{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KPX43GSXH7LDK35OZKI4E6CTVR","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":"643eb7ea30072068b52e4dee40de1a2fba4ef9cc823e22b832f26a56ee36d7aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-05T14:03:23Z","title_canon_sha256":"1d51fcc8da0e9fbdd04c53ad7fad63f7f138258a7d36b6e2419dae9fd79f16a1"},"schema_version":"1.0","source":{"id":"1806.02204","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.02204","created_at":"2026-05-18T00:14:02Z"},{"alias_kind":"arxiv_version","alias_value":"1806.02204v1","created_at":"2026-05-18T00:14:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02204","created_at":"2026-05-18T00:14:02Z"},{"alias_kind":"pith_short_12","alias_value":"KPX43GSXH7LD","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KPX43GSXH7LDK35O","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KPX43GSX","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:17df38cca9388aa79701b1df99260d0c244f3a95a7753485d6286c98baf2a194","target":"graph","created_at":"2026-05-18T00:14:02Z","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 start a systematic study of the topology, geometry and singularities of the Prony varieties $S_q(\\mu)$, defined by the first $q+1$ equations of the classical Prony system\n  $$\\sum_{j=1}^d a_j x_j^k = \\mu_k, \\ k= 0,1,\\ldots \\ .$$ Prony varieties, being a generalization of the Vandermonde varieties, introduced in [5,21], present a significant independent mathematical interest (compare [5,19,21]). The importance of Prony varieties in the study of the error amplification patterns in solving Prony system was shown in [1-4,19]. In [19] a survey of these results was given, from the point of view o","authors_text":"Gil Goldman, Yehonatan Salman, Yosef Yomdin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-05T14:03:23Z","title":"Geometry and Singularities of Prony varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02204","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":"sha256:96f18519cf7fd7e303f0a939414f542f83986d684f77e35d71d2603fc776b1e2","target":"record","created_at":"2026-05-18T00:14:02Z","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":"643eb7ea30072068b52e4dee40de1a2fba4ef9cc823e22b832f26a56ee36d7aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-05T14:03:23Z","title_canon_sha256":"1d51fcc8da0e9fbdd04c53ad7fad63f7f138258a7d36b6e2419dae9fd79f16a1"},"schema_version":"1.0","source":{"id":"1806.02204","kind":"arxiv","version":1}},"canonical_sha256":"53efcd9a573fd6356faeca91c27853ac62731b70c3bcf2002603e4ee8051ca9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53efcd9a573fd6356faeca91c27853ac62731b70c3bcf2002603e4ee8051ca9d","first_computed_at":"2026-05-18T00:14:02.352375Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:02.352375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LyWMCCvovkqCgV4friU1hZv66SfBtBl1smy7WQr9b5W8QC+chd1fQvDbXCHehQE3oHGqUavcFOSQBsTDJbrBDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:02.353145Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.02204","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96f18519cf7fd7e303f0a939414f542f83986d684f77e35d71d2603fc776b1e2","sha256:17df38cca9388aa79701b1df99260d0c244f3a95a7753485d6286c98baf2a194"],"state_sha256":"ef8b490df487c50232ffe359f902d26f91dbe5baa1061e54e856ea3f43871f65"}