{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GHKA72OTDOAAIPHMOP2MWHRBT3","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":"8bf09e583ff56c15bc70a4d141fcbfa4212919a32ec5b970f14f0a9102d79520","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2026-05-25T11:56:11Z","title_canon_sha256":"ef2f75166d174aa2f3f3d577e86d01b5c1b7714678573a5451bbc881634f526a"},"schema_version":"1.0","source":{"id":"2605.25743","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.25743","created_at":"2026-05-26T02:04:52Z"},{"alias_kind":"arxiv_version","alias_value":"2605.25743v1","created_at":"2026-05-26T02:04:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25743","created_at":"2026-05-26T02:04:52Z"},{"alias_kind":"pith_short_12","alias_value":"GHKA72OTDOAA","created_at":"2026-05-26T02:04:52Z"},{"alias_kind":"pith_short_16","alias_value":"GHKA72OTDOAAIPHM","created_at":"2026-05-26T02:04:52Z"},{"alias_kind":"pith_short_8","alias_value":"GHKA72OT","created_at":"2026-05-26T02:04:52Z"}],"graph_snapshots":[{"event_id":"sha256:a337cf9f3cd850af9ba68fe656b3450e2870807aafcc72f80d225d4008f9da93","target":"graph","created_at":"2026-05-26T02:04:52Z","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/2605.25743/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $P$ be a monic polynomial of degree $n$ with roots $x_1,\\ldots,x_n$. We study the discriminants of the derivatives $P^{(k)}$ as symmetric translation-invariant polynomials in the original roots. The general ``square-graph cone'' positivity problem was formulated by Alexandersson and Shapiro. The main result of this note proves this conjecture for the terminal cubic family $k=n-3$: we give an explicit positive square-graph expansion for $\\disc(P^{(n-3)})$. We also record closed central-moment formulas for the terminal quadratic, cubic and quartic cases, introduce normalized terminal polynom","authors_text":"Boris Shapiro","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2026-05-25T11:56:11Z","title":"Discriminants of derivatives and symmetric difference polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25743","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":"sha256:2ba8eba839b6cd305ebc532ebffba9f7714fcf8b88723aaa8d4a0a65df30f780","target":"record","created_at":"2026-05-26T02:04:52Z","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":"8bf09e583ff56c15bc70a4d141fcbfa4212919a32ec5b970f14f0a9102d79520","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2026-05-25T11:56:11Z","title_canon_sha256":"ef2f75166d174aa2f3f3d577e86d01b5c1b7714678573a5451bbc881634f526a"},"schema_version":"1.0","source":{"id":"2605.25743","kind":"arxiv","version":1}},"canonical_sha256":"31d40fe9d31b80043cec73f4cb1e219efb5f664a451788d0427d2216ca11ddfd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31d40fe9d31b80043cec73f4cb1e219efb5f664a451788d0427d2216ca11ddfd","first_computed_at":"2026-05-26T02:04:52.899953Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:04:52.899953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LzKET9HdtxqVHHRJDl0KpLiYgiZ/kkmAcQSNQg3wPZNhMqSe474oDpj7oqECvqf7nWzcmnnlZ1Dotg160HA3Aw==","signature_status":"signed_v1","signed_at":"2026-05-26T02:04:52.900540Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.25743","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ba8eba839b6cd305ebc532ebffba9f7714fcf8b88723aaa8d4a0a65df30f780","sha256:a337cf9f3cd850af9ba68fe656b3450e2870807aafcc72f80d225d4008f9da93"],"state_sha256":"9c7f58c4768348d5c532e0c80f84f4905b3b26753cd25d971a28e101b90e8a08"}