{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:VN3ZHXXZ7FCHPQQQJEYJ5ZIYBW","short_pith_number":"pith:VN3ZHXXZ","schema_version":"1.0","canonical_sha256":"ab7793def9f94477c21049309ee5180d9cf7c3ed5c9b530ea15fca14c8e0fdfb","source":{"kind":"arxiv","id":"1808.08548","version":1},"attestation_state":"computed","paper":{"title":"Whitney's Theorem, Triangular Sets and Probabilistic Descent on Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG"],"primary_cat":"math.OC","authors_text":"David W. Dreisigmeyer","submitted_at":"2018-08-26T13:17:37Z","abstract_excerpt":"We examine doing probabilistic descent over manifolds implicitly defined by a set of polynomials with rational coefficients. The system of polynomials is assumed to be triangularized. An application of Whitney's embedding theorem allows us to work in a reduced dimensional embedding space. A numerical continuation method applied to the reduced-dimensional embedded manifold is used to drive the procedure."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1808.08548","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-26T13:17:37Z","cross_cats_sorted":["math.AG","math.DG"],"title_canon_sha256":"1f216a78652739c6e14d63c635a5c971b15d9c60d2252d5c5b9f378207645a7e","abstract_canon_sha256":"4784ed05b17ca6008e8d7c72f922887282ca37669c4c998fd0ea1306a1792665"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:16.103421Z","signature_b64":"pd6E6aPMBU9oGP9ncWjgabkG2n08orId3b3MTVQ3S3HI3VgdDFUgfUTg8AEEjFWVYNkg/g0WQj4YySlOa6UtBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab7793def9f94477c21049309ee5180d9cf7c3ed5c9b530ea15fca14c8e0fdfb","last_reissued_at":"2026-05-18T00:07:16.102667Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:16.102667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Whitney's Theorem, Triangular Sets and Probabilistic Descent on Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DG"],"primary_cat":"math.OC","authors_text":"David W. Dreisigmeyer","submitted_at":"2018-08-26T13:17:37Z","abstract_excerpt":"We examine doing probabilistic descent over manifolds implicitly defined by a set of polynomials with rational coefficients. The system of polynomials is assumed to be triangularized. An application of Whitney's embedding theorem allows us to work in a reduced dimensional embedding space. A numerical continuation method applied to the reduced-dimensional embedded manifold is used to drive the procedure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08548","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1808.08548","created_at":"2026-05-18T00:07:16.102781+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.08548v1","created_at":"2026-05-18T00:07:16.102781+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08548","created_at":"2026-05-18T00:07:16.102781+00:00"},{"alias_kind":"pith_short_12","alias_value":"VN3ZHXXZ7FCH","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"VN3ZHXXZ7FCHPQQQ","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"VN3ZHXXZ","created_at":"2026-05-18T12:32:59.047623+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VN3ZHXXZ7FCHPQQQJEYJ5ZIYBW","json":"https://pith.science/pith/VN3ZHXXZ7FCHPQQQJEYJ5ZIYBW.json","graph_json":"https://pith.science/api/pith-number/VN3ZHXXZ7FCHPQQQJEYJ5ZIYBW/graph.json","events_json":"https://pith.science/api/pith-number/VN3ZHXXZ7FCHPQQQJEYJ5ZIYBW/events.json","paper":"https://pith.science/paper/VN3ZHXXZ"},"agent_actions":{"view_html":"https://pith.science/pith/VN3ZHXXZ7FCHPQQQJEYJ5ZIYBW","download_json":"https://pith.science/pith/VN3ZHXXZ7FCHPQQQJEYJ5ZIYBW.json","view_paper":"https://pith.science/paper/VN3ZHXXZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.08548&json=true","fetch_graph":"https://pith.science/api/pith-number/VN3ZHXXZ7FCHPQQQJEYJ5ZIYBW/graph.json","fetch_events":"https://pith.science/api/pith-number/VN3ZHXXZ7FCHPQQQJEYJ5ZIYBW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VN3ZHXXZ7FCHPQQQJEYJ5ZIYBW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VN3ZHXXZ7FCHPQQQJEYJ5ZIYBW/action/storage_attestation","attest_author":"https://pith.science/pith/VN3ZHXXZ7FCHPQQQJEYJ5ZIYBW/action/author_attestation","sign_citation":"https://pith.science/pith/VN3ZHXXZ7FCHPQQQJEYJ5ZIYBW/action/citation_signature","submit_replication":"https://pith.science/pith/VN3ZHXXZ7FCHPQQQJEYJ5ZIYBW/action/replication_record"}},"created_at":"2026-05-18T00:07:16.102781+00:00","updated_at":"2026-05-18T00:07:16.102781+00:00"}