{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SFM3WABEUCQSZSG2JWNEAU545F","short_pith_number":"pith:SFM3WABE","canonical_record":{"source":{"id":"1603.01183","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-03T17:11:28Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b7dbc360c17e7e989d0bb54de6a5007ded7da0208ed365ecd1a9cecfa7f65273","abstract_canon_sha256":"57bf97bc8853b498bb7e6d05245e88c3e6245d83133de54600a9ab27c480522a"},"schema_version":"1.0"},"canonical_sha256":"9159bb0024a0a12cc8da4d9a4053bce947a3f76040e2063b5701000ffaaf246d","source":{"kind":"arxiv","id":"1603.01183","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01183","created_at":"2026-05-18T01:19:39Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01183v1","created_at":"2026-05-18T01:19:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01183","created_at":"2026-05-18T01:19:39Z"},{"alias_kind":"pith_short_12","alias_value":"SFM3WABEUCQS","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SFM3WABEUCQSZSG2","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SFM3WABE","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SFM3WABEUCQSZSG2JWNEAU545F","target":"record","payload":{"canonical_record":{"source":{"id":"1603.01183","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-03T17:11:28Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b7dbc360c17e7e989d0bb54de6a5007ded7da0208ed365ecd1a9cecfa7f65273","abstract_canon_sha256":"57bf97bc8853b498bb7e6d05245e88c3e6245d83133de54600a9ab27c480522a"},"schema_version":"1.0"},"canonical_sha256":"9159bb0024a0a12cc8da4d9a4053bce947a3f76040e2063b5701000ffaaf246d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:39.469020Z","signature_b64":"92OyUEjh760tzAR99ITgNclm7oq+9aHbuq/DSUyAZiljpz0pdn4mr4bZW5kAghgS+ehzc9RFiq5fR43C7GwFAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9159bb0024a0a12cc8da4d9a4053bce947a3f76040e2063b5701000ffaaf246d","last_reissued_at":"2026-05-18T01:19:39.468384Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:39.468384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.01183","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nuasji2pEPCaoEqUAgOZO0mjxbflpMtC5JygRnhzsyQuWvvJGw9coMtyqSkFsXXzsrX4CZZPeoDefOH+PjxGDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:10:57.775664Z"},"content_sha256":"4d8e4f3cfe808ba7f7634a5973183121d40dbfc15084f3f446ed263dfbd0ee8b","schema_version":"1.0","event_id":"sha256:4d8e4f3cfe808ba7f7634a5973183121d40dbfc15084f3f446ed263dfbd0ee8b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SFM3WABEUCQSZSG2JWNEAU545F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solving systems of polynomial inequalities with algebraic geometry methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DS","authors_text":"Antonio Tornamb\\`e, Corrado Possieri, Laura Menini","submitted_at":"2016-03-03T17:11:28Z","abstract_excerpt":"The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which taken from the literature, are proposed to compute solutions of such a system. An example of how such procedures can be used to solve the static output feedback stabilization problem for a linear parametrically-varying system is reported."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01183","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tLEvycNSin2HJZ5CIouBHF7HFd/YXddqrQGEE5oXH3aUHyD2sCGAPPr9r6V3fVpHnoFY1nk+20v4bhJoYCL+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T16:10:57.776000Z"},"content_sha256":"e56e52bb6b836ceb6184421ba9d76974ff93c60cebdc04dd3e8d7d3ebe70e73e","schema_version":"1.0","event_id":"sha256:e56e52bb6b836ceb6184421ba9d76974ff93c60cebdc04dd3e8d7d3ebe70e73e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SFM3WABEUCQSZSG2JWNEAU545F/bundle.json","state_url":"https://pith.science/pith/SFM3WABEUCQSZSG2JWNEAU545F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SFM3WABEUCQSZSG2JWNEAU545F/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T16:10:57Z","links":{"resolver":"https://pith.science/pith/SFM3WABEUCQSZSG2JWNEAU545F","bundle":"https://pith.science/pith/SFM3WABEUCQSZSG2JWNEAU545F/bundle.json","state":"https://pith.science/pith/SFM3WABEUCQSZSG2JWNEAU545F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SFM3WABEUCQSZSG2JWNEAU545F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SFM3WABEUCQSZSG2JWNEAU545F","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":"57bf97bc8853b498bb7e6d05245e88c3e6245d83133de54600a9ab27c480522a","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-03T17:11:28Z","title_canon_sha256":"b7dbc360c17e7e989d0bb54de6a5007ded7da0208ed365ecd1a9cecfa7f65273"},"schema_version":"1.0","source":{"id":"1603.01183","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01183","created_at":"2026-05-18T01:19:39Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01183v1","created_at":"2026-05-18T01:19:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01183","created_at":"2026-05-18T01:19:39Z"},{"alias_kind":"pith_short_12","alias_value":"SFM3WABEUCQS","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SFM3WABEUCQSZSG2","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SFM3WABE","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:e56e52bb6b836ceb6184421ba9d76974ff93c60cebdc04dd3e8d7d3ebe70e73e","target":"graph","created_at":"2026-05-18T01:19:39Z","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 goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which taken from the literature, are proposed to compute solutions of such a system. An example of how such procedures can be used to solve the static output feedback stabilization problem for a linear parametrically-varying system is reported.","authors_text":"Antonio Tornamb\\`e, Corrado Possieri, Laura Menini","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-03T17:11:28Z","title":"Solving systems of polynomial inequalities with algebraic geometry methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01183","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":"sha256:4d8e4f3cfe808ba7f7634a5973183121d40dbfc15084f3f446ed263dfbd0ee8b","target":"record","created_at":"2026-05-18T01:19:39Z","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":"57bf97bc8853b498bb7e6d05245e88c3e6245d83133de54600a9ab27c480522a","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-03T17:11:28Z","title_canon_sha256":"b7dbc360c17e7e989d0bb54de6a5007ded7da0208ed365ecd1a9cecfa7f65273"},"schema_version":"1.0","source":{"id":"1603.01183","kind":"arxiv","version":1}},"canonical_sha256":"9159bb0024a0a12cc8da4d9a4053bce947a3f76040e2063b5701000ffaaf246d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9159bb0024a0a12cc8da4d9a4053bce947a3f76040e2063b5701000ffaaf246d","first_computed_at":"2026-05-18T01:19:39.468384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:39.468384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"92OyUEjh760tzAR99ITgNclm7oq+9aHbuq/DSUyAZiljpz0pdn4mr4bZW5kAghgS+ehzc9RFiq5fR43C7GwFAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:39.469020Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.01183","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d8e4f3cfe808ba7f7634a5973183121d40dbfc15084f3f446ed263dfbd0ee8b","sha256:e56e52bb6b836ceb6184421ba9d76974ff93c60cebdc04dd3e8d7d3ebe70e73e"],"state_sha256":"a141a4d262d2e977db2a55bae0cbc7122f31b7aeb60607ae50f73c30ae09b1c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2ZbDjyapMltJ27sM0S96yFk+WyKCpqHoPC8Muayo43RefZzbgtNgyzYHmUz1/BxAK/CGTW0RJDYB2sus74xuAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T16:10:57.777855Z","bundle_sha256":"b1c7c3471b4d72fa16de4f75ad2e2735fefe76e59743e1031508b1c54e925176"}}