{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:7VOUEM6FSJRXSFHGZHBLR6OZRH","short_pith_number":"pith:7VOUEM6F","schema_version":"1.0","canonical_sha256":"fd5d4233c592637914e6c9c2b8f9d989d44bc5a9d9171a0243a54b370081e5c6","source":{"kind":"arxiv","id":"1307.3231","version":1},"attestation_state":"computed","paper":{"title":"Certification of Bounds of Non-linear Functions: the Templates Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.SC","authors_text":"Benjamin Werner, St\\'ephane Gaubert, Victor Magron, Xavier Allamigeon","submitted_at":"2013-07-10T09:53:14Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.3231","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-07-10T09:53:14Z","cross_cats_sorted":["cs.LO"],"title_canon_sha256":"9b873643879429bfb2f64d1c1dcc4f296092964b1dfc4d64658d4e2544ae828f","abstract_canon_sha256":"c972e1904c9d51011a2bf7449ad862cb726876c38ffb41177c18a1890331fb75"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:05.147125Z","signature_b64":"aXBGO0dwvAptME+Tf3nkASOu3D5tnW/vgnvMVoL8qP39yBMrW0n6LfvNeliqAYGb6q4aSZ5pFRPThulgM7Y5Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd5d4233c592637914e6c9c2b8f9d989d44bc5a9d9171a0243a54b370081e5c6","last_reissued_at":"2026-05-18T02:54:05.146528Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:05.146528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Certification of Bounds of Non-linear Functions: the Templates Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.SC","authors_text":"Benjamin Werner, St\\'ephane Gaubert, Victor Magron, Xavier Allamigeon","submitted_at":"2013-07-10T09:53:14Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3231","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1307.3231","created_at":"2026-05-18T02:54:05.146629+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.3231v1","created_at":"2026-05-18T02:54:05.146629+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3231","created_at":"2026-05-18T02:54:05.146629+00:00"},{"alias_kind":"pith_short_12","alias_value":"7VOUEM6FSJRX","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"7VOUEM6FSJRXSFHG","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"7VOUEM6F","created_at":"2026-05-18T12:27:38.830355+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7VOUEM6FSJRXSFHGZHBLR6OZRH","json":"https://pith.science/pith/7VOUEM6FSJRXSFHGZHBLR6OZRH.json","graph_json":"https://pith.science/api/pith-number/7VOUEM6FSJRXSFHGZHBLR6OZRH/graph.json","events_json":"https://pith.science/api/pith-number/7VOUEM6FSJRXSFHGZHBLR6OZRH/events.json","paper":"https://pith.science/paper/7VOUEM6F"},"agent_actions":{"view_html":"https://pith.science/pith/7VOUEM6FSJRXSFHGZHBLR6OZRH","download_json":"https://pith.science/pith/7VOUEM6FSJRXSFHGZHBLR6OZRH.json","view_paper":"https://pith.science/paper/7VOUEM6F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.3231&json=true","fetch_graph":"https://pith.science/api/pith-number/7VOUEM6FSJRXSFHGZHBLR6OZRH/graph.json","fetch_events":"https://pith.science/api/pith-number/7VOUEM6FSJRXSFHGZHBLR6OZRH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7VOUEM6FSJRXSFHGZHBLR6OZRH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7VOUEM6FSJRXSFHGZHBLR6OZRH/action/storage_attestation","attest_author":"https://pith.science/pith/7VOUEM6FSJRXSFHGZHBLR6OZRH/action/author_attestation","sign_citation":"https://pith.science/pith/7VOUEM6FSJRXSFHGZHBLR6OZRH/action/citation_signature","submit_replication":"https://pith.science/pith/7VOUEM6FSJRXSFHGZHBLR6OZRH/action/replication_record"}},"created_at":"2026-05-18T02:54:05.146629+00:00","updated_at":"2026-05-18T02:54:05.146629+00:00"}