{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XAMYMG7FYEYP22UL44YTPZXBGR","short_pith_number":"pith:XAMYMG7F","canonical_record":{"source":{"id":"1112.4930","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-12-21T06:33:08Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"583bfede318607e9e3bb0349426bfefda69416c68c89a0b8badff78e7bb90f12","abstract_canon_sha256":"075d6f83689241779c66661e46132f723f9fb33cd75893090a17565afd46aa29"},"schema_version":"1.0"},"canonical_sha256":"b819861be5c130fd6a8be73137e6e134794e47ebb2a490989d19e69bdc7bbede","source":{"kind":"arxiv","id":"1112.4930","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4930","created_at":"2026-05-18T04:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4930v2","created_at":"2026-05-18T04:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4930","created_at":"2026-05-18T04:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"XAMYMG7FYEYP","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XAMYMG7FYEYP22UL","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XAMYMG7F","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XAMYMG7FYEYP22UL44YTPZXBGR","target":"record","payload":{"canonical_record":{"source":{"id":"1112.4930","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-12-21T06:33:08Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"583bfede318607e9e3bb0349426bfefda69416c68c89a0b8badff78e7bb90f12","abstract_canon_sha256":"075d6f83689241779c66661e46132f723f9fb33cd75893090a17565afd46aa29"},"schema_version":"1.0"},"canonical_sha256":"b819861be5c130fd6a8be73137e6e134794e47ebb2a490989d19e69bdc7bbede","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:46.732251Z","signature_b64":"acLsfB7NpyxvRHbapVK3NTeGnixDAU9mVTcYJvvpqgK+qPZ+RsLoL06Q2rfK2ItnnJj+UKpfWAflyrJhgURfCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b819861be5c130fd6a8be73137e6e134794e47ebb2a490989d19e69bdc7bbede","last_reissued_at":"2026-05-18T04:05:46.731816Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:46.731816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.4930","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ReoYuBulbiQ2zb6Not6yQxeFPLSapgOEeokgetfBAwTABr3bn6AJP+hBGLf9yv83qP1Iv//yy6rD94bhsfhwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T00:06:43.125504Z"},"content_sha256":"368e9b11a0f219854c96f5656ab49fa59796b578a54f4fd9e98a73dc5c40ff17","schema_version":"1.0","event_id":"sha256:368e9b11a0f219854c96f5656ab49fa59796b578a54f4fd9e98a73dc5c40ff17"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XAMYMG7FYEYP22UL44YTPZXBGR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost normal operators mod Hilbert-Schmidt and the K-theory of the Banach algebras $E\\Lambda(\\Omega)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.OA","authors_text":"Dan-Virgil Voiculescu","submitted_at":"2011-12-21T06:33:08Z","abstract_excerpt":"Is there a mod Hilbert-Schmidt analogue of the BDF-theorem, with the Pincus g-function playing the role of the index ? We show that part of the question is about the K-theory of certain Banach algebras. These Banach algebras, related to Lipschitz functions and dirichlet algebras have nice Banach space duality properties. Moreover their corona algebras are C*-algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4930","kind":"arxiv","version":2},"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":"2026-05-18T04:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O9wTieH0txx8w4dFQFFn8mUoBcnn5CYK5V/FbFTIjW9lhxP+zHNRHz5vp/wTpZHAoq0yjROwJWYOXf/2o0ihCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T00:06:43.126193Z"},"content_sha256":"bf775eea19ed4c66668247c3187c29e050d262f5332d7e4409c42affd866734a","schema_version":"1.0","event_id":"sha256:bf775eea19ed4c66668247c3187c29e050d262f5332d7e4409c42affd866734a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XAMYMG7FYEYP22UL44YTPZXBGR/bundle.json","state_url":"https://pith.science/pith/XAMYMG7FYEYP22UL44YTPZXBGR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XAMYMG7FYEYP22UL44YTPZXBGR/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":"2026-06-10T00:06:43Z","links":{"resolver":"https://pith.science/pith/XAMYMG7FYEYP22UL44YTPZXBGR","bundle":"https://pith.science/pith/XAMYMG7FYEYP22UL44YTPZXBGR/bundle.json","state":"https://pith.science/pith/XAMYMG7FYEYP22UL44YTPZXBGR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XAMYMG7FYEYP22UL44YTPZXBGR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XAMYMG7FYEYP22UL44YTPZXBGR","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":"075d6f83689241779c66661e46132f723f9fb33cd75893090a17565afd46aa29","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-12-21T06:33:08Z","title_canon_sha256":"583bfede318607e9e3bb0349426bfefda69416c68c89a0b8badff78e7bb90f12"},"schema_version":"1.0","source":{"id":"1112.4930","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4930","created_at":"2026-05-18T04:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4930v2","created_at":"2026-05-18T04:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4930","created_at":"2026-05-18T04:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"XAMYMG7FYEYP","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XAMYMG7FYEYP22UL","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XAMYMG7F","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:bf775eea19ed4c66668247c3187c29e050d262f5332d7e4409c42affd866734a","target":"graph","created_at":"2026-05-18T04:05:46Z","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":"Is there a mod Hilbert-Schmidt analogue of the BDF-theorem, with the Pincus g-function playing the role of the index ? We show that part of the question is about the K-theory of certain Banach algebras. These Banach algebras, related to Lipschitz functions and dirichlet algebras have nice Banach space duality properties. Moreover their corona algebras are C*-algebras.","authors_text":"Dan-Virgil Voiculescu","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-12-21T06:33:08Z","title":"Almost normal operators mod Hilbert-Schmidt and the K-theory of the Banach algebras $E\\Lambda(\\Omega)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4930","kind":"arxiv","version":2},"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":"sha256:368e9b11a0f219854c96f5656ab49fa59796b578a54f4fd9e98a73dc5c40ff17","target":"record","created_at":"2026-05-18T04:05:46Z","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":"075d6f83689241779c66661e46132f723f9fb33cd75893090a17565afd46aa29","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-12-21T06:33:08Z","title_canon_sha256":"583bfede318607e9e3bb0349426bfefda69416c68c89a0b8badff78e7bb90f12"},"schema_version":"1.0","source":{"id":"1112.4930","kind":"arxiv","version":2}},"canonical_sha256":"b819861be5c130fd6a8be73137e6e134794e47ebb2a490989d19e69bdc7bbede","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b819861be5c130fd6a8be73137e6e134794e47ebb2a490989d19e69bdc7bbede","first_computed_at":"2026-05-18T04:05:46.731816Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:46.731816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"acLsfB7NpyxvRHbapVK3NTeGnixDAU9mVTcYJvvpqgK+qPZ+RsLoL06Q2rfK2ItnnJj+UKpfWAflyrJhgURfCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:46.732251Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4930","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:368e9b11a0f219854c96f5656ab49fa59796b578a54f4fd9e98a73dc5c40ff17","sha256:bf775eea19ed4c66668247c3187c29e050d262f5332d7e4409c42affd866734a"],"state_sha256":"0e45ec1d89a88846ec3a174237b2d64452801e20f3b7099201fb11a2e16e7450"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1s4t8BZ4TI8VSADqOQrTFUqYCxe8OsdBIqUzeWrB4DBrQ6XjAD817Ts/Ty/VEDNGMZdMPRCWk/FeR3Dhe3bBAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T00:06:43.130620Z","bundle_sha256":"671458628a2d01cb32e185f480c219767062819c3238723d382eb5c3b5d7bf33"}}