{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:KOVAOFQDVSY6XBOHKDQ2C6JX7M","short_pith_number":"pith:KOVAOFQD","canonical_record":{"source":{"id":"1112.2328","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SE","submitted_at":"2011-12-11T07:17:34Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"0b9ce70530f92be6f9c6094f48f43ef7aff796391d991fb1e9f4ce5f2073f5ef","abstract_canon_sha256":"5d074e6bfc1def75be7ba8fcb589492d1ae72620477b8f2ed528cd37413892d3"},"schema_version":"1.0"},"canonical_sha256":"53aa071603acb1eb85c750e1a17937fb3ea397259a32c804b644995e79ab6951","source":{"kind":"arxiv","id":"1112.2328","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2328","created_at":"2026-05-18T02:21:27Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2328v1","created_at":"2026-05-18T02:21:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2328","created_at":"2026-05-18T02:21:27Z"},{"alias_kind":"pith_short_12","alias_value":"KOVAOFQDVSY6","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KOVAOFQDVSY6XBOH","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KOVAOFQD","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:KOVAOFQDVSY6XBOHKDQ2C6JX7M","target":"record","payload":{"canonical_record":{"source":{"id":"1112.2328","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SE","submitted_at":"2011-12-11T07:17:34Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"0b9ce70530f92be6f9c6094f48f43ef7aff796391d991fb1e9f4ce5f2073f5ef","abstract_canon_sha256":"5d074e6bfc1def75be7ba8fcb589492d1ae72620477b8f2ed528cd37413892d3"},"schema_version":"1.0"},"canonical_sha256":"53aa071603acb1eb85c750e1a17937fb3ea397259a32c804b644995e79ab6951","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:27.309663Z","signature_b64":"tujZ2oUqgqMMZp/i7p98sruOXtoerM5VPs7FAFz9U8ved4HtgaEhprBtrmtJQPUXl+f4mjEucDPkjOzQ8bqHDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53aa071603acb1eb85c750e1a17937fb3ea397259a32c804b644995e79ab6951","last_reissued_at":"2026-05-18T02:21:27.309034Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:27.309034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.2328","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":"2026-05-18T02:21:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EC1hB263auN2DtGr/8XVNmZOtm8HGzmvxaKTiupyn6neoJu5njEWFh44KdWdj7wEQI5AdGMdaEVfmuMEVWDMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:31:09.588270Z"},"content_sha256":"b41a58f3775d76dcada3e8b15df8b004516762236aa19c87f9eca3991db45017","schema_version":"1.0","event_id":"sha256:b41a58f3775d76dcada3e8b15df8b004516762236aa19c87f9eca3991db45017"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:KOVAOFQDVSY6XBOHKDQ2C6JX7M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact Safety Verification of Hybrid Systems Using Sums-Of-Squares Representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.SE","authors_text":"Min Wu, Wang Lin, Zhenbing Zeng, Zhengfeng Yang","submitted_at":"2011-12-11T07:17:34Z","abstract_excerpt":"In this paper we discuss how to generate inductive invariants for safety verification of hybrid systems. A hybrid symbolic-numeric method is presented to compute inequality inductive invariants of the given systems. A numerical invariant of the given system can be obtained by solving a parameterized polynomial optimization problem via sum-of-squares (SOS) relaxation. And a method based on Gauss-Newton refinement and rational vector recovery is deployed to obtain the invariants with rational coefficients, which exactly satisfy the conditions of invariants. Several examples are given to illustra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2328","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":"2026-05-18T02:21:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PBLAWcSgpSzYpYHRVJXqbUyZ7+iPr5/A/5tBVnSTRVCgT/X93HNy4MI4rxrVJoYXrkguGo1/7XGi1SrdkakVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:31:09.588674Z"},"content_sha256":"9975c7d4a45f73f31f752e0c00d0f67f883cc551af0032a82ea921c524ebd031","schema_version":"1.0","event_id":"sha256:9975c7d4a45f73f31f752e0c00d0f67f883cc551af0032a82ea921c524ebd031"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KOVAOFQDVSY6XBOHKDQ2C6JX7M/bundle.json","state_url":"https://pith.science