{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VSXSZK3N2TMQLSXJIEVPODW44Q","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fc0e8f020a5ddf2722cf73fa5c8b7c3b027f7d53405389dee7198464205d5b10","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-20T22:04:54Z","title_canon_sha256":"dc948a2168dd47b4251a14c123d2f22e67bea0d48d1e2df1bd5e52820d9b2543"},"schema_version":"1.0","source":{"id":"2607.18537","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18537","created_at":"2026-07-22T00:22:53Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18537v1","created_at":"2026-07-22T00:22:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18537","created_at":"2026-07-22T00:22:53Z"},{"alias_kind":"pith_short_12","alias_value":"VSXSZK3N2TMQ","created_at":"2026-07-22T00:22:53Z"},{"alias_kind":"pith_short_16","alias_value":"VSXSZK3N2TMQLSXJ","created_at":"2026-07-22T00:22:53Z"},{"alias_kind":"pith_short_8","alias_value":"VSXSZK3N","created_at":"2026-07-22T00:22:53Z"}],"graph_snapshots":[{"event_id":"sha256:79f81755de76a3d39f8028cc2a3aaadaa9c6cebdd8d2cd7d8017850a64d4d21b","target":"graph","created_at":"2026-07-22T00:22:53Z","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/2607.18537/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the generation of state $k$-designs from time evolution under a fixed Hamiltonian. Specifically, we consider the ensemble $\\mathcal{E}=\\left\\{e^{-iHt}|\\psi_0\\rangle | \\ t\\sim \\mathrm{Unif}[0,T],\\, |\\psi_0\\rangle\\sim \\mathcal{E}'\\right\\}$, where the initial states are sampled from an ensemble $\\mathcal{E}'$. For Hamiltonians drawn from the Gaussian unitary ensemble, we derive a simple relation between the frame potential of the evolved ensemble $\\mathcal{E}$ and that of the initial ensemble $\\mathcal{E}'$ in the large evolution time limit. This relation shows that $\\mathcal{E}$ forms a","authors_text":"Shengxian Hou, Zhi-Cheng Yang, Zong-Yue Hou","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-20T22:04:54Z","title":"State $k$-designs from Hamiltonian evolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18537","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":"sha256:61005a3a5eb2cd6f70665f8793f3329d7198fddef51d85ceddcd497a6a39e3f4","target":"record","created_at":"2026-07-22T00:22:53Z","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":"fc0e8f020a5ddf2722cf73fa5c8b7c3b027f7d53405389dee7198464205d5b10","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-20T22:04:54Z","title_canon_sha256":"dc948a2168dd47b4251a14c123d2f22e67bea0d48d1e2df1bd5e52820d9b2543"},"schema_version":"1.0","source":{"id":"2607.18537","kind":"arxiv","version":1}},"canonical_sha256":"acaf2cab6dd4d905cae9412af70edce4157d9763b4c7334fa4d1e99f8d703183","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acaf2cab6dd4d905cae9412af70edce4157d9763b4c7334fa4d1e99f8d703183","first_computed_at":"2026-07-22T00:22:53.260536Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-22T00:22:53.260536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qJosjzJPN+TAiTG3xRvp566Ut6gzSHufBeeInV6T/CQzFawI4NDUbtOgjDKFlbhkzRc/nbhAaad8osQokLLiCw==","signature_status":"signed_v1","signed_at":"2026-07-22T00:22:53.261357Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.18537","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61005a3a5eb2cd6f70665f8793f3329d7198fddef51d85ceddcd497a6a39e3f4","sha256:79f81755de76a3d39f8028cc2a3aaadaa9c6cebdd8d2cd7d8017850a64d4d21b","sha256:5d365ed612dcc272a35c4bc4d2181d7e7d5feb2f4b46c6b6540ed77c5edbfbc3"],"state_sha256":"0f1ee36c6e7de4838e1a68c4b464eed197276446af60ecc4c5a4ddde39779b37"}