Pith Number

pith:ZVLIX2T7

pith:2026:ZVLIX2T7XAP25L4DLD35EJ3YVW

not attested not anchored not stored refs pending

Relative Langlands duality and Koszul duality

Alexander Braverman, Michael Finkelberg, Roman Travkin

Assuming the local conjecture for S-dual hyperspherical varieties holds and a polarization condition is met, S^1-equivariant localization produces an equivalence between the Z/2-graded B-equivariant D-modules on Y and the Z/2-graded unipotе

arxiv:2604.14085 v3 · 2026-04-15 · math.AG · math.RT · math.SG

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\pithnumber{ZVLIX2T7XAP25L4DLD35EJ3YVW}

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4 Citations open

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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

Using a variant of the S^1-equivariant localization of arxiv:0706.0322, we deduce an equivalence between the Z/2-graded B-equivariant category (D_ψ(Y)-mod)^{Z/2})^B and the Z/2-graded unipotent B^vee-monodromic category (Q(X^vee)-mod^{Z/2})^{B^vee,mon}.

C2weakest assumption

The local conjecture of Ben-Zvi, Sakellaridis and Venkatesh holds for this pair of S-dual hyperspherical varieties, and X ≃ T^*_ψ(Y) is polarized so that Q(X)=D_ψ(Y).

C3one line summary

Assuming the Ben-Zvi-Sakellaridis-Venkatesh local conjecture and polarization of X, a variant of S^1-equivariant localization yields an equivalence between the Z/2-graded B-equivariant (D_ψ(Y)-mod)^{Z/2} and the Z/2-graded unipotent B^vee-monodromic (Q(X^vee)-mod^{Z/2})^{B^vee,mon}.

Receipt and verification

First computed	2026-05-22T02:04:41.055626Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd568bea7fb81faeaf8358f7d22778ad8f858d65f493cf2049d5d9313eeff363

Aliases

arxiv: 2604.14085 · arxiv_version: 2604.14085v3 · doi: 10.48550/arxiv.2604.14085 · pith_short_12: ZVLIX2T7XAP2 · pith_short_16: ZVLIX2T7XAP25L4D · pith_short_8: ZVLIX2T7

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZVLIX2T7XAP25L4DLD35EJ3YVW \
  | 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: cd568bea7fb81faeaf8358f7d22778ad8f858d65f493cf2049d5d9313eeff363

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce1665d3791c92a2332e270333d65ebf7cb431e1cd5e8f1037ae30d674bc11fc",
    "cross_cats_sorted": [
      "math.RT",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-04-15T16:59:00Z",
    "title_canon_sha256": "b44c0382377292d6acdc721d55a4e550c7527d8056e32f249c0d397832455d79"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.14085",
    "kind": "arxiv",
    "version": 3
  }
}