{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:7HUH5PZPY4IKIR564OU3BFAAIY","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":"6e9a9d708d9ce0cc69ee4c162a9efc49cef09760f654709927a72fb82faae935","cross_cats_sorted":["gr-qc"],"license":"","primary_cat":"astro-ph","submitted_at":"1998-07-02T08:28:10Z","title_canon_sha256":"8272a184abc48e594c95a1a9094d38d812ea6bc4eca476fc6caaffeaead8a70d"},"schema_version":"1.0","source":{"id":"astro-ph/9807018","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/9807018","created_at":"2026-07-04T16:06:49Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/9807018v1","created_at":"2026-07-04T16:06:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/9807018","created_at":"2026-07-04T16:06:49Z"},{"alias_kind":"pith_short_12","alias_value":"7HUH5PZPY4IK","created_at":"2026-07-04T16:06:49Z"},{"alias_kind":"pith_short_16","alias_value":"7HUH5PZPY4IKIR56","created_at":"2026-07-04T16:06:49Z"},{"alias_kind":"pith_short_8","alias_value":"7HUH5PZP","created_at":"2026-07-04T16:06:49Z"}],"graph_snapshots":[{"event_id":"sha256:e37343ebde0dbf6b0d985e596938a507888a90a3cad78448df52467c4464a49b","target":"graph","created_at":"2026-07-04T16:06:49Z","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/9807018/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study black hole MACHO binary formation through three-body interactions in the early universe at $t\\sim 10^{-5}$s. The probability distribution functions of the eccentricity and the semimajor axis of binaries as well as of the coalescence time are obtained assuming that the black holes are randomly formed in space. We confirm that the previous order-of-magnitude estimate for the binary parameters is valid within $\\sim 50%$ error. We find that the coalescence rate of the black hole MACHO binaries is $\\sim 5 \\times 10^{-2} \\times 2^{\\pm 1}$ events/year/galaxy taking into consideration several","authors_text":"Kunihito Ioka, Takahiro Tanaka, Takashi Nakamura, Takeshi Chiba","cross_cats":["gr-qc"],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"1998-07-02T08:28:10Z","title":"Black Hole Binary Formation in the Expanding Universe --- Three Body Problem Approximation ---"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/9807018","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:ed7ca46cb51c868395b12d1c701ff7eccff98028fbf190efdc0a7f97a456aa39","target":"record","created_at":"2026-07-04T16:06:49Z","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":"6e9a9d708d9ce0cc69ee4c162a9efc49cef09760f654709927a72fb82faae935","cross_cats_sorted":["gr-qc"],"license":"","primary_cat":"astro-ph","submitted_at":"1998-07-02T08:28:10Z","title_canon_sha256":"8272a184abc48e594c95a1a9094d38d812ea6bc4eca476fc6caaffeaead8a70d"},"schema_version":"1.0","source":{"id":"astro-ph/9807018","kind":"arxiv","version":1}},"canonical_sha256":"f9e87ebf2fc710a447bee3a9b09400461901f0793ec40166afdf72bafbe2fe6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9e87ebf2fc710a447bee3a9b09400461901f0793ec40166afdf72bafbe2fe6c","first_computed_at":"2026-07-04T16:06:49.729285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:06:49.729285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rOdc8onZGwBsWF8rLfpoDgzKhQJgJPWvaANbuiLbxmedZfekG3NonpJSnvpH9lilSK6hgBaOePbPkwbzpFQCAg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:06:49.729724Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/9807018","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed7ca46cb51c868395b12d1c701ff7eccff98028fbf190efdc0a7f97a456aa39","sha256:e37343ebde0dbf6b0d985e596938a507888a90a3cad78448df52467c4464a49b"],"state_sha256":"73406e47457be9f9ebdf52cf4b4c96f62996275203b02086483be6433f0bf1ce"}