{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:S6MCLPMUSIDL3UCEXFT7WN3SH3","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":"316ee8e882767ef858c36a6843157b2e27214b1b50c2d954c67d024f0ed6c27e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2016-10-22T12:04:12Z","title_canon_sha256":"e645eb0b1fd60e14e226e35a03136f4099a35a06a3fa7163b926a84b19a57f90"},"schema_version":"1.0","source":{"id":"1610.07038","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.07038","created_at":"2026-05-18T00:23:59Z"},{"alias_kind":"arxiv_version","alias_value":"1610.07038v2","created_at":"2026-05-18T00:23:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07038","created_at":"2026-05-18T00:23:59Z"},{"alias_kind":"pith_short_12","alias_value":"S6MCLPMUSIDL","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"S6MCLPMUSIDL3UCE","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"S6MCLPMU","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:d25fff88f9ec0ed56844b53cfb718ca6e5a9f9aacd8af0394259bd9036ff565f","target":"graph","created_at":"2026-05-18T00:23:59Z","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":"Floating point error is an inevitable drawback of embedded systems implementation. Computing rigorous upper bounds of roundoff errors is absolutely necessary to the validation of critical software. This problem is even more challenging when addressing non-linear programs. In this paper, we propose and compare two new methods based on Bernstein expansions and sparse Krivine-Stengle representations, adapted from the field of the global optimization to compute upper bounds of roundoff errors for programs implementing polynomial functions. We release two related software package FPBern and FPKiSte","authors_text":"Alexandre Rocca, Thao Dang, Victor Magron","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2016-10-22T12:04:12Z","title":"Certified Roundoff Error Bounds using Bernstein Expansions and Sparse Krivine-Stengle Representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07038","kind":"arxiv","version":2},"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":"sha256:8d0b89c39819cbd37fd55b8fe9f88186be22b3e0fe009c467f8b91ffe5da085e","target":"record","created_at":"2026-05-18T00:23:59Z","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":"316ee8e882767ef858c36a6843157b2e27214b1b50c2d954c67d024f0ed6c27e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2016-10-22T12:04:12Z","title_canon_sha256":"e645eb0b1fd60e14e226e35a03136f4099a35a06a3fa7163b926a84b19a57f90"},"schema_version":"1.0","source":{"id":"1610.07038","kind":"arxiv","version":2}},"canonical_sha256":"979825bd949206bdd044b967fb37723edf183ddb992aadd6ce634641616b9c74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"979825bd949206bdd044b967fb37723edf183ddb992aadd6ce634641616b9c74","first_computed_at":"2026-05-18T00:23:59.183827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:59.183827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IAkKAg8v3w4pU10MeS9lDDxiu8Iu7NLtbxhrxnJIf5GP8A4F5qdZ1tetUYPt5/v+OWFrEYJVm4UqNqjge/dwDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:59.184438Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.07038","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d0b89c39819cbd37fd55b8fe9f88186be22b3e0fe009c467f8b91ffe5da085e","sha256:d25fff88f9ec0ed56844b53cfb718ca6e5a9f9aacd8af0394259bd9036ff565f"],"state_sha256":"0470983b38a1f03ee7748e896b9d82c50bc53516bba6d3204c94d6249de75da5"}