{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:OR56KGM4VT2F4LX66P5MOIKF7T","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":"33429bd0575098ae0a6c175b728d00707c5752d80e42bb77e810cd4a7e331bfb","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"1996-09-25T22:32:53Z","title_canon_sha256":"f89179a06da0e8e8850153038726eff01e292444058f3e73f17345bc3e8dad4f"},"schema_version":"1.0","source":{"id":"astro-ph/9609179","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/9609179","created_at":"2026-05-18T01:40:19Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/9609179v1","created_at":"2026-05-18T01:40:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/9609179","created_at":"2026-05-18T01:40:19Z"},{"alias_kind":"pith_short_12","alias_value":"OR56KGM4VT2F","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"OR56KGM4VT2F4LX6","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"OR56KGM4","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:f9d2b5af8f556c97ed980f7348baab5b23031f2e6b6554b49d884431679b0068","target":"graph","created_at":"2026-05-18T01:40:19Z","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"},"paper":{"abstract_excerpt":"A new class of geometric statistics for analyzing galaxy catalogs is presented. Filament statistics quantify filamentarity and planarity in large scale structure in a manner consistent with catalog visualizations. These statistics are based on sequences of spatial links which follow local high-density structures. From these link sequences we compute the discrete curvature, planarity, and torsion. Filament statistics are applied to CDM and CHDM ($\\Omega_\\nu = 0.3$) simulations of Klypin \\etal (1996), the CfA1-like mock redshift catalogs of Nolthenius, Klypin and Primack (1994, 1996), and the Cf","authors_text":"Anatoly Klypin (NMSU), Doug Hellinger (UCSC), Joel Primack (UCSC), Richard Nolthenius (UCSC), Romeel Dav\\'e (UCSC)","cross_cats":[],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"1996-09-25T22:32:53Z","title":"Filament and Shape Statistics: A Quantitative Comparison of Cold + Hot and Cold Dark Matter Cosmologies vs. CfA1 Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/9609179","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":"sha256:5ad2be7cad059a5cdab8036f6d902d47c1f3a36009516007fe4b0735a9c7ab05","target":"record","created_at":"2026-05-18T01:40:19Z","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":"33429bd0575098ae0a6c175b728d00707c5752d80e42bb77e810cd4a7e331bfb","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"1996-09-25T22:32:53Z","title_canon_sha256":"f89179a06da0e8e8850153038726eff01e292444058f3e73f17345bc3e8dad4f"},"schema_version":"1.0","source":{"id":"astro-ph/9609179","kind":"arxiv","version":1}},"canonical_sha256":"747be5199cacf45e2efef3fac72145fce636a0ef3c81ccad7b81e7b5b2387b3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"747be5199cacf45e2efef3fac72145fce636a0ef3c81ccad7b81e7b5b2387b3a","first_computed_at":"2026-05-18T01:40:19.214363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:40:19.214363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kWKC5AKfVwtQqMTbJ16MUfd3N1RWBdY9whv+GGJFRYs6Ymb3A/U0zNfKEYnoxod6bKvuWWcTPaNXuwO7kjwHCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:40:19.214852Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/9609179","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ad2be7cad059a5cdab8036f6d902d47c1f3a36009516007fe4b0735a9c7ab05","sha256:f9d2b5af8f556c97ed980f7348baab5b23031f2e6b6554b49d884431679b0068"],"state_sha256":"3c78abb6e3784ef6071ec185a9a5ebb514859ad18e8fc5a040ac5d63d950d11c"}