{"paper":{"title":"Higher-order local constraints from reciprocal symmetry and entanglement entropy of charged-particle multiplicity distributions in $pp$ collisions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Reciprocal symmetry of the scaling function implies local algebraic constraints on multiplicity distributions at the mean.","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Alex Prygarin, Claudelle Capasia Madjuogang Sandeu, Mustapha Ouchen","submitted_at":"2026-05-09T06:45:19Z","abstract_excerpt":"The KNO-violating term $f_s$ of the charged-particle multiplicity distribution in $pp$ collisions measures the relative deviation of $\\langle n\\rangle P_n$ from $e^{-z}$, with $z=n/\\langle n\\rangle$, and is reported to obey the reciprocal symmetry $f_s(z)=f_s(1/z)$, taken here as input. Being an evenness condition in $\\ln z$, it generates a tower of local constraints on the derivatives of $P_n$ at the mean. The lowest member holds for the ATLAS data at $7$, $8$ and $13$~TeV at the few-per-cent level, while the third-derivative residual testing the next member is not determined with a controlle"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The k=1 constraint <n>³ P'''(<n>) + 6 <n>² P''(<n>) = 5 P(<n>) holds in ATLAS 13 TeV data (δ₃ = -0.02 ± 0.11), the symmetry is consistent at leading orders near z=1, and the entanglement entropy is given by the model-independent expression S = ln<n> + 1 - ½ ∫ e^{-z} f_s²(z) dz + O(f_s³).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the observed reciprocal symmetry f_s(z)=f_s(1/z) is sufficiently accurate near z=1 for the Taylor expansion of h(u) to yield usable local constraints, and that the χ² rejection of global symmetry does not invalidate the local claims or the entropy derivation.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Reciprocal symmetry f_s(z)=f_s(1/z) implies local constraints on multiplicity distributions at n=<n> that hold to leading order in ATLAS data, plus a model-independent entanglement entropy expression S=ln<n>+1-½∫e^{-z}f_s²(z)dz+O(f_s³).","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Reciprocal symmetry of the scaling function implies local algebraic constraints on multiplicity distributions at the mean.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5ba18c3da275530b848e582b58fc45d7de450de2f89c9d11d36d3435da9d458b"},"source":{"id":"2605.08736","kind":"arxiv","version":2},"verdict":{"id":"0330064d-80f5-40e4-af3e-038dfd3db168","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T01:40:49.908342Z","strongest_claim":"The k=1 constraint <n>³ P'''(<n>) + 6 <n>² P''(<n>) = 5 P(<n>) holds in ATLAS 13 TeV data (δ₃ = -0.02 ± 0.11), the symmetry is consistent at leading orders near z=1, and the entanglement entropy is given by the model-independent expression S = ln<n> + 1 - ½ ∫ e^{-z} f_s²(z) dz + O(f_s³).","one_line_summary":"Reciprocal symmetry f_s(z)=f_s(1/z) implies local constraints on multiplicity distributions at n=<n> that hold to leading order in ATLAS data, plus a model-independent entanglement entropy expression S=ln<n>+1-½∫e^{-z}f_s²(z)dz+O(f_s³).","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the observed reciprocal symmetry f_s(z)=f_s(1/z) is sufficiently accurate near z=1 for the Taylor expansion of h(u) to yield usable local constraints, and that the χ² rejection of global symmetry does not invalidate the local claims or the entropy derivation.","pith_extraction_headline":"Reciprocal symmetry of the scaling function implies local algebraic constraints on multiplicity distributions at the mean."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.08736/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T09:02:01.941209Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T22:35:16.867205Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T14:31:17.574157Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T10:50:48.545528Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"9fabbbbec5c1aa61261919cd692c18ede3c7f9eff02dae20a437a81d8ceb3d22"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"85cd634e66967e35985046e520334e80ba9b7a76cccb4aba6a915ee0dfd3cf3e"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}