{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XJAXHV2MIDZO3EYFMA7DMUIKVX","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":"2d68456b22faf7af89a21af69c25dae910a71788eca856f4de0a2f3c99727be8","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-01-17T10:07:43Z","title_canon_sha256":"2d88872b694e29d46617be4fea89ef069c61dcebf95b2c1c4cb9d57b8be8cb3d"},"schema_version":"1.0","source":{"id":"1301.4031","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4031","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4031v1","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4031","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"XJAXHV2MIDZO","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XJAXHV2MIDZO3EYF","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XJAXHV2M","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:a081dbe94e25528a8c3f7edbe2df57739ce1a283e29f2fc38b0053e12a1be78d","target":"graph","created_at":"2026-05-17T23:53:17Z","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":"We examine the minimal magnitude of perturbations necessary to change the number $N$ of static equilibrium points of a convex solid $K$. We call the normalized volume of the minimally necessary truncation robustness and we seek shapes with maximal robustness for fixed values of $N$. While the upward robustness (referring to the increase of $N$) of smooth, homogeneous convex solids is known to be zero, little is known about their downward robustness. The difficulty of the latter problem is related to the coupling (via integrals) between the geometry of the hull $\\bd K$ and the location of the c","authors_text":"G. Domokos, Z. L\\'angi","cross_cats":["math-ph","math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-01-17T10:07:43Z","title":"The robustness of equilibria on convex solids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4031","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:dde22a0e7db08a73ca6af8bf60835a37d4ba96ae160e6299bf326c9b004b086d","target":"record","created_at":"2026-05-17T23:53:17Z","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":"2d68456b22faf7af89a21af69c25dae910a71788eca856f4de0a2f3c99727be8","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-01-17T10:07:43Z","title_canon_sha256":"2d88872b694e29d46617be4fea89ef069c61dcebf95b2c1c4cb9d57b8be8cb3d"},"schema_version":"1.0","source":{"id":"1301.4031","kind":"arxiv","version":1}},"canonical_sha256":"ba4173d74c40f2ed9305603e36510aaddb1346fe4d78e8f28d903b26692dfd89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba4173d74c40f2ed9305603e36510aaddb1346fe4d78e8f28d903b26692dfd89","first_computed_at":"2026-05-17T23:53:17.988914Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:17.988914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5YvVHa5aSCp6bZGwBBV3e1iWi786perelTGnvFPO53XkoQGjGvQvlDQQElzuYlDiLexX3gdHl5b7TtwOQhfXBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:17.989526Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.4031","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dde22a0e7db08a73ca6af8bf60835a37d4ba96ae160e6299bf326c9b004b086d","sha256:a081dbe94e25528a8c3f7edbe2df57739ce1a283e29f2fc38b0053e12a1be78d"],"state_sha256":"ca337766d8d0f8dd2b9cef3a6639d4b677b93ac3e92d12dc2b0c3aac9d301532"}