{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:WHOZ5MLFFPAEXRMKCXAMRBFI2W","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":"c8d7c9beeab6c421fe525484943e71ee3ac4e95f351c8ce0f4acf635982f8ef9","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2000-11-15T10:27:14Z","title_canon_sha256":"2e5f39705c733483a1788e69a41a4debc311fdd91267aa093b5a174643405203"},"schema_version":"1.0","source":{"id":"astro-ph/0011293","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0011293","created_at":"2026-07-04T16:17:36Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0011293v1","created_at":"2026-07-04T16:17:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0011293","created_at":"2026-07-04T16:17:36Z"},{"alias_kind":"pith_short_12","alias_value":"WHOZ5MLFFPAE","created_at":"2026-07-04T16:17:36Z"},{"alias_kind":"pith_short_16","alias_value":"WHOZ5MLFFPAEXRMK","created_at":"2026-07-04T16:17:36Z"},{"alias_kind":"pith_short_8","alias_value":"WHOZ5MLF","created_at":"2026-07-04T16:17:36Z"}],"graph_snapshots":[{"event_id":"sha256:0c990a7f205a8e09dcdd52ecc4bea6c0ac3fc82447eb767a3e91486327c55d3a","target":"graph","created_at":"2026-07-04T16:17:36Z","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/0011293/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a numerical study of topological descriptors of initially Gaussian and scale-free density perturbations evolving via gravitational instability in an expanding universe. We carefully evaluate and avoid numerical contamination in making accurate measurements on simulated fields on a grid in a finite box. Independent of extent of non linearity, the measured Euler number of the excursion set at the percolation threshold, $\\delta_c$, is positive and nearly equal to the number of isolated components, suggesting that these structures are trees. Our study of critical point counts reconciles","authors_text":"Dmitry Pogosyan, Stephane Colombi, Tarun Souradeep","cross_cats":[],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2000-11-15T10:27:14Z","title":"Tree structure of the percolating Universe"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0011293","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":"sha256:906784f252f8492d51948cb1231d204f76262c6559ce5dd93536b77738858fa1","target":"record","created_at":"2026-07-04T16:17:36Z","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":"c8d7c9beeab6c421fe525484943e71ee3ac4e95f351c8ce0f4acf635982f8ef9","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2000-11-15T10:27:14Z","title_canon_sha256":"2e5f39705c733483a1788e69a41a4debc311fdd91267aa093b5a174643405203"},"schema_version":"1.0","source":{"id":"astro-ph/0011293","kind":"arxiv","version":1}},"canonical_sha256":"b1dd9eb1652bc04bc58a15c0c884a8d5898ff0897bad72734d05719ad8780ec2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1dd9eb1652bc04bc58a15c0c884a8d5898ff0897bad72734d05719ad8780ec2","first_computed_at":"2026-07-04T16:17:36.954093Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:17:36.954093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1KLFN0a3YOHsmgzNeg/OPaMQQP6SA3tyDIHJLjZ7q842htMoDNPmfWs3ecV1XLHKyXxwVzj6NUwh1PaGuCxoAg==","signature_status":"signed_v1","signed_at":"2026-07-04T16:17:36.954549Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/0011293","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:906784f252f8492d51948cb1231d204f76262c6559ce5dd93536b77738858fa1","sha256:0c990a7f205a8e09dcdd52ecc4bea6c0ac3fc82447eb767a3e91486327c55d3a"],"state_sha256":"d8c63bf3d0409502dd766cc3640cfc490f6766c0ba5236ed012a68d29082d77b"}