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The symmetry imposes a local constraint on the multiplicity distribution at $n=\\langle n\\rangle$, namely $P'(\\langle n\\rangle)=-P(\\langle n\\rangle)/\\langle n\\rangle$, which we verify directly in the da"},"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":"2605.00128","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2026-04-30T18:31:38Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"75b4539c695c9bd1e683e9cd6548f3c750917724c754c2f3072913b1959ea38a","abstract_canon_sha256":"93f651912181a7ff695fb0c8c06b0924ca45145a73a92a5ca4c9d1d6c2411371"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:04:11.591861Z","signature_b64":"rPna7xSZBlNiu1N77aioh4Vknupu63SSF+9SAY6ZkDrJtulH85YPxv8A5XSbo5vE4O9Z4jgSlFJ8D7TNvxTcCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1654d798af9f4ee0c5e7bbe7330ef82a4042f6fccfd48f83899338eb4de595b6","last_reissued_at":"2026-05-26T02:04:11.591223Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:04:11.591223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reciprocal symmetry and KNO scaling violation in proton-proton collisions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A reciprocal symmetry z ↔ 1/z in KNO scaling violations of proton-proton collisions imposes a local constraint that allows extraction of entanglement entropy from the central region of the multiplicity distribution.","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Alex Prygarin, Mustapha Ouchen","submitted_at":"2026-04-30T18:31:38Z","abstract_excerpt":"We analyze the charged particle multiplicity distributions in $p-p$ collisions and discuss the violation of the Koba--Nielsen--Olesen (KNO) scaling. 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