{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7VOUEM6FSJRXSFHGZHBLR6OZRH","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":"c972e1904c9d51011a2bf7449ad862cb726876c38ffb41177c18a1890331fb75","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-07-10T09:53:14Z","title_canon_sha256":"9b873643879429bfb2f64d1c1dcc4f296092964b1dfc4d64658d4e2544ae828f"},"schema_version":"1.0","source":{"id":"1307.3231","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3231","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3231v1","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3231","created_at":"2026-05-18T02:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"7VOUEM6FSJRX","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7VOUEM6FSJRXSFHG","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7VOUEM6F","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:d1d287bdb5007d7b385cfaf68b4fc9d8fc6351195404a701d4fcc7e967297123","target":"graph","created_at":"2026-05-18T02:54:05Z","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 aim of this work is to certify lower bounds for real-valued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof system such as Coq. The application range for such a tool is widespread; for instance Hales' proof of Kepler's conjecture yields thousands of inequalities. We introduce an approximation algorithm, which combines ideas of the max-plus basis method (in optimal control) and of the linear templates method developed by Manna et al. (in static analysis). This algorithm consists in bounding som","authors_text":"Benjamin Werner, St\\'ephane Gaubert, Victor Magron, Xavier Allamigeon","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-07-10T09:53:14Z","title":"Certification of Bounds of Non-linear Functions: the Templates Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3231","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":"sha256:0edf06fbbbd75ddc3ba9a1ebdcd890b1861d3a425794600e8575a30b6bb735ee","target":"record","created_at":"2026-05-18T02:54:05Z","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":"c972e1904c9d51011a2bf7449ad862cb726876c38ffb41177c18a1890331fb75","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-07-10T09:53:14Z","title_canon_sha256":"9b873643879429bfb2f64d1c1dcc4f296092964b1dfc4d64658d4e2544ae828f"},"schema_version":"1.0","source":{"id":"1307.3231","kind":"arxiv","version":1}},"canonical_sha256":"fd5d4233c592637914e6c9c2b8f9d989d44bc5a9d9171a0243a54b370081e5c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd5d4233c592637914e6c9c2b8f9d989d44bc5a9d9171a0243a54b370081e5c6","first_computed_at":"2026-05-18T02:54:05.146528Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:05.146528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aXBGO0dwvAptME+Tf3nkASOu3D5tnW/vgnvMVoL8qP39yBMrW0n6LfvNeliqAYGb6q4aSZ5pFRPThulgM7Y5Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:05.147125Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.3231","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0edf06fbbbd75ddc3ba9a1ebdcd890b1861d3a425794600e8575a30b6bb735ee","sha256:d1d287bdb5007d7b385cfaf68b4fc9d8fc6351195404a701d4fcc7e967297123"],"state_sha256":"00f1bbfa14b359a513e75def9eb82fc795342da6099f727a64e27bdfd438cd41"}