Pith Number

pith:NHYVBOKM

pith:2026:NHYVBOKM3P4VTM6RKXAB3FIBTZ

not attested not anchored not stored refs pending

Higher-order local constraints from reciprocal symmetry and entanglement entropy of charged-particle multiplicity distributions in $pp$ collisions

Alex Prygarin, Claudelle Capasia Madjuogang Sandeu, Mustapha Ouchen

Reciprocal symmetry of the scaling function implies local algebraic constraints on multiplicity distributions at the mean.

arxiv:2605.08736 v2 · 2026-05-09 · hep-ph

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\usepackage{pith}
\pithnumber{NHYVBOKM3P4VTM6RKXAB3FIBTZ}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest 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).

C2weakest 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.

C3one 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).

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-07-27T01:20:17.552596Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69f150b94cdbf959b3d155c01d95019e4603a12370a7556a3f045b78f9451ea5

Aliases

arxiv: 2605.08736 · arxiv_version: 2605.08736v2 · doi: 10.48550/arxiv.2605.08736 · pith_short_12: NHYVBOKM3P4V · pith_short_16: NHYVBOKM3P4VTM6R · pith_short_8: NHYVBOKM

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/NHYVBOKM3P4VTM6RKXAB3FIBTZ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 69f150b94cdbf959b3d155c01d95019e4603a12370a7556a3f045b78f9451ea5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "683e967ff719c66aa831a6651a08023d6b2db074987e0a90f0624d1a8516318d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2026-05-09T06:45:19Z",
    "title_canon_sha256": "099eaf32adf6087c7821ade388952ee12a3ff6eee66f588f9d55ae0a06a0d6b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.08736",
    "kind": "arxiv",
    "version": 2
  }
}