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We consider a $q$-ary noisy permutation channel where the transmitted vector is first permuted by a permutation chosen uniformly at random, and then passed through a DMC with strictly positive entries in its transition probability matrix $U$. In an earlier work, we showed that over $q$-ary noiseless permutation channel, $2^{c_n n^{q-1}}$ messa"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2412.11091","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2024-12-15T07:22:06Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"cc065ea275a782916b7622a8a5315ad4fe4bba5205355ca18318af382568bffa","abstract_canon_sha256":"e35c1e26c5a28eda9bf3e3a9e9f23bb9b69d4e23ea9e86759b8d3ff8379b6b4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:22:34.839349Z","signature_b64":"iNVeoTFTIbAdFUOgC8f7n6Fwy8OXCbZ+/VJlU7CiZ/rGGqVX2r4U5RSoWEGLkzAJCyeWczkOOxH4xDYM9O7fDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c178c790fd436e866e41569be5a1bbe507b3b4e7a47c79dc5fc816d162d2df12","last_reissued_at":"2026-07-05T11:22:34.838797Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:22:34.838797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Identification Over Noisy Permutation Channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Abhishek Sarkar, Bikash Kumar Dey","submitted_at":"2024-12-15T07:22:06Z","abstract_excerpt":"We study message identification over the noisy permutation channel. 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