Pith Number

pith:PIAXHQUN

pith:2006:PIAXHQUNFUNACPLMXFXE2KASJL

not attested not anchored not stored refs pending

Quantum Grothendieck Polynomials

C. Lenart, T. Maeno

arxiv:math/0608232 v1 · 2006-08-09 · math.CO · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PIAXHQUNFUNACPLMXFXE2KASJL}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

2 papers in Pith

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	2026-07-04T14:56:05.884659Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a0173c28d2d1a013d6cb96e4d28124ae27dd54effab7281f71daf862f638442

Aliases

arxiv: math/0608232 · arxiv_version: math/0608232v1 · doi: 10.48550/arxiv.math/0608232 · pith_short_12: PIAXHQUNFUNA · pith_short_16: PIAXHQUNFUNACPLM · pith_short_8: PIAXHQUN

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/PIAXHQUNFUNACPLMXFXE2KASJL \
  | 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: 7a0173c28d2d1a013d6cb96e4d28124ae27dd54effab7281f71daf862f638442

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9d9b6158e4284e2c307e82c70ff40774e550c7472ea6c33a3353343d9b057d8",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2006-08-09T22:39:29Z",
    "title_canon_sha256": "d8067a830caca42b6353edeafa41fcc3be5d6575a4995eaa743079c9af308956"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0608232",
    "kind": "arxiv",
    "version": 1
  }
}