Pith Number

pith:J3GHCFGQ

pith:2026:J3GHCFGQIMK5JTVAHYXD5K2TS2

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A Derived Legendrian Category for Shifted Contact Stacks

Efe \.Izbudak, Kadri \.Ilker Berktav

The derived Legendrian category F_c(X) is constructed for any n-shifted contact derived Artin stack X using Legendrian correspondences.

arxiv:2605.13792 v1 · 2026-05-13 · math.AG · math.SG

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Record completeness

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4 Citations open

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Claims

C1strongest claim

We construct the derived Legendrian category F_c(X) for an n-shifted contact derived Artin stack X and the (∞,2)-category Leg_n of Legendrian correspondences... We also establish that F_c(X) embeds into an (∞,2)-category of spans defined by the AKSZ construction. We further evaluate topological cobordisms as Lagrangian correspondences to define derived Legendrian surgery.

C2weakest assumption

The existence of n-shifted contact structures on derived Artin stacks X together with the well-definedness of equivariant descent for morphism spaces and composition in the derived setting.

C3one line summary

A new derived Legendrian category is built for shifted contact stacks in derived algebraic geometry, embedding into span categories and enabling Legendrian surgery.

References

8 extracted · 8 resolved · 2 Pith anchors

[1] Equivariant Quotients of Derived Symplectic Spaces and Legendrian Intersection Theorem 2026 · arXiv:2605.08394

[2] T. Pantev, B. To¨en, M. Vaqui´e, G. Vezzosi,Shifted Symplectic Structures, Publ. Math. Inst. Hautes ´Etudes Sci. 117 (2013), 271-328 2013

[3] Calaque,Shifted cotangent stacks are shifted symplectic, Ann 2019

[4] D. Calaque, R. Haugseng, C. Scheimbauer,The AKSZ Construction in Derived Algebraic Geometry as an Extended T opological Field Theory, arXiv:2108.02473, 2022 2022

[5] K. ˙I. Berktav,Shifted Contact Structures and Their Local Theory, Ann. Fac. Sci. Toulouse, Math., Serie 6, Vol. 33(4): 1019-1057, 2024 2024

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:15.604143Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ecc7114d04315d4cea03e2e3eab53968e4d9c87265a92abfaabc8319d2479ae

Aliases

arxiv: 2605.13792 · arxiv_version: 2605.13792v1 · doi: 10.48550/arxiv.2605.13792 · pith_short_12: J3GHCFGQIMK5 · pith_short_16: J3GHCFGQIMK5JTVA · pith_short_8: J3GHCFGQ

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/J3GHCFGQIMK5JTVAHYXD5K2TS2 \
  | 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: 4ecc7114d04315d4cea03e2e3eab53968e4d9c87265a92abfaabc8319d2479ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e553851cf9eb812e7caacf376afc7352c095d37cf5ad4dd98cbf94e49f152c0c",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-13T17:12:35Z",
    "title_canon_sha256": "f052f45a5e66b9e9d73046db1dd8dea9a6f41ca61b36f83fe79c8398a85a15af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13792",
    "kind": "arxiv",
    "version": 1
  }
}