{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ICJ5V7IPT2UIHTDKD6F52LGOMN","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":"00837be8126b72e67f541f463ca7d158ff18928b4e7442931437c40cb619835c","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-08T21:12:40Z","title_canon_sha256":"94c4d4f93bd5dfcbca98e439b2c96172a921f17bc1a85dce6ff346078898f702"},"schema_version":"1.0","source":{"id":"2607.07923","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.07923","created_at":"2026-07-10T00:19:04Z"},{"alias_kind":"arxiv_version","alias_value":"2607.07923v1","created_at":"2026-07-10T00:19:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07923","created_at":"2026-07-10T00:19:04Z"},{"alias_kind":"pith_short_12","alias_value":"ICJ5V7IPT2UI","created_at":"2026-07-10T00:19:04Z"},{"alias_kind":"pith_short_16","alias_value":"ICJ5V7IPT2UIHTDK","created_at":"2026-07-10T00:19:04Z"},{"alias_kind":"pith_short_8","alias_value":"ICJ5V7IP","created_at":"2026-07-10T00:19:04Z"}],"graph_snapshots":[{"event_id":"sha256:3bfa3faf2d1ea02180c1aff09a47beb378b291e3dfe98c3356e43701454c35aa","target":"graph","created_at":"2026-07-10T00:19:04Z","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/2607.07923/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study robust high-order time splittings for nonlinear Schr\\\"odinger equations whose linear part is defined by the Laplacian and an arbitrary three-dimensional rotation operator. After Fourier pseudospectral discretization, a continuous exact factorization of the linear flow need not yield a method self-adjoint fixed-grid propagator. For the original stage-wise explicit exact integrator, we identify a quadratic even term in the local logarithm and show that its visibility is state-dependent, so the observed temporal order of accuracy can depend on the initial data. We then formulate fixed-gr","authors_text":"Fei Xue, Tianqi Zhang","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-08T21:12:40Z","title":"Admissible Discrete Linear Propagators for High-Order Time Splittings of Rotational Nonlinear Schr\\\"odinger Equations with Arbitrary Three-Dimensional Rotation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07923","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:d12510853ba4dda400fd300adf993583cd6245a3a694d0dae5a10890e14afb25","target":"record","created_at":"2026-07-10T00:19:04Z","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":"00837be8126b72e67f541f463ca7d158ff18928b4e7442931437c40cb619835c","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2026-07-08T21:12:40Z","title_canon_sha256":"94c4d4f93bd5dfcbca98e439b2c96172a921f17bc1a85dce6ff346078898f702"},"schema_version":"1.0","source":{"id":"2607.07923","kind":"arxiv","version":1}},"canonical_sha256":"4093dafd0f9ea883cc6a1f8bdd2cce634a0ad1419b022e1846dbd18dab623352","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4093dafd0f9ea883cc6a1f8bdd2cce634a0ad1419b022e1846dbd18dab623352","first_computed_at":"2026-07-10T00:19:04.913742Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-10T00:19:04.913742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M6PJxerlnVpT6+zAseafyg9cMHllSLtaAVYSUAZNWUG9dojBuoBMLAxNT5Bpb8eHowEYWZyDJIeTC8vzyz2TDg==","signature_status":"signed_v1","signed_at":"2026-07-10T00:19:04.914165Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.07923","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d12510853ba4dda400fd300adf993583cd6245a3a694d0dae5a10890e14afb25","sha256:3bfa3faf2d1ea02180c1aff09a47beb378b291e3dfe98c3356e43701454c35aa"],"state_sha256":"18cdb5cab8bf7b8a0d2445ba6d9ddba787110a81ffd9223b861d773286348fd6"}