{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:7SIRTX5VZ4SYTZWMXI352F6JPX","short_pith_number":"pith:7SIRTX5V","canonical_record":{"source":{"id":"math/0212136","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2002-12-10T06:16:13Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"85b2ffe2587333f7a0d1faabb9db73814b1d49756415f6f042c7092c5be80cd5","abstract_canon_sha256":"2ab6db9cc43c1a94909dd9ac427c0d81697bc371de3893cf5bca57b2c105e9bf"},"schema_version":"1.0"},"canonical_sha256":"fc9119dfb5cf2589e6ccba37dd17c97dc115b317f9f04e08dc52ce32f26715d1","source":{"kind":"arxiv","id":"math/0212136","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0212136","created_at":"2026-07-04T14:36:49Z"},{"alias_kind":"arxiv_version","alias_value":"math/0212136v1","created_at":"2026-07-04T14:36:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0212136","created_at":"2026-07-04T14:36:49Z"},{"alias_kind":"pith_short_12","alias_value":"7SIRTX5VZ4SY","created_at":"2026-07-04T14:36:49Z"},{"alias_kind":"pith_short_16","alias_value":"7SIRTX5VZ4SYTZWM","created_at":"2026-07-04T14:36:49Z"},{"alias_kind":"pith_short_8","alias_value":"7SIRTX5V","created_at":"2026-07-04T14:36:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:7SIRTX5VZ4SYTZWMXI352F6JPX","target":"record","payload":{"canonical_record":{"source":{"id":"math/0212136","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2002-12-10T06:16:13Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"85b2ffe2587333f7a0d1faabb9db73814b1d49756415f6f042c7092c5be80cd5","abstract_canon_sha256":"2ab6db9cc43c1a94909dd9ac427c0d81697bc371de3893cf5bca57b2c105e9bf"},"schema_version":"1.0"},"canonical_sha256":"fc9119dfb5cf2589e6ccba37dd17c97dc115b317f9f04e08dc52ce32f26715d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:36:49.042380Z","signature_b64":"gOezP86UsdYQi8WZek37AOgwVpHXrC/squmjyjNFSTYjWMTHhwguZ1DTPN992xYpb1bxjo4RvnauQNqCJsOjAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc9119dfb5cf2589e6ccba37dd17c97dc115b317f9f04e08dc52ce32f26715d1","last_reissued_at":"2026-07-04T14:36:49.041994Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:36:49.041994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0212136","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":"2026-07-04T14:36:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xCqemKRAkz/DPlETnZd4HbfqSrnIl/8bvmPtrNFG+uG3hHmfQaieV78pqqE8TbiuP1t8FlG+KS8bEXapL00cDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:15:51.240721Z"},"content_sha256":"e458ca402a6bd2cf26abf7986856fe899313fbe5d6b35c6eea006fac850a97f5","schema_version":"1.0","event_id":"sha256:e458ca402a6bd2cf26abf7986856fe899313fbe5d6b35c6eea006fac850a97f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:7SIRTX5VZ4SYTZWMXI352F6JPX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Notes on Operator Categories","license":"","headline":"","cross_cats":["math.CT"],"primary_cat":"math.OA","authors_text":"Shigeru Yamagami","submitted_at":"2002-12-10T06:16:13Z","abstract_excerpt":"The bicategory of normal functors between W*-categories is monoidally equivalent to the bicategory of W*-bimodules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0212136","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/math/0212136/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:36:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rEc2/7SGSiN8VtiltafhrXaGCg8dCxD3AsRdaQUv+r64b8NIlC/vVyUWl4LxpWT6octkrsdsnoBXqgcaBTdsBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:15:51.241902Z"},"content_sha256":"65fd91cfb7b973e16cf30e3429d26ec1bbbd8aef3821570cc33dc821e55e8918","schema_version":"1.0","event_id":"sha256:65fd91cfb7b973e16cf30e3429d26ec1bbbd8aef3821570cc33dc821e55e8918"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7SIRTX5VZ4SYTZWMXI352F6JPX/bundle.json","state_url":"https://pith.science/pith/7SIRTX5VZ4SYTZWMXI352F6JPX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7SIRTX5VZ4SYTZWMXI352F6JPX/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":"2026-08-16T19:15:51Z","links":{"resolver":"https://pith.science/pith/7SIRTX5VZ4SYTZWMXI352F6JPX","bundle":"https://pith.science/pith/7SIRTX5VZ4SYTZWMXI352F6JPX/bundle.json","state":"https://pith.science/pith/7SIRTX5VZ4SYTZWMXI352F6JPX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7SIRTX5VZ4SYTZWMXI352F6JPX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:7SIRTX5VZ4SYTZWMXI352F6JPX","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":"2ab6db9cc43c1a94909dd9ac427c0d81697bc371de3893cf5bca57b2c105e9bf","cross_cats_sorted":["math.CT"],"license":"","primary_cat":"math.OA","submitted_at":"2002-12-10T06:16:13Z","title_canon_sha256":"85b2ffe2587333f7a0d1faabb9db73814b1d49756415f6f042c7092c5be80cd5"},"schema_version":"1.0","source":{"id":"math/0212136","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0212136","created_at":"2026-07-04T14:36:49Z"},{"alias_kind":"arxiv_version","alias_value":"math/0212136v1","created_at":"2026-07-04T14:36:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0212136","created_at":"2026-07-04T14:36:49Z"},{"alias_kind":"pith_short_12","alias_value":"7SIRTX5VZ4SY","created_at":"2026-07-04T14:36:49Z"},{"alias_kind":"pith_short_16","alias_value":"7SIRTX5VZ4SYTZWM","created_at":"2026-07-04T14:36:49Z"},{"alias_kind":"pith_short_8","alias_value":"7SIRTX5V","created_at":"2026-07-04T14:36:49Z"}],"graph_snapshots":[{"event_id":"sha256:65fd91cfb7b973e16cf30e3429d26ec1bbbd8aef3821570cc33dc821e55e8918","target":"graph","created_at":"2026-07-04T14:36:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0212136/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The bicategory of normal functors between W*-categories is monoidally equivalent to the bicategory of W*-bimodules.","authors_text":"Shigeru Yamagami","cross_cats":["math.CT"],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2002-12-10T06:16:13Z","title":"Notes on Operator Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0212136","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:e458ca402a6bd2cf26abf7986856fe899313fbe5d6b35c6eea006fac850a97f5","target":"record","created_at":"2026-07-04T14:36:49Z","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":"2ab6db9cc43c1a94909dd9ac427c0d81697bc371de3893cf5bca57b2c105e9bf","cross_cats_sorted":["math.CT"],"license":"","primary_cat":"math.OA","submitted_at":"2002-12-10T06:16:13Z","title_canon_sha256":"85b2ffe2587333f7a0d1faabb9db73814b1d49756415f6f042c7092c5be80cd5"},"schema_version":"1.0","source":{"id":"math/0212136","kind":"arxiv","version":1}},"canonical_sha256":"fc9119dfb5cf2589e6ccba37dd17c97dc115b317f9f04e08dc52ce32f26715d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc9119dfb5cf2589e6ccba37dd17c97dc115b317f9f04e08dc52ce32f26715d1","first_computed_at":"2026-07-04T14:36:49.041994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:36:49.041994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gOezP86UsdYQi8WZek37AOgwVpHXrC/squmjyjNFSTYjWMTHhwguZ1DTPN992xYpb1bxjo4RvnauQNqCJsOjAQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:36:49.042380Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0212136","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e458ca402a6bd2cf26abf7986856fe899313fbe5d6b35c6eea006fac850a97f5","sha256:65fd91cfb7b973e16cf30e3429d26ec1bbbd8aef3821570cc33dc821e55e8918"],"state_sha256":"963dd7356f2a79f7f06e26e4ddf2b8c1c7fa5120cbddb2f1954b37bc76c8de05"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n5IoNxatZCP9Edpt2TBoJkL0yKRUKi0Q1DMo9C41oOOIXujeivWVY3oAdtoe9qka6yt/1AzACH5fDAHIvtVaBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T19:15:51.248602Z","bundle_sha256":"99f6c5d6eb1d180a60cf5fc34efd36a89b4eea522c0806ca753f7fc534f1b001"}}