{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:CSEODKRRZLBDEJRFK7ZRIVZOMO","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":"85410bc7e6dcac71cc0719e015c6e5ee1f31592fc3cdab135307a7c6bf77fa0f","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2025-02-07T20:17:28Z","title_canon_sha256":"4f5d5b1df2d335394b9318d9f6916498e817f9225e4e6a4176fc90f139bfe796"},"schema_version":"1.0","source":{"id":"2502.05306","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.05306","created_at":"2026-07-05T11:57:34Z"},{"alias_kind":"arxiv_version","alias_value":"2502.05306v3","created_at":"2026-07-05T11:57:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.05306","created_at":"2026-07-05T11:57:34Z"},{"alias_kind":"pith_short_12","alias_value":"CSEODKRRZLBD","created_at":"2026-07-05T11:57:34Z"},{"alias_kind":"pith_short_16","alias_value":"CSEODKRRZLBDEJRF","created_at":"2026-07-05T11:57:34Z"},{"alias_kind":"pith_short_8","alias_value":"CSEODKRR","created_at":"2026-07-05T11:57:34Z"}],"graph_snapshots":[{"event_id":"sha256:fde875b637611ac04fd297fbcd1619a52a8c3832976957b309b674154c62b576","target":"graph","created_at":"2026-07-05T11:57:34Z","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/2502.05306/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Drazin inverses are a special kind of generalized inverses that can be defined for endomorphisms in any category. A natural question to ask is whether one can somehow extend the notion of Drazin inverse to arbitrary maps - not simply endomorphisms. It turns out that this is possible and, indeed, natural to do so for dagger categories. This paper, thus, introduces the notion of a dagger-Drazin inverse, which is a new kind of generalized inverse appropriate for arbitrary maps in a dagger category. This inverse is closely related to the Drazin inverse, for having dagger-Drazin inverses is equival","authors_text":"Jean-Simon Pacaud Lemay (Macquarie University), Priyaa Varshinee Srinivasan (Tallinn University of Technology), Robin Cockett (University of Calgary)","cross_cats":["quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2025-02-07T20:17:28Z","title":"Dagger-Drazin Inverses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.05306","kind":"arxiv","version":3},"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:ffa928e34fd20cff1e9ed79e11e13849200372ec57849f2a0b9b1f83f76ac5b2","target":"record","created_at":"2026-07-05T11:57:34Z","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":"85410bc7e6dcac71cc0719e015c6e5ee1f31592fc3cdab135307a7c6bf77fa0f","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2025-02-07T20:17:28Z","title_canon_sha256":"4f5d5b1df2d335394b9318d9f6916498e817f9225e4e6a4176fc90f139bfe796"},"schema_version":"1.0","source":{"id":"2502.05306","kind":"arxiv","version":3}},"canonical_sha256":"1488e1aa31cac232262557f314572e63a6dffb7896b5e53dbee7729d28a72fda","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1488e1aa31cac232262557f314572e63a6dffb7896b5e53dbee7729d28a72fda","first_computed_at":"2026-07-05T11:57:34.315523Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:57:34.315523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lA+3SHxR2SJ5cVKTzhnNLheDZgyQtg9j6cVcnNDTr+SjkCgRm1ckiphvnR+OtaNHsLFvOP5xDZIc4+DoZ6SEAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:57:34.316038Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.05306","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffa928e34fd20cff1e9ed79e11e13849200372ec57849f2a0b9b1f83f76ac5b2","sha256:fde875b637611ac04fd297fbcd1619a52a8c3832976957b309b674154c62b576"],"state_sha256":"75b987c42d2ffe7a4b75094a0659819007126170eecefb8699650a7d0a45686c"}