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We consider the differential complex of forms $u_0\\ccr{\\eps}{u_1}\\cdots\\ccr{\\eps}{u_n}$ with $\\eps$ a grading operator on a Hilbert space $\\cH$ and $u_i$ bounded operators on $\\cH$ which naturally contains the compactly supported de Rham forms on $\\R^d$ (i.e.\\ $\\eps$ is the sign of the free Dirac operator on $\\R^d$ and $\\cH$ a $L^2$--space on $\\R^d$). We present an elementary proof that the integral of $d$--forms $\\int_{\\R^d}\\trac{X_0\\dd X_1\\cdots \\dd X_d}$ f"},"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":"hep-th/9501092","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1995-01-20T13:04:11Z","cross_cats_sorted":[],"title_canon_sha256":"4e598050b95e6d4e83c4492f6a27fa476caa8b990a4d5d818b3f77c9ffbaddc3","abstract_canon_sha256":"0cbe181f0ce3ef8f83b809062d082b10efab5677d8ee8267547229f90ad8e9fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:03.798595Z","signature_b64":"4ndc3abW5YqeuZNBCfKaL8gp4yXj4V0j5pcslmbEZIAqqhKxudnAllByxrvV1Ib8v3gy13dzlLaSqPsWXI26Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eff2816ae74e30b61bfc92dd3b947caa80d06dd91483e18ae9146f65cd0b7b02","last_reissued_at":"2026-05-18T01:06:03.798069Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:03.798069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non--commutative Integration Calculus","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Edwin Langmann","submitted_at":"1995-01-20T13:04:11Z","abstract_excerpt":"We discuss a non--commutative integration calculus arising in the mathematical description of anomalies in fermion--Yang--Mills systems. 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