{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HGGQCJ2QVWWWDV5HX5E4CWD5CR","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":"d5a537187f9cc634643607ce85fb13e78e6484958ea784980ac41021c2316e00","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2025-09-02T06:28:26Z","title_canon_sha256":"41ce3f0601784da539eb13eb2baeb685cc52d599b11a31efd6a91f5671913980"},"schema_version":"1.0","source":{"id":"2509.02001","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.02001","created_at":"2026-07-05T12:03:12Z"},{"alias_kind":"arxiv_version","alias_value":"2509.02001v1","created_at":"2026-07-05T12:03:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.02001","created_at":"2026-07-05T12:03:12Z"},{"alias_kind":"pith_short_12","alias_value":"HGGQCJ2QVWWW","created_at":"2026-07-05T12:03:12Z"},{"alias_kind":"pith_short_16","alias_value":"HGGQCJ2QVWWWDV5H","created_at":"2026-07-05T12:03:12Z"},{"alias_kind":"pith_short_8","alias_value":"HGGQCJ2Q","created_at":"2026-07-05T12:03:12Z"}],"graph_snapshots":[{"event_id":"sha256:2c9428413b3a84d48dfd283927090adfba692a7c63d1df4780bc4244c43c2aca","target":"graph","created_at":"2026-07-05T12:03:12Z","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/2509.02001/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a class of good endofunctors of $C^{*}$-algebras, endow it with a structure of a bimonoidal category, and define homotopies of natural transformations between such endofunctors. For every pair of $C^{*}$-algebras and a good endofunctor, we construct a commutative monoid of generalized morphisms, and endow these monoids with a bilinear composition. This construction generalizes the homotopy category of asymptotic homomorphisms used in the definition of the Connes-Higson $E$-theory. We also introduce the notion of asymptotically adjoint good endofunctors, which has interesting appli","authors_text":"Georgii S. Makeev","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2025-09-02T06:28:26Z","title":"On generalized morphisms associated to endofunctors of C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.02001","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":"sha256:6602a3bdc99dddf95536a362f0fc82b6cd42fe865d863bdcd101074fae776a6c","target":"record","created_at":"2026-07-05T12:03:12Z","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":"d5a537187f9cc634643607ce85fb13e78e6484958ea784980ac41021c2316e00","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2025-09-02T06:28:26Z","title_canon_sha256":"41ce3f0601784da539eb13eb2baeb685cc52d599b11a31efd6a91f5671913980"},"schema_version":"1.0","source":{"id":"2509.02001","kind":"arxiv","version":1}},"canonical_sha256":"398d012750adad61d7a7bf49c1587d146f17384af55ea6acff865bcd64a02c47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"398d012750adad61d7a7bf49c1587d146f17384af55ea6acff865bcd64a02c47","first_computed_at":"2026-07-05T12:03:12.620718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:03:12.620718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y09RA/x2m8U5BUYLxcDmzlx+lSLVThlr2znPxTGR0xdukqWds4gLwJl+2yaZDBboomXQX73GmoZl/4MNvDguCw==","signature_status":"signed_v1","signed_at":"2026-07-05T12:03:12.621161Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.02001","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6602a3bdc99dddf95536a362f0fc82b6cd42fe865d863bdcd101074fae776a6c","sha256:2c9428413b3a84d48dfd283927090adfba692a7c63d1df4780bc4244c43c2aca"],"state_sha256":"0271be814eec4fbb1e620caff3df153cba5721bec452a824236703049f888c43"}