Pith Number

pith:VVC72XQ6

pith:2005:VVC72XQ6FOE4P64C5XSITOEIIT

not attested not anchored not stored refs pending

Factorial Grothendieck Polynomials

Peter J. McNamara

arxiv:math/0508192 v2 · 2005-08-11 · 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{VVC72XQ6FOE4P64C5XSITOEIIT}

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	2026-05-18T04:33:27.526136Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad45fd5e1e2b89c7fb82ede489b88844c27c7f10083b7429501809c225fea3c5

Aliases

arxiv: math/0508192 · arxiv_version: math/0508192v2 · doi: 10.48550/arxiv.math/0508192 · pith_short_12: VVC72XQ6FOE4 · pith_short_16: VVC72XQ6FOE4P64C · pith_short_8: VVC72XQ6

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/VVC72XQ6FOE4P64C5XSITOEIIT \
  | 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: ad45fd5e1e2b89c7fb82ede489b88844c27c7f10083b7429501809c225fea3c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43368ca1785305fbd4a9cb8b58275a71656db7d3666bb4f42a8fc4f218ca64f3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2005-08-11T01:20:56Z",
    "title_canon_sha256": "d7090ffc6210b73e304c33233081b56528672cbab52332261518ae34d7485e7a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0508192",
    "kind": "arxiv",
    "version": 2
  }
}