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(Stated in the opening of the abstract as the basis for solving the listed open problems.)"}},"verdict_id":"2a8e9313-2b21-4337-9c81-df2cef7482dc"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a74edaf7b608088523c0dbe7306f74a1d201e9c4cb5d090e60f04b08fc52014a","target":"record","created_at":"2026-05-20T00:02:35Z","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":"b0aa3af01b117c50a49083ec7b014c0926842fc871a31d8e738d8423f050f65e","cross_cats_sorted":["math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2026-05-15T22:11:21Z","title_canon_sha256":"1ce14febbfb5ec412b5a1a4165cbcaaedc7c30c1df52a5789e8a2698fd548fd1"},"schema_version":"1.0","source":{"id":"2605.16669","kind":"arxiv","version":1}},"canonical_sha256":"3e46b108dba19ee00fdfd4d9c80ab9a9bf7debd47b5c28e30cd2426142c8f527","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e46b108dba19ee00fdfd4d9c80ab9a9bf7debd47b5c28e30cd2426142c8f527","first_computed_at":"2026-05-20T00:02:35.455721Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:02:35.455721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YxPwdvlhEPls5oShp+dyfOglaOYyIerTiiLm1ov0YyCIh8k1OI8CQwS+yBE0Hf4026K62DMsqCdlt+QBAEB8Dw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:02:35.456566Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16669","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a74edaf7b608088523c0dbe7306f74a1d201e9c4cb5d090e60f04b08fc52014a","sha256:bafdb635cb7c90a97150cee263687c1cee48457d58e08f83c4ba84e54aba9ea4"],"state_sha256":"913ccfa6668cc86b802be46ae2bdf33acec45076c5c6474972486f972868f5e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"48KLrCYFtoMFpIXFxut9um0NS/tLIPm6wuT9Zf/ggI7mPn1IlnejLkhBiBiK2XvSo1DOnlv+kD+Gq7nMHoKNAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T12:51:31.191223Z","bundle_sha256":"bc9afa71c49ff343528fc740eda4e4d845c9921988326f6fcc6f09e090a8fc99"}}