{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6WTAX636FCKAWC2DQTURYMVFXF","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":"498ec2de02ffb38f69660202dc4f9c5f616e9042f48298401013871153a14aaf","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NA","submitted_at":"2016-05-01T00:39:38Z","title_canon_sha256":"c63f98d2eaac8930cb1775bcb8d7c13f8fb8ca68a0606b6557bd71cd960ad76c"},"schema_version":"1.0","source":{"id":"1605.00190","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00190","created_at":"2026-05-18T00:28:41Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00190v3","created_at":"2026-05-18T00:28:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00190","created_at":"2026-05-18T00:28:41Z"},{"alias_kind":"pith_short_12","alias_value":"6WTAX636FCKA","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6WTAX636FCKAWC2D","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6WTAX636","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:0b884de0da93ccd0abf7d33f37b8403d23d2cf04ae1eff594e171ca26d2ee58d","target":"graph","created_at":"2026-05-18T00:28:41Z","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":"A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuous functions) is presented. The technique is to first plot each function as a pixel matrix, and to then perform a sequence of basic matrix operations, as dictated by how variables are shared by the relations in the system. The result is a pixel matrix graphing the approximated simultaneous solution set for the system.","authors_text":"David I. Spivak","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NA","submitted_at":"2016-05-01T00:39:38Z","title":"Pixel matrices: An elementary technique for solving nonlinear systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00190","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:f0a8ff55cc6609ddfc217368c701e97d4b3c2d237070d6b866d75372a4d5b862","target":"record","created_at":"2026-05-18T00:28:41Z","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":"498ec2de02ffb38f69660202dc4f9c5f616e9042f48298401013871153a14aaf","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NA","submitted_at":"2016-05-01T00:39:38Z","title_canon_sha256":"c63f98d2eaac8930cb1775bcb8d7c13f8fb8ca68a0606b6557bd71cd960ad76c"},"schema_version":"1.0","source":{"id":"1605.00190","kind":"arxiv","version":3}},"canonical_sha256":"f5a60bfb7e28940b0b4384e91c32a5b970c63ad7d2da295c4aaa124827fe739a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5a60bfb7e28940b0b4384e91c32a5b970c63ad7d2da295c4aaa124827fe739a","first_computed_at":"2026-05-18T00:28:41.349257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:41.349257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8x/6tV7B8HxSjibYiNDlAzEA8OkijWJZAgDjE7AAMgnWtKONk0DwNCUjBdeieDLmeHTjT4phqrfiEOt4dwgpAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:41.349977Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00190","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0a8ff55cc6609ddfc217368c701e97d4b3c2d237070d6b866d75372a4d5b862","sha256:0b884de0da93ccd0abf7d33f37b8403d23d2cf04ae1eff594e171ca26d2ee58d"],"state_sha256":"f7081451ab43f1dee2104211b8339c73a3871f27892c4c72eecc09b6649eba40"}