{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZQYLB5O6MFFJCBKDENVLSDCJPE","short_pith_number":"pith:ZQYLB5O6","canonical_record":{"source":{"id":"1512.05599","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-17T14:32:54Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"692405fe683dd8ad37bf5ee0a5619cf28c3c065174f2871ac2337c6e3e36300d","abstract_canon_sha256":"c4281ef4e0dcb8ca356b0ace240c9d63da2ef4bdd67feb42f27a8c4759c21a21"},"schema_version":"1.0"},"canonical_sha256":"cc30b0f5de614a910543236ab90c49793384098b31adb7b7a238ac4b856e724b","source":{"kind":"arxiv","id":"1512.05599","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05599","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05599v2","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05599","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"pith_short_12","alias_value":"ZQYLB5O6MFFJ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZQYLB5O6MFFJCBKD","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZQYLB5O6","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZQYLB5O6MFFJCBKDENVLSDCJPE","target":"record","payload":{"canonical_record":{"source":{"id":"1512.05599","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-17T14:32:54Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"692405fe683dd8ad37bf5ee0a5619cf28c3c065174f2871ac2337c6e3e36300d","abstract_canon_sha256":"c4281ef4e0dcb8ca356b0ace240c9d63da2ef4bdd67feb42f27a8c4759c21a21"},"schema_version":"1.0"},"canonical_sha256":"cc30b0f5de614a910543236ab90c49793384098b31adb7b7a238ac4b856e724b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:07.440462Z","signature_b64":"OV0hSYYOFgTHQporzFcCKDdnhoEi0WDrwkQbNTwN1ZpcMlPfELpPWxmQNHLAUnJm5Jx2ND3IB8/+dru4qrKvAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc30b0f5de614a910543236ab90c49793384098b31adb7b7a238ac4b856e724b","last_reissued_at":"2026-05-18T00:51:07.439994Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:07.439994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.05599","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:51:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ibPIjNk7NAf6hardtCi2WBOHUAuf5WGDcnv8lez/wYhsnJKnic3wOhBKOij86bj6McnqwCbzMTVkH0GUgPdgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:28:09.038761Z"},"content_sha256":"499614f31654938b803e4dd42037dd65897f8cede580c3dd8a6f865d51093f6e","schema_version":"1.0","event_id":"sha256:499614f31654938b803e4dd42037dd65897f8cede580c3dd8a6f865d51093f6e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZQYLB5O6MFFJCBKDENVLSDCJPE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounds for deterministic and stochastic dynamical systems using sum-of-squares optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.DS","authors_text":"David Goluskin, Deqing Huang, Giovanni Fantuzzi, Sergei I. Chernyshenko","submitted_at":"2015-12-17T14:32:54Z","abstract_excerpt":"We describe methods for proving upper and lower bounds on infinite-time averages in deterministic dynamical systems and on stationary expectations in stochastic systems. The dynamics and the quantities to be bounded are assumed to be polynomial functions of the state variables. The methods are computer-assisted, using sum-of-squares polynomials to formulate sufficient conditions that can be checked by semidefinite programming. In the deterministic case, we seek tight bounds that apply to particular local attractors. An obstacle to proving such bounds is that they do not hold globally; they are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05599","kind":"arxiv","version":2},"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":"2026-05-18T00:51:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r4uI8AGSu5WXoirs2w7aCm8FTOEeRGWvSvMZN+eBNIgC6y3PqhTW0dHGgTxWzu8SWUiHXF9XVUsNcVa7KD9QDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:28:09.039426Z"},"content_sha256":"b24a848ed975b5a94c4e6df59cf2d29ca51e9c61850631854f1287a61f496b58","schema_version":"1.0","event_id":"sha256:b24a848ed975b5a94c4e6df59cf2d29ca51e9c61850631854f1287a61f496b58"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZQYLB5O6MFFJCBKDENVLSDCJPE/bundle.json","state_url":"https://pith.science