{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FXRLHN7MQJ5ACHQUDMA5JCW33X","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":"613a9ac52e50c6cdae4639880dd9c838dae23acda4367e656d072b74eca14c1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-08-03T19:48:43Z","title_canon_sha256":"21ebbf120597072a14c7445dddcb29f4349e2f3435ef1ef55f5c9fb8f946e7e3"},"schema_version":"1.0","source":{"id":"1508.00551","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00551","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00551v1","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00551","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"pith_short_12","alias_value":"FXRLHN7MQJ5A","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FXRLHN7MQJ5ACHQU","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FXRLHN7M","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:f26d10a3f9f06e8e75388e400fb6576e35bed1773a7d8824c43a0e3f6d0ce5d8","target":"graph","created_at":"2026-05-18T01:35:57Z","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 critical value of a function is the value of this function at one of its critical points. Each critical point of a differentiable multivariate function is described by the equations which consist in equating to zero all of its partial derivatives. However, in general case there is no equation for the corresponding critical value. The case of polynomials is different. In the present paper an equation for critical values of a polynomial is derived.","authors_text":"Ruslan Sharipov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-08-03T19:48:43Z","title":"Multiple discriminants and critical values of a multivariate polynomial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00551","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":"sha256:4eb7682413a89b3fc575720d524c472cf9aab51cf43872b5aa861af66aa4e62e","target":"record","created_at":"2026-05-18T01:35:57Z","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":"613a9ac52e50c6cdae4639880dd9c838dae23acda4367e656d072b74eca14c1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-08-03T19:48:43Z","title_canon_sha256":"21ebbf120597072a14c7445dddcb29f4349e2f3435ef1ef55f5c9fb8f946e7e3"},"schema_version":"1.0","source":{"id":"1508.00551","kind":"arxiv","version":1}},"canonical_sha256":"2de2b3b7ec827a011e141b01d48adbddd8c8838528b324f8a0d23e7fc0de4b34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2de2b3b7ec827a011e141b01d48adbddd8c8838528b324f8a0d23e7fc0de4b34","first_computed_at":"2026-05-18T01:35:57.830204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:57.830204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sn9DJ1LofyK36/5+L+Fsvj7tm93DGePzAYf4OK/fPQWwKCqBoop/5d+0VwXmoqf9ddCdWw0M7hp7oPbq6kO5CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:57.830704Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.00551","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4eb7682413a89b3fc575720d524c472cf9aab51cf43872b5aa861af66aa4e62e","sha256:f26d10a3f9f06e8e75388e400fb6576e35bed1773a7d8824c43a0e3f6d0ce5d8"],"state_sha256":"b6ad24ce03053fc2f69634b7156f4f8b5e7edb0539b09156c8371026c3fb1bd6"}