Pith Number

pith:ZE5YMG27

pith:2023:ZE5YMG274S3WQY543GGOYUJXR4

not attested not anchored not stored refs pending

A presentation of the torus-equivariant quantum $K$-theory ring of flag manifolds of type $A$, Part II: quantum double Grothendieck polynomials

Daisuke Sagaki, Satoshi Naito, Toshiaki Maeno

arxiv:2305.17685 v1 · 2023-05-28 · math.QA · math.AG · math.CO · math.KT · math.RT

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZE5YMG274S3WQY543GGOYUJXR4}

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Record completeness

1 Bitcoin timestamp

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.

Cited by

3 papers in Pith

On the Schubert calculus of the quantum K-theory for partial flag manifolds: a 3d A-model perspective

Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials

Schubert line defects in 3d GLSMs, part II: Partial flag manifolds and parabolic quantum polynomials

Receipt and verification

First computed	2026-07-05T06:14:47.221243Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c93b861b5fe4b76863bcd98cec51378f365614fd10c5ab7081e4f614aad66a50

Aliases

arxiv: 2305.17685 · arxiv_version: 2305.17685v1 · doi: 10.48550/arxiv.2305.17685 · pith_short_12: ZE5YMG274S3W · pith_short_16: ZE5YMG274S3WQY54 · pith_short_8: ZE5YMG27

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/ZE5YMG274S3WQY543GGOYUJXR4 \
  | 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: c93b861b5fe4b76863bcd98cec51378f365614fd10c5ab7081e4f614aad66a50

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6087422a4a961e679dc1a694637cbfcd7d19cfe0733be4743042c6a1ffea3608",
    "cross_cats_sorted": [
      "math.AG",
      "math.CO",
      "math.KT",
      "math.RT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2023-05-28T10:41:33Z",
    "title_canon_sha256": "86ff959ae24d7b3c0395e5757ae2eb8a847133032c221ce278341ab9158cae35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2305.17685",
    "kind": "arxiv",
    "version": 1
  }
}