/pith/ZQYLB5O6MFFJCBKDENVLSDCJPE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZQYLB5O6MFFJCBKDENVLSDCJPE/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":"2026-06-07T14:28:09Z","links":{"resolver":"https://pith.science/pith/ZQYLB5O6MFFJCBKDENVLSDCJPE","bundle":"https://pith.science/pith/ZQYLB5O6MFFJCBKDENVLSDCJPE/bundle.json","state":"https://pith.science/pith/ZQYLB5O6MFFJCBKDENVLSDCJPE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZQYLB5O6MFFJCBKDENVLSDCJPE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZQYLB5O6MFFJCBKDENVLSDCJPE","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":"c4281ef4e0dcb8ca356b0ace240c9d63da2ef4bdd67feb42f27a8c4759c21a21","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-17T14:32:54Z","title_canon_sha256":"692405fe683dd8ad37bf5ee0a5619cf28c3c065174f2871ac2337c6e3e36300d"},"schema_version":"1.0","source":{"id":"1512.05599","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05599","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05599v2","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05599","created_at":"2026-05-18T00:51:07Z"},{"alias_kind":"pith_short_12","alias_value":"ZQYLB5O6MFFJ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZQYLB5O6MFFJCBKD","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZQYLB5O6","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:b24a848ed975b5a94c4e6df59cf2d29ca51e9c61850631854f1287a61f496b58","target":"graph","created_at":"2026-05-18T00:51:07Z","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":"We describe methods for proving upper and lower bounds on infinite-time averages in deterministic dynamical systems and on stationary expectations in stochastic systems. The dynamics and the quantities to be bounded are assumed to be polynomial functions of the state variables. The methods are computer-assisted, using sum-of-squares polynomials to formulate sufficient conditions that can be checked by semidefinite programming. In the deterministic case, we seek tight bounds that apply to particular local attractors. An obstacle to proving such bounds is that they do not hold globally; they are","authors_text":"David Goluskin, Deqing Huang, Giovanni Fantuzzi, Sergei I. Chernyshenko","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-17T14:32:54Z","title":"Bounds for deterministic and stochastic dynamical systems using sum-of-squares optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05599","kind":"arxiv","version":2},"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":"sha256:499614f31654938b803e4dd42037dd65897f8cede580c3dd8a6f865d51093f6e","target":"record","created_at":"2026-05-18T00:51:07Z","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":"c4281ef4e0dcb8ca356b0ace240c9d63da2ef4bdd67feb42f27a8c4759c21a21","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-12-17T14:32:54Z","title_canon_sha256":"692405fe683dd8ad37bf5ee0a5619cf28c3c065174f2871ac2337c6e3e36300d"},"schema_version":"1.0","source":{"id":"1512.05599","kind":"arxiv","version":2}},"canonical_sha256":"cc30b0f5de614a910543236ab90c49793384098b31adb7b7a238ac4b856e724b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc30b0f5de614a910543236ab90c49793384098b31adb7b7a238ac4b856e724b","first_computed_at":"2026-05-18T00:51:07.439994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:07.439994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OV0hSYYOFgTHQporzFcCKDdnhoEi0WDrwkQbNTwN1ZpcMlPfELpPWxmQNHLAUnJm5Jx2ND3IB8/+dru4qrKvAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:07.440462Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.05599","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:499614f31654938b803e4dd42037dd65897f8cede580c3dd8a6f865d51093f6e","sha256:b24a848ed975b5a94c4e6df59cf2d29ca51e9c61850631854f1287a61f496b58"],"state_sha256":"039186ed89949f95e353042c7e027f51df084db20bef96e863e73f9c76cba946"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fMUk8ofP9XxY60ab+PuQfmXePRJCYHuy3GI2WMUkKBWbX3jGt3EB28/d5v3YYcYWXD+uXr65FlNDTeqda9FiAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T14:28:09.043259Z","bundle_sha256":"484697dd952b9fa5b96c87eb6326feeb3ef6f204ce25ff848c605d6fa329c73a"}}