{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FWH2RNO6G32XZBBWTCOTPCGUDD","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":"06869ae67e813ba8f6deabb9dac64f290d393314f1aff0be358b81b92e90618c","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-06-02T12:41:34Z","title_canon_sha256":"74c5f9aca158e797213e631d992d0112303dd1fee6c27cbc01e94143d93a74aa"},"schema_version":"1.0","source":{"id":"2506.01603","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.01603","created_at":"2026-05-27T01:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"2506.01603v3","created_at":"2026-05-27T01:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.01603","created_at":"2026-05-27T01:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"FWH2RNO6G32X","created_at":"2026-05-27T01:05:34Z"},{"alias_kind":"pith_short_16","alias_value":"FWH2RNO6G32XZBBW","created_at":"2026-05-27T01:05:34Z"},{"alias_kind":"pith_short_8","alias_value":"FWH2RNO6","created_at":"2026-05-27T01:05:34Z"}],"graph_snapshots":[{"event_id":"sha256:2d374bb8fcaee8fbc08e1ff1cda287629779580cb0be6910f30382b5347ff45b","target":"graph","created_at":"2026-05-27T01:05:34Z","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/2506.01603/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The shadow of an abstract simplicial complex $K$ with vertices in $\\mathbb{R}^N$ is a subset of $\\mathbb{R}^N$ defined as the union of the convex hulls of simplices of $K$. The Vietoris--Rips complex of a metric space $(S,d)$ at scale $\\beta$ is an abstract simplicial complex whose each $k$-simplex corresponds to $(k+1)$ points of $S$ within diameter $\\beta$. In case $S\\subset\\mathbb R^2$ and $d(a,b)=\\|a-b\\|$ the standard Euclidean metric, the natural shadow projection of the Vietoris--Rips complex is already proved by Chambers et al. to induce isomorphisms on $\\pi_0$ and $\\pi_1$. We extend th","authors_text":"Atish Mitra, Rafal Komendarczyk, Sushovan Majhi","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-06-02T12:41:34Z","title":"Vietoris--Rips Shadow for Euclidean Graph Reconstruction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.01603","kind":"arxiv","version":3},"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:e6ca26b441069f043de27fc7339fac0b6ded2593d1ddaf58dae11a5acfc2dc65","target":"record","created_at":"2026-05-27T01:05:34Z","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":"06869ae67e813ba8f6deabb9dac64f290d393314f1aff0be358b81b92e90618c","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-06-02T12:41:34Z","title_canon_sha256":"74c5f9aca158e797213e631d992d0112303dd1fee6c27cbc01e94143d93a74aa"},"schema_version":"1.0","source":{"id":"2506.01603","kind":"arxiv","version":3}},"canonical_sha256":"2d8fa8b5de36f57c8436989d3788d418d17fa2eb6ced50d533e0547a922969ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d8fa8b5de36f57c8436989d3788d418d17fa2eb6ced50d533e0547a922969ea","first_computed_at":"2026-05-27T01:05:34.950505Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T01:05:34.950505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WfGIm+p7gTS+6tEVQlieWJ1NVrW5sDd9ASqwclntUGdUHnpAKHGmiqypP9/+kzipXhgQIdzbbKrazMGjp+GiCg==","signature_status":"signed_v1","signed_at":"2026-05-27T01:05:34.951273Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.01603","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6ca26b441069f043de27fc7339fac0b6ded2593d1ddaf58dae11a5acfc2dc65","sha256:2d374bb8fcaee8fbc08e1ff1cda287629779580cb0be6910f30382b5347ff45b"],"state_sha256":"149d030ef979067da2545b1e975c86b648a78a9d65f4bdebcde1befac8c52c24"}