/pith/KOVAOFQDVSY6XBOHKDQ2C6JX7M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KOVAOFQDVSY6XBOHKDQ2C6JX7M/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":"2026-05-28T10:31:09Z","links":{"resolver":"https://pith.science/pith/KOVAOFQDVSY6XBOHKDQ2C6JX7M","bundle":"https://pith.science/pith/KOVAOFQDVSY6XBOHKDQ2C6JX7M/bundle.json","state":"https://pith.science/pith/KOVAOFQDVSY6XBOHKDQ2C6JX7M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KOVAOFQDVSY6XBOHKDQ2C6JX7M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KOVAOFQDVSY6XBOHKDQ2C6JX7M","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":"5d074e6bfc1def75be7ba8fcb589492d1ae72620477b8f2ed528cd37413892d3","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SE","submitted_at":"2011-12-11T07:17:34Z","title_canon_sha256":"0b9ce70530f92be6f9c6094f48f43ef7aff796391d991fb1e9f4ce5f2073f5ef"},"schema_version":"1.0","source":{"id":"1112.2328","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2328","created_at":"2026-05-18T02:21:27Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2328v1","created_at":"2026-05-18T02:21:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2328","created_at":"2026-05-18T02:21:27Z"},{"alias_kind":"pith_short_12","alias_value":"KOVAOFQDVSY6","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KOVAOFQDVSY6XBOH","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KOVAOFQD","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:9975c7d4a45f73f31f752e0c00d0f67f883cc551af0032a82ea921c524ebd031","target":"graph","created_at":"2026-05-18T02:21:27Z","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":"In this paper we discuss how to generate inductive invariants for safety verification of hybrid systems. A hybrid symbolic-numeric method is presented to compute inequality inductive invariants of the given systems. A numerical invariant of the given system can be obtained by solving a parameterized polynomial optimization problem via sum-of-squares (SOS) relaxation. And a method based on Gauss-Newton refinement and rational vector recovery is deployed to obtain the invariants with rational coefficients, which exactly satisfy the conditions of invariants. Several examples are given to illustra","authors_text":"Min Wu, Wang Lin, Zhenbing Zeng, Zhengfeng Yang","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SE","submitted_at":"2011-12-11T07:17:34Z","title":"Exact Safety Verification of Hybrid Systems Using Sums-Of-Squares Representation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2328","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:b41a58f3775d76dcada3e8b15df8b004516762236aa19c87f9eca3991db45017","target":"record","created_at":"2026-05-18T02:21:27Z","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":"5d074e6bfc1def75be7ba8fcb589492d1ae72620477b8f2ed528cd37413892d3","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SE","submitted_at":"2011-12-11T07:17:34Z","title_canon_sha256":"0b9ce70530f92be6f9c6094f48f43ef7aff796391d991fb1e9f4ce5f2073f5ef"},"schema_version":"1.0","source":{"id":"1112.2328","kind":"arxiv","version":1}},"canonical_sha256":"53aa071603acb1eb85c750e1a17937fb3ea397259a32c804b644995e79ab6951","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53aa071603acb1eb85c750e1a17937fb3ea397259a32c804b644995e79ab6951","first_computed_at":"2026-05-18T02:21:27.309034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:27.309034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tujZ2oUqgqMMZp/i7p98sruOXtoerM5VPs7FAFz9U8ved4HtgaEhprBtrmtJQPUXl+f4mjEucDPkjOzQ8bqHDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:27.309663Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2328","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b41a58f3775d76dcada3e8b15df8b004516762236aa19c87f9eca3991db45017","sha256:9975c7d4a45f73f31f752e0c00d0f67f883cc551af0032a82ea921c524ebd031"],"state_sha256":"bb5cb674d87149375e9845d60fa4cf3a49aa32b538ab7ced3034c08ab884062c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TnCWHVfNYynILtQJbywljMMO+0YGpBmIunOywU0P39f+WEcGuQm2LgUPU7/EETR8q0XIC7et/Mgm9tF+1uocCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:31:09.590588Z","bundle_sha256":"0eccb60dae4c1fad9c023d57c7dece1f4c85f7c804feb719acdf29ccbdca6ebc"}}