{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WUVMIV7RJJPTXLBABYEPB4YWP7","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":"1ab8a9e88c01b9a533e7cbdc3877c97c151ef585db4a936cd12d5350fd6ce3e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-05-25T16:11:43Z","title_canon_sha256":"c54eb349aff6a01f8b0ececf2a2cd04d99dbaae678916c4aacb16b47c4a9dee0"},"schema_version":"1.0","source":{"id":"2605.25992","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.25992","created_at":"2026-05-26T02:05:22Z"},{"alias_kind":"arxiv_version","alias_value":"2605.25992v1","created_at":"2026-05-26T02:05:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25992","created_at":"2026-05-26T02:05:22Z"},{"alias_kind":"pith_short_12","alias_value":"WUVMIV7RJJPT","created_at":"2026-05-26T02:05:22Z"},{"alias_kind":"pith_short_16","alias_value":"WUVMIV7RJJPTXLBA","created_at":"2026-05-26T02:05:22Z"},{"alias_kind":"pith_short_8","alias_value":"WUVMIV7R","created_at":"2026-05-26T02:05:22Z"}],"graph_snapshots":[{"event_id":"sha256:34c413839040810003cae2d127074865ec22def2963fed2cc0c304e05461b29e","target":"graph","created_at":"2026-05-26T02:05:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.25992/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An observation by J-P. Serre implies that cubic polynomials are unique among generic monic polynomials of degree 2 or higher in that they have a root that is a power series in the discriminant of the polynomial. We provide formulas for this root of a cubic that work in any characteristic. In the special case of a cubic real polynomial with positive discriminant, the series converges and therefore provides an explicit formula for a root; when that polynomial is depressed, the root we provide is the longest root. The proofs are a combination of elementary techniques from algebra, combinatorics, ","authors_text":"Jason Bland, Joel Rosenberg, Skip Garibaldi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-05-25T16:11:43Z","title":"Root of a cubic polynomial as a power series in the discriminant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25992","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:b528835919ba3bff4dd11e6159c2f62df80c1666e4a0c0fe91b884e161d5950f","target":"record","created_at":"2026-05-26T02:05:22Z","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":"1ab8a9e88c01b9a533e7cbdc3877c97c151ef585db4a936cd12d5350fd6ce3e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2026-05-25T16:11:43Z","title_canon_sha256":"c54eb349aff6a01f8b0ececf2a2cd04d99dbaae678916c4aacb16b47c4a9dee0"},"schema_version":"1.0","source":{"id":"2605.25992","kind":"arxiv","version":1}},"canonical_sha256":"b52ac457f14a5f3bac200e08f0f3167fc9311cb9a986e1cbfb8f5ca661cf26f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b52ac457f14a5f3bac200e08f0f3167fc9311cb9a986e1cbfb8f5ca661cf26f0","first_computed_at":"2026-05-26T02:05:22.209135Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:05:22.209135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z/Pgv1XwmoEEJBP3uY8lZOgqKl2FJiqGrOuuoYSb4zs6FLp4JnnnlR7JCge3R7QQEIJVJbuI392N/P8mXW5BCQ==","signature_status":"signed_v1","signed_at":"2026-05-26T02:05:22.209991Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.25992","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b528835919ba3bff4dd11e6159c2f62df80c1666e4a0c0fe91b884e161d5950f","sha256:34c413839040810003cae2d127074865ec22def2963fed2cc0c304e05461b29e"],"state_sha256":"2efaf8780cbbedffbdd0e95a574a0cd3a94586bd4d4b0a2a722ca2e79e39eb1c"}