{"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. We extract the deviations from the leading exponential behavior of the KNO scaled probability and identify a reciprocal symmetry $z\\leftrightarrow 1/z$ in the KNO violating corrections observed in the ATLAS and CMS data at $\\sqrt{s}=7,\\,8,\\,13$~TeV. 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"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We extract the deviations from the leading exponential behavior of the KNO scaled probability and identify a reciprocal symmetry z↔1/z in the KNO violating corrections observed in the ATLAS and CMS data at √s=7,8,13 TeV. The symmetry imposes a local constraint on the multiplicity distribution at n=⟨n⟩, namely P'(⟨n⟩)=−P(⟨n⟩)/⟨n⟩, which we verify directly in the data. We use this constraint to extract the entanglement entropy from the well-measured region n≃⟨n⟩, avoiding the large uncertainties associated with the distribution tail.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the observed z↔1/z symmetry in the KNO-violating corrections is a genuine physical feature of the multiplicity distribution rather than an artifact of the specific data sets, binning choices, or analysis procedure, and that the resulting local constraint at n=⟨n⟩ is sufficient by itself to determine the entanglement entropy without further model assumptions about the global shape of P(n).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A z ↔ 1/z reciprocal symmetry is found in KNO scaling violations in pp collisions, imposing the constraint P'(⟨n⟩) = −P(⟨n⟩)/⟨n⟩ that enables entanglement entropy extraction from the well-measured multiplicity region.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"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.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"037ec3e7d60c6c37a28870e1848dff120243ac4119d79a8749acb38bfb910cfe"},"source":{"id":"2605.00128","kind":"arxiv","version":2},"verdict":{"id":"d057ecb2-665f-48ab-8434-1cc9bd9059c0","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T20:22:18.974773Z","strongest_claim":"We extract the deviations from the leading exponential behavior of the KNO scaled probability and identify a reciprocal symmetry z↔1/z in the KNO violating corrections observed in the ATLAS and CMS data at √s=7,8,13 TeV. The symmetry imposes a local constraint on the multiplicity distribution at n=⟨n⟩, namely P'(⟨n⟩)=−P(⟨n⟩)/⟨n⟩, which we verify directly in the data. We use this constraint to extract the entanglement entropy from the well-measured region n≃⟨n⟩, avoiding the large uncertainties associated with the distribution tail.","one_line_summary":"A z ↔ 1/z reciprocal symmetry is found in KNO scaling violations in pp collisions, imposing the constraint P'(⟨n⟩) = −P(⟨n⟩)/⟨n⟩ that enables entanglement entropy extraction from the well-measured multiplicity region.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the observed z↔1/z symmetry in the KNO-violating corrections is a genuine physical feature of the multiplicity distribution rather than an artifact of the specific data sets, binning choices, or analysis procedure, and that the resulting local constraint at n=⟨n⟩ is sufficient by itself to determine the entanglement entropy without further model assumptions about the global shape of P(n).","pith_extraction_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."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.00128/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T20:37:32.438390Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T18:28:01.860016Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"dc2d6a821133b57a58b9a6d3d7eef6b1d9f199d1bd79e255a2135769494c6eb0"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}