{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:Z662HV5STLDH6CBGO2VCEROTSR","short_pith_number":"pith:Z662HV5S","schema_version":"1.0","canonical_sha256":"cfbda3d7b29ac67f082676aa2245d3944003d207d7d3fa66d58adfe9c5371257","source":{"kind":"arxiv","id":"1710.00201","version":1},"attestation_state":"computed","paper":{"title":"Full Szeg\\H{o}-type trace asymptotics for ergodic operators on large boxes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Adrian Dietlein","submitted_at":"2017-09-30T13:54:17Z","abstract_excerpt":"We prove full Szeg\\H{o}-type large-box trace asymptotics for selfadjoint $\\mathbb{Z}^d$-ergodic operators $\\Omega\\ni \\omega\\mapsto H_\\omega$ acting on $L^2(\\mathbb{R}^d)$. More precisely, let $g$ be a bounded, compactly supported and real-valued function such that the (averaged) operator kernel of $g(H_\\omega)$ decays sufficiently fast, and let $h$ be a sufficiently smooth compactly supported function. We then prove a full asymptotic expansion of the averaged trace of the operator $h(g(H_\\omega)_{[-L,L]^d})$ in terms of the length-scale $L$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1710.00201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-09-30T13:54:17Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"84e810425cdfa69285118a79b1a6783c0e049a7038a4130d5ff85b166448b82e","abstract_canon_sha256":"e752635445dd3b34a8e98091d0adcdde4996b0f02072047d3da655009e9791ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:19.713521Z","signature_b64":"0nqgZaiK6SMSqVOZmeXEoI9ATTZQcLcNZCHTKwK3NIZAdT8pcf+dq5KwePDOxbAZoSxRWOjn9x1F/OgiQ9+lCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfbda3d7b29ac67f082676aa2245d3944003d207d7d3fa66d58adfe9c5371257","last_reissued_at":"2026-05-18T00:09:19.712886Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:19.712886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Full Szeg\\H{o}-type trace asymptotics for ergodic operators on large boxes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Adrian Dietlein","submitted_at":"2017-09-30T13:54:17Z","abstract_excerpt":"We prove full Szeg\\H{o}-type large-box trace asymptotics for selfadjoint $\\mathbb{Z}^d$-ergodic operators $\\Omega\\ni \\omega\\mapsto H_\\omega$ acting on $L^2(\\mathbb{R}^d)$. More precisely, let $g$ be a bounded, compactly supported and real-valued function such that the (averaged) operator kernel of $g(H_\\omega)$ decays sufficiently fast, and let $h$ be a sufficiently smooth compactly supported function. We then prove a full asymptotic expansion of the averaged trace of the operator $h(g(H_\\omega)_{[-L,L]^d})$ in terms of the length-scale $L$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00201","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1710.00201","created_at":"2026-05-18T00:09:19.712973+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.00201v1","created_at":"2026-05-18T00:09:19.712973+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00201","created_at":"2026-05-18T00:09:19.712973+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z662HV5STLDH","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z662HV5STLDH6CBG","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z662HV5S","created_at":"2026-05-18T12:31:59.375834+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z662HV5STLDH6CBGO2VCEROTSR","json":"https://pith.science/pith/Z662HV5STLDH6CBGO2VCEROTSR.json","graph_json":"https://pith.science/api/pith-number/Z662HV5STLDH6CBGO2VCEROTSR/graph.json","events_json":"https://pith.science/api/pith-number/Z662HV5STLDH6CBGO2VCEROTSR/events.json","paper":"https://pith.science/paper/Z662HV5S"},"agent_actions":{"view_html":"https://pith.science/pith/Z662HV5STLDH6CBGO2VCEROTSR","download_json":"https://pith.science/pith/Z662HV5STLDH6CBGO2VCEROTSR.json","view_paper":"https://pith.science/paper/Z662HV5S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.00201&json=true","fetch_graph":"https://pith.science/api/pith-number/Z662HV5STLDH6CBGO2VCEROTSR/graph.json","fetch_events":"https://pith.science/api/pith-number/Z662HV5STLDH6CBGO2VCEROTSR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z662HV5STLDH6CBGO2VCEROTSR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z662HV5STLDH6CBGO2VCEROTSR/action/storage_attestation","attest_author":"https://pith.science/pith/Z662HV5STLDH6CBGO2VCEROTSR/action/author_attestation","sign_citation":"https://pith.science/pith/Z662HV5STLDH6CBGO2VCEROTSR/action/citation_signature","submit_replication":"https://pith.science/pith/Z662HV5STLDH6CBGO2VCEROTSR/action/replication_record"}},"created_at":"2026-05-18T00:09:19.712973+00:00","updated_at":"2026-05-18T00:09:19.712973+00:00"}