{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:Q2SE7G3GJ6IHGJAHFDGIHRWLPX","short_pith_number":"pith:Q2SE7G3G","schema_version":"1.0","canonical_sha256":"86a44f9b664f9073240728cc83c6cb7df628630b83cb6e16d552bed2277a0ae4","source":{"kind":"arxiv","id":"2506.21950","version":1},"attestation_state":"computed","paper":{"title":"Trace Formulas in Noncommutative Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","math.SP"],"primary_cat":"math.OA","authors_text":"Eva-Maria Hekkelman","submitted_at":"2025-06-27T06:46:18Z","abstract_excerpt":"Trace formulas appear in many forms in noncommutative geometry (NCG). In the first part of this thesis, we obtain results for asymptotic expansions of trace formulas like heat trace expansions by adapting the theory of Multiple Operator Integration to NCG. More broadly, this construction provides a natural language for operator integrals in NCG, which systematises and simplifies operator integral arguments throughout the literature. Towards this end, we construct a functional calculus for abstract pseudodifferential operators and generalise Peller's construction of multiple operator integrals "},"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":"2506.21950","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2025-06-27T06:46:18Z","cross_cats_sorted":["math-ph","math.FA","math.MP","math.SP"],"title_canon_sha256":"ac3c03979a7e314bf729b664b794d24ff0b07a0b38e020d0d958fe6ada3f52b4","abstract_canon_sha256":"cd84da4bc245b30fa32ca8e36e0673c4dc4f3adab207c204d0730ef6a3d83524"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:28:18.990186Z","signature_b64":"A0t59JvZ07nLAryMavydoPREwja9OhBkRffdHUQTQTNxAI/2xx7zU4G1tYIEwqyKy4z0pTc58zkGfCzLoYRrCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86a44f9b664f9073240728cc83c6cb7df628630b83cb6e16d552bed2277a0ae4","last_reissued_at":"2026-07-05T11:28:18.989794Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:28:18.989794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Trace Formulas in Noncommutative Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","math.SP"],"primary_cat":"math.OA","authors_text":"Eva-Maria Hekkelman","submitted_at":"2025-06-27T06:46:18Z","abstract_excerpt":"Trace formulas appear in many forms in noncommutative geometry (NCG). In the first part of this thesis, we obtain results for asymptotic expansions of trace formulas like heat trace expansions by adapting the theory of Multiple Operator Integration to NCG. More broadly, this construction provides a natural language for operator integrals in NCG, which systematises and simplifies operator integral arguments throughout the literature. Towards this end, we construct a functional calculus for abstract pseudodifferential operators and generalise Peller's construction of multiple operator integrals "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.21950","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.21950/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.21950","created_at":"2026-07-05T11:28:18.989848+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.21950v1","created_at":"2026-07-05T11:28:18.989848+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.21950","created_at":"2026-07-05T11:28:18.989848+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q2SE7G3GJ6IH","created_at":"2026-07-05T11:28:18.989848+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q2SE7G3GJ6IHGJAH","created_at":"2026-07-05T11:28:18.989848+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q2SE7G3G","created_at":"2026-07-05T11:28:18.989848+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/Q2SE7G3GJ6IHGJAHFDGIHRWLPX","json":"https://pith.science/pith/Q2SE7G3GJ6IHGJAHFDGIHRWLPX.json","graph_json":"https://pith.science/api/pith-number/Q2SE7G3GJ6IHGJAHFDGIHRWLPX/graph.json","events_json":"https://pith.science/api/pith-number/Q2SE7G3GJ6IHGJAHFDGIHRWLPX/events.json","paper":"https://pith.science/paper/Q2SE7G3G"},"agent_actions":{"view_html":"https://pith.science/pith/Q2SE7G3GJ6IHGJAHFDGIHRWLPX","download_json":"https://pith.science/pith/Q2SE7G3GJ6IHGJAHFDGIHRWLPX.json","view_paper":"https://pith.science/paper/Q2SE7G3G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.21950&json=true","fetch_graph":"https://pith.science/api/pith-number/Q2SE7G3GJ6IHGJAHFDGIHRWLPX/graph.json","fetch_events":"https://pith.science/api/pith-number/Q2SE7G3GJ6IHGJAHFDGIHRWLPX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q2SE7G3GJ6IHGJAHFDGIHRWLPX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q2SE7G3GJ6IHGJAHFDGIHRWLPX/action/storage_attestation","attest_author":"https://pith.science/pith/Q2SE7G3GJ6IHGJAHFDGIHRWLPX/action/author_attestation","sign_citation":"https://pith.science/pith/Q2SE7G3GJ6IHGJAHFDGIHRWLPX/action/citation_signature","submit_replication":"https://pith.science/pith/Q2SE7G3GJ6IHGJAHFDGIHRWLPX/action/replication_record"}},"created_at":"2026-07-05T11:28:18.989848+00:00","updated_at":"2026-07-05T11:28:18.989848+00:00"}