{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:GZMI3F5EAGUTIL2URXIZIRGDLU","short_pith_number":"pith:GZMI3F5E","canonical_record":{"source":{"id":"1804.01583","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2018-04-04T19:41:52Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"6044fd7e74adeb38d1c1a53dd04d0900dc8974e9d918d7c4bc4c2f5a3eae3a4e","abstract_canon_sha256":"1e161df46a50ccc9f1d617129ba72b1732a534beb38865950470189b050c374b"},"schema_version":"1.0"},"canonical_sha256":"36588d97a401a9342f548dd19444c35d2f203c7a30d6900ab1d44e72054c8574","source":{"kind":"arxiv","id":"1804.01583","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.01583","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"arxiv_version","alias_value":"1804.01583v3","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01583","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"pith_short_12","alias_value":"GZMI3F5EAGUT","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GZMI3F5EAGUTIL2U","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GZMI3F5E","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:GZMI3F5EAGUTIL2URXIZIRGDLU","target":"record","payload":{"canonical_record":{"source":{"id":"1804.01583","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2018-04-04T19:41:52Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"6044fd7e74adeb38d1c1a53dd04d0900dc8974e9d918d7c4bc4c2f5a3eae3a4e","abstract_canon_sha256":"1e161df46a50ccc9f1d617129ba72b1732a534beb38865950470189b050c374b"},"schema_version":"1.0"},"canonical_sha256":"36588d97a401a9342f548dd19444c35d2f203c7a30d6900ab1d44e72054c8574","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:59.048774Z","signature_b64":"g8B4kMLRFEMmDXU4r6S/82iPgtZfHRDjaewUhnfJB206jmFWFaqBdQ5o5PUZ2GFSsxKMSylZIuYgusOEEBKgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36588d97a401a9342f548dd19444c35d2f203c7a30d6900ab1d44e72054c8574","last_reissued_at":"2026-05-17T23:51:59.048302Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:59.048302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.01583","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:51:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lLHWAlNb9B2u/QBOqQ1TM+S7k7NwuGyAqovUJLG5Iihs4YBCKZtrvEFIgwPjlmsli59x27RzlF1ChzexxATmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:49:58.803291Z"},"content_sha256":"1bc7ccc089a29b7b5f3f94e55e22c1fb8ce434c43a03f6ce04f558e6743959f3","schema_version":"1.0","event_id":"sha256:1bc7ccc089a29b7b5f3f94e55e22c1fb8ce434c43a03f6ce04f558e6743959f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:GZMI3F5EAGUTIL2URXIZIRGDLU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical Verification of Affine Systems with up to a Billion Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"cs.NA","authors_text":"Hoang-Dung Tran, Stanley Bak, Taylor T. Johnson","submitted_at":"2018-04-04T19:41:52Z","abstract_excerpt":"Affine systems reachability is the basis of many verification methods. With further computation, methods exist to reason about richer models with inputs, nonlinear differential equations, and hybrid dynamics. As such, the scalability of affine systems verification is a prerequisite to scalable analysis for more complex systems. In this paper, we improve the scalability of affine systems verification, in terms of the number of dimensions (variables) in the system.\n  The reachable states of affine systems can be written in terms of the matrix exponential, and safety checking can be performed at "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01583","kind":"arxiv","version":3},"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":"2026-05-17T23:51:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ciA5xzTLY4hz00VaSKvaBTOIqr7lll7/p67DU6Tll+kSQlStKSt6G+d6a0z2r5SDeqFrS8R+uaufCwhUA+oqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:49:58.803646Z"},"content_sha256":"dd1bb559ce408c4dbe70e50fe8f19b760c143d1fcb3aa72c4f8127ba4fdc2563","schema_version":"1.0","event_id":"sha256:dd1bb559ce408c4dbe70e50fe8f19b760c143d1fcb3aa72c4f8127ba4fdc2563"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GZMI3F5EAGUTIL2URXIZIRGDLU/bundle.json","state_url":"https://pith.science/pith