{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:W6EB4FLI6BJJMVJBZZDBVX54SA","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":"ba810c8d67b73298d989f549877aedf1c8bc453e27affdfeb5efe0abefe3ba75","cross_cats_sorted":["hep-ph","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-03-19T20:00:16Z","title_canon_sha256":"f36d0802c3a0817a527d8fda20c8e056dfa4a54b3a416f1d225bb10ab6b7f3f6"},"schema_version":"1.0","source":{"id":"1203.4235","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4235","created_at":"2026-05-18T01:58:05Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4235v1","created_at":"2026-05-18T01:58:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4235","created_at":"2026-05-18T01:58:05Z"},{"alias_kind":"pith_short_12","alias_value":"W6EB4FLI6BJJ","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"W6EB4FLI6BJJMVJB","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"W6EB4FLI","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:d4665a6efabe963d18d9ca6ca4f75101022c5a238b124896122e785055fbb6b5","target":"graph","created_at":"2026-05-18T01:58:05Z","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":"The interplay rich between algebraic geometry and string and gauge theories has recently been immensely aided by advances in computational algebra. However, these symbolic (Gr\\\"{o}bner) methods are severely limited by algorithmic issues such as exponential space complexity and being highly sequential. In this paper, we introduce a novel paradigm of numerical algebraic geometry which in a plethora of situations overcomes these short-comings. Its so-called 'embarrassing parallelizability' allows us to solve many problems and extract physical information which elude the symbolic methods. We descr","authors_text":"Dhagash Mehta, Jonathan D. Hauenstein, Yang-Hui He","cross_cats":["hep-ph","math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-03-19T20:00:16Z","title":"Numerical Algebraic Geometry: A New Perspective on String and Gauge Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4235","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:d42f41ca9d65afdea77c95124e0b194a266f8e2683cc055293500d167c415534","target":"record","created_at":"2026-05-18T01:58:05Z","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":"ba810c8d67b73298d989f549877aedf1c8bc453e27affdfeb5efe0abefe3ba75","cross_cats_sorted":["hep-ph","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-03-19T20:00:16Z","title_canon_sha256":"f36d0802c3a0817a527d8fda20c8e056dfa4a54b3a416f1d225bb10ab6b7f3f6"},"schema_version":"1.0","source":{"id":"1203.4235","kind":"arxiv","version":1}},"canonical_sha256":"b7881e1568f052965521ce461adfbc901043b7633d09b04e89d62cf8f9459ee1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7881e1568f052965521ce461adfbc901043b7633d09b04e89d62cf8f9459ee1","first_computed_at":"2026-05-18T01:58:05.970849Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:05.970849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N7B8B9KDiLjNsBHMT5By1rAUlGOTyC8+8+cINOM8aJzXF4phLsUvVvqXujEHJwNb86d3AxOx2iuMTRQgnytDAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:05.971370Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.4235","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d42f41ca9d65afdea77c95124e0b194a266f8e2683cc055293500d167c415534","sha256:d4665a6efabe963d18d9ca6ca4f75101022c5a238b124896122e785055fbb6b5"],"state_sha256":"7696d3d0dc6cdb5ba49d1c63030e167612de8c89eb1edbab41a9ae8f82cb8960"}