{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HI5ZEEJSVO5ZNM7XPXV7HSO46U","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":"438e834179b956bc9fbb6b79f06a73ea33501d8359c6a54ea8d3cbd32a7cd129","cross_cats_sorted":["cs.MS","cs.SC","cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-05-20T06:26:45Z","title_canon_sha256":"3dc64e622be5a874be1469b9b0cb31fc591ce5cca0adbca5f1034dbd6fcd8bdf"},"schema_version":"1.0","source":{"id":"2505.13980","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.13980","created_at":"2026-07-05T11:05:54Z"},{"alias_kind":"arxiv_version","alias_value":"2505.13980v1","created_at":"2026-07-05T11:05:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.13980","created_at":"2026-07-05T11:05:54Z"},{"alias_kind":"pith_short_12","alias_value":"HI5ZEEJSVO5Z","created_at":"2026-07-05T11:05:54Z"},{"alias_kind":"pith_short_16","alias_value":"HI5ZEEJSVO5ZNM7X","created_at":"2026-07-05T11:05:54Z"},{"alias_kind":"pith_short_8","alias_value":"HI5ZEEJS","created_at":"2026-07-05T11:05:54Z"}],"graph_snapshots":[{"event_id":"sha256:e0e7e48b317d6d9a2426eb36c2455de9e60ca8e547e79b1aea01800e254a1c77","target":"graph","created_at":"2026-07-05T11:05:54Z","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/2505.13980/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The computation of the $L_\\infty $-norm is an important issue in $H_{\\infty}$ control, particularly for analyzing system stability and robustness. This paper focuses on symbolic computation methods for determining the $L_{\\infty} $-norm of finite-dimensional linear systems, highlighting their advantages in achieving exact solutions where numerical methods often encounter limitations. Key techniques such as Sturm-Habicht sequences, Rational Univariate Representations (RUR), and Cylindrical Algebraic Decomposition (CAD) are surveyed, with an emphasis on their theoretical foundations, practical i","authors_text":"Alban Quadrat, Fabrice Rouillier, Grace Younes","cross_cats":["cs.MS","cs.SC","cs.SY","eess.SY"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-05-20T06:26:45Z","title":"Symbolic and Numerical Tools for $L_{\\infty}$-Norm Calculation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.13980","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":"sha256:4f659d918d9c94083fdbc09d37672d07f2cdf30b895f173786a03c66ed39ebdb","target":"record","created_at":"2026-07-05T11:05:54Z","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":"438e834179b956bc9fbb6b79f06a73ea33501d8359c6a54ea8d3cbd32a7cd129","cross_cats_sorted":["cs.MS","cs.SC","cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-05-20T06:26:45Z","title_canon_sha256":"3dc64e622be5a874be1469b9b0cb31fc591ce5cca0adbca5f1034dbd6fcd8bdf"},"schema_version":"1.0","source":{"id":"2505.13980","kind":"arxiv","version":1}},"canonical_sha256":"3a3b921132abbb96b3f77debf3c9dcf52cfc5aa94f55ec931c78e331b257d06d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a3b921132abbb96b3f77debf3c9dcf52cfc5aa94f55ec931c78e331b257d06d","first_computed_at":"2026-07-05T11:05:54.218816Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:05:54.218816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PBv8G26KtrjD3147gcaoFfJ5EBFDNfZHxarse2W0jpgIBqBfW8kw1QUF+6zzLHXOJfh25/VVXlEz1zv5dNduDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:05:54.219242Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.13980","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f659d918d9c94083fdbc09d37672d07f2cdf30b895f173786a03c66ed39ebdb","sha256:e0e7e48b317d6d9a2426eb36c2455de9e60ca8e547e79b1aea01800e254a1c77"],"state_sha256":"0bf4493802606070deda7dc70d1a15d6db3fdf1ae0b59e24983a1a59c958187c"}