{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:BKTET7IQFLGUSDOACTCFJBB2ZR","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":"f1af00d4f5c7de53c8241df9f38f5f16333102f328cda825f0cf3c3e14b8901b","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2003-02-18T19:22:46Z","title_canon_sha256":"061febd7bf7c6f77759f790cd810d3f6f71537d3627030f2c9d08270b595d18a"},"schema_version":"1.0","source":{"id":"astro-ph/0302358","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0302358","created_at":"2026-07-04T14:12:36Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0302358v2","created_at":"2026-07-04T14:12:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0302358","created_at":"2026-07-04T14:12:36Z"},{"alias_kind":"pith_short_12","alias_value":"BKTET7IQFLGU","created_at":"2026-07-04T14:12:36Z"},{"alias_kind":"pith_short_16","alias_value":"BKTET7IQFLGUSDOA","created_at":"2026-07-04T14:12:36Z"},{"alias_kind":"pith_short_8","alias_value":"BKTET7IQ","created_at":"2026-07-04T14:12:36Z"}],"graph_snapshots":[{"event_id":"sha256:305f8f4b508345f1f80952b0c3ea87ee05f6142e293144cb0fbf606683cefc5e","target":"graph","created_at":"2026-07-04T14:12:36Z","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/0302358/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We have analyzed the dependences of the threshold value of amplitude of linear density fluctuation collapsed at the current epoch, $\\delta_c$, and its overdensity after virialization, $\\Delta_c$, on matter density content, 3D curvature parameter and cosmological constant. Though the range for the threshold values of perturbation amplitude is quite narrow - $1.55\\le \\delta_c\\le 1.75$ in the region of parameters $-0.4\\le\\Omega_k\\le0.4$, $0\\le\\Omega_{\\Lambda}\\le 1$, $0.1\\le\\Omega_m\\le 1$, the difference in the concentrations of rich clusters of galaxies (calculated within the Press-Schechter form","authors_text":"B. Novosyadlyj (Astronomical Observatory of Ivan Franko National University of L'viv), Yu. Kulinich","cross_cats":[],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2003-02-18T19:22:46Z","title":"Spherical collapse and mass function of rich clusters in models with curvature and cosmological constant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0302358","kind":"arxiv","version":2},"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":"sha256:401b0c7f7f5d462567a6fda2a724881aa63119b69bfece514953d5194a5646eb","target":"record","created_at":"2026-07-04T14:12:36Z","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":"f1af00d4f5c7de53c8241df9f38f5f16333102f328cda825f0cf3c3e14b8901b","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2003-02-18T19:22:46Z","title_canon_sha256":"061febd7bf7c6f77759f790cd810d3f6f71537d3627030f2c9d08270b595d18a"},"schema_version":"1.0","source":{"id":"astro-ph/0302358","kind":"arxiv","version":2}},"canonical_sha256":"0aa649fd102acd490dc014c454843acc63a0d19f8c25ce8353860d4bf4092424","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0aa649fd102acd490dc014c454843acc63a0d19f8c25ce8353860d4bf4092424","first_computed_at":"2026-07-04T14:12:36.637870Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:12:36.637870Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xzhMBCPpVhsveC9goxnodb5xltbLVvKjbVtICd/MerrQvoVrG7+ERLT4qSfsXXpLnDhSvtMtNK2/1UYweb73AA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:12:36.638272Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/0302358","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:401b0c7f7f5d462567a6fda2a724881aa63119b69bfece514953d5194a5646eb","sha256:305f8f4b508345f1f80952b0c3ea87ee05f6142e293144cb0fbf606683cefc5e"],"state_sha256":"51b1d5bd4ff3b986adc370c257ad333bd0b16bff73376dbd463c343509843a2f"}