Pith Number

pith:4ZHPZHD5

pith:2018:4ZHPZHD57NIJ4KHFD3YL3BGLM4

not attested not anchored not stored refs pending

Identities on Factorial Grothendieck Polynomials

Peter L. Guo, Sophie C.C. Sun

arxiv:1812.04390 v1 · 2018-12-11 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4ZHPZHD57NIJ4KHFD3YL3BGLM4}

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	2026-05-17T23:58:32.340598Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e64efc9c7dfb509e28e51ef0bd84cb670b90bc7d446b095ed907bf982e77e206

Aliases

arxiv: 1812.04390 · arxiv_version: 1812.04390v1 · doi: 10.48550/arxiv.1812.04390 · pith_short_12: 4ZHPZHD57NIJ · pith_short_16: 4ZHPZHD57NIJ4KHF · pith_short_8: 4ZHPZHD5

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/4ZHPZHD57NIJ4KHFD3YL3BGLM4 \
  | 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: e64efc9c7dfb509e28e51ef0bd84cb670b90bc7d446b095ed907bf982e77e206

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6d0fc4cb53a5069535ce0a15a3f7340aa12c44d25863e4662438fbb115790aa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-12-11T13:39:00Z",
    "title_canon_sha256": "41136c4a8447522dd29fa9e6646b5e1d68a75964ef7b18a1a7655b546a46f956"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.04390",
    "kind": "arxiv",
    "version": 1
  }
}