{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WMQRU3FJCDRYF6AKPFKU6ACJ2J","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":"249fc7c4820621f82069daf7bc69fb2880dde3f954246a23c73a8410b92573bc","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-13T10:45:39Z","title_canon_sha256":"b4ee4609190bba0653057bab707d99a12dad733858fbce41b9387dfbf717391e"},"schema_version":"1.0","source":{"id":"2505.08427","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.08427","created_at":"2026-07-05T11:02:30Z"},{"alias_kind":"arxiv_version","alias_value":"2505.08427v1","created_at":"2026-07-05T11:02:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.08427","created_at":"2026-07-05T11:02:30Z"},{"alias_kind":"pith_short_12","alias_value":"WMQRU3FJCDRY","created_at":"2026-07-05T11:02:30Z"},{"alias_kind":"pith_short_16","alias_value":"WMQRU3FJCDRYF6AK","created_at":"2026-07-05T11:02:30Z"},{"alias_kind":"pith_short_8","alias_value":"WMQRU3FJ","created_at":"2026-07-05T11:02:30Z"}],"graph_snapshots":[{"event_id":"sha256:c62c4ff72d93e312034c5ea52ec8e62bbf3a82279c63f72df1d5f24df4307fa1","target":"graph","created_at":"2026-07-05T11:02:30Z","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/2505.08427/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The reach of a submanifold of $\\mathbb{R}^N$ is defined as the largest radius of a tubular neighbourhood around the submanifold that avoids self-intersections. While essential in geometric and topological applications, computing the reach explicitly is notoriously difficult. In this paper, we introduce a rigorous and practical method to compute a guaranteed lower bound for the reach of a submanifold described as the common zero-set of finitely many smooth functions, not necessarily polynomials. Our algorithm uses techniques from numerically verified proofs and is particularly suitable for high","authors_text":"Daniel Platt, Ra\\'ul S\\'anchez Gal\\'an","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-13T10:45:39Z","title":"Lower bounds for the reach and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.08427","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":"sha256:817007feecf95ff45546d0ee078fba0f7bf5c587987c274e06344d0730993a6b","target":"record","created_at":"2026-07-05T11:02:30Z","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":"249fc7c4820621f82069daf7bc69fb2880dde3f954246a23c73a8410b92573bc","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-13T10:45:39Z","title_canon_sha256":"b4ee4609190bba0653057bab707d99a12dad733858fbce41b9387dfbf717391e"},"schema_version":"1.0","source":{"id":"2505.08427","kind":"arxiv","version":1}},"canonical_sha256":"b3211a6ca910e382f80a79554f0049d272551b7b3342e8555d8926c572fd7723","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3211a6ca910e382f80a79554f0049d272551b7b3342e8555d8926c572fd7723","first_computed_at":"2026-07-05T11:02:30.384030Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:02:30.384030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g7A6zFvU2y2VJSmRzRX0NjvvNgDiStPOV3HNhUxhyiEIr+VugoLvFr9ltvlLIaIA5/edbj88IUMAHF3FI/p6Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T11:02:30.384550Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.08427","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:817007feecf95ff45546d0ee078fba0f7bf5c587987c274e06344d0730993a6b","sha256:c62c4ff72d93e312034c5ea52ec8e62bbf3a82279c63f72df1d5f24df4307fa1"],"state_sha256":"c6e91911a90bd2a5223becba64c18e42314bbac050bf0dbc4d865eeb957953c2"}