Pith Number

pith:LMJSQVYX

pith:2026:LMJSQVYXE7YCQHFV4XJ3Q47D5T

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On conjectural fermionic formulas for the Macdonald index in Argyres-Douglas theories

Chanh Tran, Shane Chern, Tanay Wakhare

The authors prove a fermionic-bosonic duality that confirms the conjectural fermionic formula for the Macdonald index in Argyres-Douglas theories of type (A1, D2k+1).

arxiv:2605.02251 v2 · 2026-05-04 · math.CO · hep-th · math.NT

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\pithnumber{LMJSQVYXE7YCQHFV4XJ3Q47D5T}

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4 Citations open

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Claims

C1strongest claim

We prove a fermionic-bosonic duality relation for the Macdonald index in Argyres-Douglas theories of type (A1, D2k+1), thereby yielding a conjectural fermionic formula due to Andrews et al.

C2weakest assumption

The new conjugate Bailey pair constructed via orthogonal polynomials and basic hypergeometric series exactly matches the structure of the Macdonald index for the specific (A1, D2k+1) theories without further restrictions or adjustments.

C3one line summary

Proof of a fermionic-bosonic duality for the Macdonald index in (A1, D2k+1) Argyres-Douglas theories via a new conjugate Bailey pair from orthogonal polynomials and hypergeometric series.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-27T01:05:55.961882Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5b1328571727f0281cb5e5d3b873e3ecfef434f1e833f103340b7e9d9d722f96

Aliases

arxiv: 2605.02251 · arxiv_version: 2605.02251v2 · doi: 10.48550/arxiv.2605.02251 · pith_short_12: LMJSQVYXE7YC · pith_short_16: LMJSQVYXE7YCQHFV · pith_short_8: LMJSQVYX

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LMJSQVYXE7YCQHFV4XJ3Q47D5T \
  | 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: 5b1328571727f0281cb5e5d3b873e3ecfef434f1e833f103340b7e9d9d722f96

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d751839b1c8b5b0291adee17782d0e319e5bcb3f131b5ee7d9ad4b85ee981e24",
    "cross_cats_sorted": [
      "hep-th",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-04T05:55:10Z",
    "title_canon_sha256": "1acd52cf83f0f9bcf47d67a92b2593eea61fe5678774ba4964ecb61f9b729dc8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.02251",
    "kind": "arxiv",
    "version": 2
  }
}