Pith Number

pith:6KSVSC7K

pith:2025:6KSVSC7KZYV4TBGTBJVKH7BNU4

not attested not anchored not stored refs pending

Hybrid Grothendieck polynomials

Jiaji Liu, Mingyang Kang, Peter L. Guo

arxiv:2505.19072 v1 · 2025-05-25 · math.CO · math.AG · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6KSVSC7KZYV4TBGTBJVKH7BNU4}

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.

Receipt and verification

First computed	2026-07-05T11:09:24.406872Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f2a5590beace2bc984d30a6aa3fc2da706954705daf882480525170adb86b24a

Aliases

arxiv: 2505.19072 · arxiv_version: 2505.19072v1 · doi: 10.48550/arxiv.2505.19072 · pith_short_12: 6KSVSC7KZYV4 · pith_short_16: 6KSVSC7KZYV4TBGT · pith_short_8: 6KSVSC7K

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/6KSVSC7KZYV4TBGTBJVKH7BNU4 \
  | 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: f2a5590beace2bc984d30a6aa3fc2da706954705daf882480525170adb86b24a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26a057df90897d5ecfeb84725be01889a54914286a609caaece5af1d8d87a5fb",
    "cross_cats_sorted": [
      "math.AG",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-05-25T10:10:30Z",
    "title_canon_sha256": "eaf2e18292bcf30f65161e9cdf76ee12cb56ed5677291a1509ab188d9a7971f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.19072",
    "kind": "arxiv",
    "version": 1
  }
}