Pith Number

pith:D7DJXFRT

pith:2026:D7DJXFRTLRVZSJ7EC2PCM45D7R

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Impurity-induced geometric correlations and fractional quantization in quantum Hall systems

M. A. Hidalgo

Correlated ionized impurities induce coherent coupling between cyclotron orbits that splits Landau levels into fractional sublevels with an odd-denominator hierarchy.

arxiv:2605.15022 v1 · 2026-05-14 · cond-mat.mes-hall

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Claims

C1strongest claim

A correlated distribution of ionized impurities partially modifies the Landau-level degeneracy through coherent coupling between cyclotron orbits, generating fractional energy sublevels. The odd-denominator hierarchy emerges naturally from the intrinsic guiding-center quantization and the correlated cyclotron motion.

C2weakest assumption

That a correlated impurity distribution can be treated as producing coherent coupling between cyclotron orbits that splits Landau levels into stable fractional sublevels without violating the standard Landau-level structure or requiring additional interactions.

C3one line summary

Impurity-induced geometric correlations within a Landau level generate fractional quantum Hall states via coherent coupling of cyclotron orbits.

References

12 extracted · 12 resolved · 0 Pith anchors

[1] The absence of a robust incom- pressible state at filling factor 1/2 follows naturally from cancellation of the geometric correlations responsible for odd-denominator states (p=0)

[2] R. B. Laughlin, Physical Review B23, 5632 (1981) 1981

[3] R. B. Laughlin, Physical Review Letters50, 1395 (1983) 1983

[4] Jain, Advances in Physics41, 105 (1992) 1992

[5] C. Cohen-Tannoudji, B. Diu, and F. Lalo¨ e,Quantum Me- chanics, Volume 1: Basic Concepts, Tools, and Applica- tions, 2nd ed. (John Wiley & Sons, 2019) 2019

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:38:54.672860Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1fc69b96335c6b9927e4169e2673a3fc5e0e3466973c180fa9a1b254647b5f60

Aliases

arxiv: 2605.15022 · arxiv_version: 2605.15022v1 · doi: 10.48550/arxiv.2605.15022 · pith_short_12: D7DJXFRTLRVZ · pith_short_16: D7DJXFRTLRVZSJ7E · pith_short_8: D7DJXFRT

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/D7DJXFRTLRVZSJ7EC2PCM45D7R \
  | 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: 1fc69b96335c6b9927e4169e2673a3fc5e0e3466973c180fa9a1b254647b5f60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d733397edf52f9b97e1a73a3fed81d24bd45603273196b088bae72f0d387f93",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.mes-hall",
    "submitted_at": "2026-05-14T16:21:36Z",
    "title_canon_sha256": "e92cf9a6ac49777c0d29993b463c29881cce40d5c9bafea8a1532029c69a9c66"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15022",
    "kind": "arxiv",
    "version": 1
  }
}