{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:R5ELDBXQ4EINPLSFMQE43LC5Q4","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":"3fbcdea5aace22d868475126a7553ea6e8a540218aee6a352eb9ff5f9b5744f7","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-04T12:12:08Z","title_canon_sha256":"572addfc8852b3ae5135f59259b96f5c4432d1d3703ead9cd69643d6a16d8031"},"schema_version":"1.0","source":{"id":"2606.06071","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06071","created_at":"2026-06-05T01:15:32Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06071v1","created_at":"2026-06-05T01:15:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06071","created_at":"2026-06-05T01:15:32Z"},{"alias_kind":"pith_short_12","alias_value":"R5ELDBXQ4EIN","created_at":"2026-06-05T01:15:32Z"},{"alias_kind":"pith_short_16","alias_value":"R5ELDBXQ4EINPLSF","created_at":"2026-06-05T01:15:32Z"},{"alias_kind":"pith_short_8","alias_value":"R5ELDBXQ","created_at":"2026-06-05T01:15:32Z"}],"graph_snapshots":[{"event_id":"sha256:7be6c3cfc75701df83d8dcbb8bbec7330d7821f68231350e762bae815560b15e","target":"graph","created_at":"2026-06-05T01:15:32Z","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/2606.06071/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper studies the weak convergence order of structure-preserving stochastic theta methods for a class of index-$1$ stochastic differential algebraic equations with time-dependent singular matrices. The singular matrix is allowed to vary in time but preserves a fixed differential-algebraic splitting, thereby extending the constant singular-matrix setting while retaining the projector structure required for constraint preservation. By exploiting the index-$1$ algebraic-differential decomposition of the exact solution, we establish an abstract weak convergence theorem for constraint-preservi","authors_text":"Caiyuan Zhu, Lin Chen, Yiwei Zhou, Ziheng Chen","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-04T12:12:08Z","title":"Weak order one convergence of structure-preserving stochastic theta methods for stochastic differential algebraic equations with time-dependent singular matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06071","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":"sha256:28e0c823966a213f401fadedfaa5afd98d2c7365ff8bd2d3466728ea019a80b0","target":"record","created_at":"2026-06-05T01:15:32Z","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":"3fbcdea5aace22d868475126a7553ea6e8a540218aee6a352eb9ff5f9b5744f7","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-06-04T12:12:08Z","title_canon_sha256":"572addfc8852b3ae5135f59259b96f5c4432d1d3703ead9cd69643d6a16d8031"},"schema_version":"1.0","source":{"id":"2606.06071","kind":"arxiv","version":1}},"canonical_sha256":"8f48b186f0e110d7ae456409cdac5d8721467c26db78a0c7ed205ca1db5df8f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f48b186f0e110d7ae456409cdac5d8721467c26db78a0c7ed205ca1db5df8f2","first_computed_at":"2026-06-05T01:15:32.053762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:32.053762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t3Ngsiczv/OSzIIZrJBwvz1BJMfAwc2ScUeJfV4lKjzo33h5dctlU7yhhV94r1uej/JOVVCpJXI3185N5H1RAQ==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:32.054201Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.06071","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28e0c823966a213f401fadedfaa5afd98d2c7365ff8bd2d3466728ea019a80b0","sha256:7be6c3cfc75701df83d8dcbb8bbec7330d7821f68231350e762bae815560b15e"],"state_sha256":"be553d0638ac4c96ed080be81966adca5aa0fcdbd0848ae6b6472207db2e6dec"}