502b89c29240537a7d38f7","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"1996-10-16T06:19:29Z","title_canon_sha256":"0a269b899693e7851aa8427ae249d393bb31e4858547030f0eb02f2ac9827062"},"schema_version":"1.0","source":{"id":"astro-ph/9610121","kind":"arxiv","version":1}},"canonical_sha256":"867b84e51ab2af8d11eea7139b253fe879edcb6634f248981a7c2be12f8b548d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"867b84e51ab2af8d11eea7139b253fe879edcb6634f248981a7c2be12f8b548d","first_computed_at":"2026-07-04T16:00:16.734059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:00:16.734059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dP7rLH6Sksj6VGhgyQuDtf1uebK7P7kkLxVAqjLpRcpeExaPdCK+91pCMCEHIOSe3HAuH7bnPaZ8tqob8MqWAQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:00:16.734459Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/9610121","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca21895cb7f0774ab92b76286441d38d27221a56fc6cf6b8346aa29881c61638","sha256:9d17149dc9bda1c1d7d23b90b6631a8b5a5889e0444e5027742f50067614f49e"],"state_sha256":"f23005c82cb20100081bc60884f0f0eed107b43f4e36b30464cc05681b17bbce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4G3V+7QNt53slWIDtKAnUCzvSU0P1XhVhtK1ALu6ZyHuHy+URfgrbCpeyAfABd+RM4Fsj1deO9maTL6BRkVODw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T00:34:16.139465Z","bundle_sha256":"bf62ca6a090d21749b40f28c744086edbacd743b11cf47f0842f29d53ad790f6"}}