{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:644M3NU4Q4HCXF6O73EHEJP4PB","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":"6e9c76e39d243c47940f08bdcf8aee194e4a8f20e26dcfa2435591efd38f662d","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-22T21:28:25Z","title_canon_sha256":"fc730a02dcbc4ff73dbf6b5731e003eec183c90847a6448d3b58ed7033beb57f"},"schema_version":"1.0","source":{"id":"1708.06825","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.06825","created_at":"2026-05-18T00:19:27Z"},{"alias_kind":"arxiv_version","alias_value":"1708.06825v3","created_at":"2026-05-18T00:19:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06825","created_at":"2026-05-18T00:19:27Z"},{"alias_kind":"pith_short_12","alias_value":"644M3NU4Q4HC","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"644M3NU4Q4HCXF6O","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"644M3NU4","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:b3fbed99ee7b38abff826640281a81455902fa70d28c75b624e8c998bd3b2035","target":"graph","created_at":"2026-05-18T00:19:27Z","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":"Let $H$ denote the harmonic oscillator Hamiltonian on $\\mathbb{R}^d,$ perturbed by an isotropic pseudodifferential operator of order $1.$ We consider the Schr\\\"odinger propagator $U(t)=e^{-itH},$ and find that while $\\operatorname{singsupp} \\operatorname{Tr} U(t) \\subset 2 \\pi \\mathbb{Z}$ as in the unperturbed case, there exists a large class of perturbations in dimension $d \\geq 2$ for which the singularities of $\\operatorname{Tr} U(t)$ at nonzero multiples of $2 \\pi$ are weaker than the singularity at $t=0$. The remainder term in the Weyl law is of order $o(\\lambda^{d-1})$, improving in thes","authors_text":"Jared Wunsch, Moritz Doll, Oran Gannot","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-22T21:28:25Z","title":"Refined Weyl law for homogeneous perturbations of the harmonic oscillator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06825","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:c77e3e431f5e31edf94cd9fe4b3e5c6461e0f748ed19c5cae18f2392bf7d7964","target":"record","created_at":"2026-05-18T00:19:27Z","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":"6e9c76e39d243c47940f08bdcf8aee194e4a8f20e26dcfa2435591efd38f662d","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-22T21:28:25Z","title_canon_sha256":"fc730a02dcbc4ff73dbf6b5731e003eec183c90847a6448d3b58ed7033beb57f"},"schema_version":"1.0","source":{"id":"1708.06825","kind":"arxiv","version":3}},"canonical_sha256":"f738cdb69c870e2b97cefec87225fc7855c74021913eb06819ad34ea727d98f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f738cdb69c870e2b97cefec87225fc7855c74021913eb06819ad34ea727d98f9","first_computed_at":"2026-05-18T00:19:27.192905Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:27.192905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W2xc8+rVQKhS7ZARyY0qNWtzcYMbT21u3q8iLPk+0xYicfnPokZ8Vk3VWjvUCNddC3iamc6UQ9FKysdrl0RDDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:27.193470Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.06825","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c77e3e431f5e31edf94cd9fe4b3e5c6461e0f748ed19c5cae18f2392bf7d7964","sha256:b3fbed99ee7b38abff826640281a81455902fa70d28c75b624e8c998bd3b2035"],"state_sha256":"e70e07334bdaa47a5515017d1b75efa64456deb86b44085301b46569773af8fe"}