{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SADTRCKQXA2P3GOX753M2UI4YI","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":"7043b0b62ea249736e2a7e2caf81f2ef9dee13e4beb7c940d1ed235676fdaa60","cross_cats_sorted":["math.CA","math.CV","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-15T22:35:53Z","title_canon_sha256":"8c974eb48e5bc527b92af2a23a3c043d6b20b747596ed032c06ce266b1e5761d"},"schema_version":"1.0","source":{"id":"1603.04910","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04910","created_at":"2026-05-18T00:42:55Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04910v1","created_at":"2026-05-18T00:42:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04910","created_at":"2026-05-18T00:42:55Z"},{"alias_kind":"pith_short_12","alias_value":"SADTRCKQXA2P","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SADTRCKQXA2P3GOX","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SADTRCKQ","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:4718d064aac203f1ba0717569d41f2701c2385b7d758a4b3fb26695db34f4b95","target":"graph","created_at":"2026-05-18T00:42:55Z","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 study Schatten--von Neumann properties of multiple operator integrals with integrands in the Haagerup tensor product of $L^\\infty$ spaces. We obtain sharp, best possible estimates. This allowed us to obtain sharp Schatten--von Neumann estimates in the case of {\\it Haagerup-like} tensor products.","authors_text":"Alexei Aleksandrov, Vladimir Peller","cross_cats":["math.CA","math.CV","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-15T22:35:53Z","title":"Multiple operator integrals, Haagerup and Haagerup-like tensor products, and operator ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04910","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":"sha256:63cc969fbc8819f87b93f8ae1f60764e945840ddb52a6ad56a60bf6465c7d384","target":"record","created_at":"2026-05-18T00:42:55Z","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":"7043b0b62ea249736e2a7e2caf81f2ef9dee13e4beb7c940d1ed235676fdaa60","cross_cats_sorted":["math.CA","math.CV","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-15T22:35:53Z","title_canon_sha256":"8c974eb48e5bc527b92af2a23a3c043d6b20b747596ed032c06ce266b1e5761d"},"schema_version":"1.0","source":{"id":"1603.04910","kind":"arxiv","version":1}},"canonical_sha256":"9007388950b834fd99d7ff76cd511cc2088c173cdc26de5cd890162036d51ee9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9007388950b834fd99d7ff76cd511cc2088c173cdc26de5cd890162036d51ee9","first_computed_at":"2026-05-18T00:42:55.610379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:55.610379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ES3va5bRpbpnClr7QzRZjhQwkgDoj9cXIOWYQPfdteLV6dGQBLl1fsjQFSarfBv6A2Kcyvn5L1PC76FjGGxgDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:55.611046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04910","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63cc969fbc8819f87b93f8ae1f60764e945840ddb52a6ad56a60bf6465c7d384","sha256:4718d064aac203f1ba0717569d41f2701c2385b7d758a4b3fb26695db34f4b95"],"state_sha256":"e887407a42c2e7c089b8e6f3f882a73af92d1e83e4bb747eddd6fef6a3469362"}