/GZMI3F5EAGUTIL2URXIZIRGDLU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GZMI3F5EAGUTIL2URXIZIRGDLU/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":"2026-06-03T17:49:58Z","links":{"resolver":"https://pith.science/pith/GZMI3F5EAGUTIL2URXIZIRGDLU","bundle":"https://pith.science/pith/GZMI3F5EAGUTIL2URXIZIRGDLU/bundle.json","state":"https://pith.science/pith/GZMI3F5EAGUTIL2URXIZIRGDLU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GZMI3F5EAGUTIL2URXIZIRGDLU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GZMI3F5EAGUTIL2URXIZIRGDLU","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":"1e161df46a50ccc9f1d617129ba72b1732a534beb38865950470189b050c374b","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2018-04-04T19:41:52Z","title_canon_sha256":"6044fd7e74adeb38d1c1a53dd04d0900dc8974e9d918d7c4bc4c2f5a3eae3a4e"},"schema_version":"1.0","source":{"id":"1804.01583","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.01583","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"arxiv_version","alias_value":"1804.01583v3","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01583","created_at":"2026-05-17T23:51:59Z"},{"alias_kind":"pith_short_12","alias_value":"GZMI3F5EAGUT","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GZMI3F5EAGUTIL2U","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GZMI3F5E","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:dd1bb559ce408c4dbe70e50fe8f19b760c143d1fcb3aa72c4f8127ba4fdc2563","target":"graph","created_at":"2026-05-17T23:51:59Z","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":"Affine systems reachability is the basis of many verification methods. With further computation, methods exist to reason about richer models with inputs, nonlinear differential equations, and hybrid dynamics. As such, the scalability of affine systems verification is a prerequisite to scalable analysis for more complex systems. In this paper, we improve the scalability of affine systems verification, in terms of the number of dimensions (variables) in the system.\n  The reachable states of affine systems can be written in terms of the matrix exponential, and safety checking can be performed at ","authors_text":"Hoang-Dung Tran, Stanley Bak, Taylor T. Johnson","cross_cats":["cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2018-04-04T19:41:52Z","title":"Numerical Verification of Affine Systems with up to a Billion Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01583","kind":"arxiv","version":3},"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":"sha256:1bc7ccc089a29b7b5f3f94e55e22c1fb8ce434c43a03f6ce04f558e6743959f3","target":"record","created_at":"2026-05-17T23:51:59Z","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":"1e161df46a50ccc9f1d617129ba72b1732a534beb38865950470189b050c374b","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2018-04-04T19:41:52Z","title_canon_sha256":"6044fd7e74adeb38d1c1a53dd04d0900dc8974e9d918d7c4bc4c2f5a3eae3a4e"},"schema_version":"1.0","source":{"id":"1804.01583","kind":"arxiv","version":3}},"canonical_sha256":"36588d97a401a9342f548dd19444c35d2f203c7a30d6900ab1d44e72054c8574","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36588d97a401a9342f548dd19444c35d2f203c7a30d6900ab1d44e72054c8574","first_computed_at":"2026-05-17T23:51:59.048302Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:59.048302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g8B4kMLRFEMmDXU4r6S/82iPgtZfHRDjaewUhnfJB206jmFWFaqBdQ5o5PUZ2GFSsxKMSylZIuYgusOEEBKgBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:59.048774Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.01583","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bc7ccc089a29b7b5f3f94e55e22c1fb8ce434c43a03f6ce04f558e6743959f3","sha256:dd1bb559ce408c4dbe70e50fe8f19b760c143d1fcb3aa72c4f8127ba4fdc2563"],"state_sha256":"3f21b4e6ded63202c5e44eca964ae6e8f04f6b825f53c9ea7495998eea1bf3f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VhrGfG3pBIxlqr5YOXXzZQ8lo1wyWMGxV1X8PlNa+GzwHBT0ZRodHm+SgBpXgtGiVd9z1/hBst9SeaNOMx8dBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T17:49:58.805478Z","bundle_sha256":"f7085a99860c9855da9ee073fd5df6084b75375bdf18330f48c171d838f06949"}}