{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1995:57ZIC2XHJYYLMG74SLOTXFD4VK","short_pith_number":"pith:57ZIC2XH","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"},"canonical_sha256":"eff2816ae74e30b61bfc92dd3b947caa80d06dd91483e18ae9146f65cd0b7b02","source":{"kind":"arxiv","id":"hep-th/9501092","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9501092","created_at":"2026-05-18T01:06:03Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9501092v1","created_at":"2026-05-18T01:06:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9501092","created_at":"2026-05-18T01:06:03Z"},{"alias_kind":"pith_short_12","alias_value":"57ZIC2XHJYYL","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"57ZIC2XHJYYLMG74","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"57ZIC2XH","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1995:57ZIC2XHJYYLMG74SLOTXFD4VK","target":"record","payload":{"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"},"canonical_sha256":"eff2816ae74e30b61bfc92dd3b947caa80d06dd91483e18ae9146f65cd0b7b02","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"},"source_kind":"arxiv","source_id":"hep-th/9501092","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:06:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/nEqS6P1TQuGeWcqJaiKFiyBELyI8hfHceY0TLktjoq4/4Imp8Q49foMlTq+WDDA5Dd++i7jL6LOdL4cVWP8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:44:33.199888Z"},"content_sha256":"96634c28a17fe07d83fa908c0641c0f05cccf2fa17400a9c24dd12cab9af94d5","schema_version":"1.0","event_id":"sha256:96634c28a17fe07d83fa908c0641c0f05cccf2fa17400a9c24dd12cab9af94d5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1995:57ZIC2XHJYYLMG74SLOTXFD4VK","target":"graph","payload":{"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. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9501092","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:06:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hmhREY91GJYpgQ606GdlqnFGa27w0iUApVtFHOQ7d52Zh3ltZNFrcLz4UXYXvmcsifHzwX0jWUTbqljvS8VPAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:44:33.200537Z"},"content_sha256":"26b5d945bb18bfc8b6d907489c258ce5f96f756c6521fc3465866f41404b6638","schema_version":"1.0","event_id":"sha256:26b5d945bb18bfc8b6d907489c258ce5f96f756c6521fc3465866f41404b6638"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/57ZIC2XHJYYLMG74SLOTXFD4VK/bundle.json","state_url":"https://pith.science/pith/57ZIC2XHJYYLMG74SLOTXFD4VK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/57ZIC2XHJYYLMG74SLOTXFD4VK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T21:44:33Z","links":{"resolver":"https://pith.science/pith/57ZIC2XHJYYLMG74SLOTXFD4VK","bundle":"https://pith.science/pith/57ZIC2XHJYYLMG74SLOTXFD4VK/bundle.json","state":"https://pith.science/pith/57ZIC2XHJYYLMG74SLOTXFD4VK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/57ZIC2XHJYYLMG74SLOTXFD4VK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:57ZIC2XHJYYLMG74SLOTXFD4VK","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":"0cbe181f0ce3ef8f83b809062d082b10efab5677d8ee8267547229f90ad8e9fa","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1995-01-20T13:04:11Z","title_canon_sha256":"4e598050b95e6d4e83c4492f6a27fa476caa8b990a4d5d818b3f77c9ffbaddc3"},"schema_version":"1.0","source":{"id":"hep-th/9501092","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9501092","created_at":"2026-05-18T01:06:03Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9501092v1","created_at":"2026-05-18T01:06:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9501092","created_at":"2026-05-18T01:06:03Z"},{"alias_kind":"pith_short_12","alias_value":"57ZIC2XHJYYL","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"57ZIC2XHJYYLMG74","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"57ZIC2XH","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:26b5d945bb18bfc8b6d907489c258ce5f96f756c6521fc3465866f41404b6638","target":"graph","created_at":"2026-05-18T01:06:03Z","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":"We discuss a non--commutative integration calculus arising in the mathematical description of anomalies in fermion--Yang--Mills systems. 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","authors_text":"Edwin Langmann","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1995-01-20T13:04:11Z","title":"Non--commutative Integration Calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9501092","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":"sha256:96634c28a17fe07d83fa908c0641c0f05cccf2fa17400a9c24dd12cab9af94d5","target":"record","created_at":"2026-05-18T01:06:03Z","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":"0cbe181f0ce3ef8f83b809062d082b10efab5677d8ee8267547229f90ad8e9fa","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1995-01-20T13:04:11Z","title_canon_sha256":"4e598050b95e6d4e83c4492f6a27fa476caa8b990a4d5d818b3f77c9ffbaddc3"},"schema_version":"1.0","source":{"id":"hep-th/9501092","kind":"arxiv","version":1}},"canonical_sha256":"eff2816ae74e30b61bfc92dd3b947caa80d06dd91483e18ae9146f65cd0b7b02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eff2816ae74e30b61bfc92dd3b947caa80d06dd91483e18ae9146f65cd0b7b02","first_computed_at":"2026-05-18T01:06:03.798069Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:03.798069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4ndc3abW5YqeuZNBCfKaL8gp4yXj4V0j5pcslmbEZIAqqhKxudnAllByxrvV1Ib8v3gy13dzlLaSqPsWXI26Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:03.798595Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9501092","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96634c28a17fe07d83fa908c0641c0f05cccf2fa17400a9c24dd12cab9af94d5","sha256:26b5d945bb18bfc8b6d907489c258ce5f96f756c6521fc3465866f41404b6638"],"state_sha256":"2e33769c1c005733dd88d929a359bd1645a06aa6094294e6b7a4a22e1667f65b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SL+mAI+ookJN63/QID2z1jLn5XcFIh7YTHUUPtAHREu2pLF+G73PVmIV8eMqNzcvDNa0r7uKr6y2wm8yJBbfCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:44:33.203698Z","bundle_sha256":"bb3b2b3fd876a4117965a5a78542fb21411b564c950597c14a52d9f411097d98"}}