Pith Number

pith:5ZAC4W6P

pith:2010:5ZAC4W6PHO4LOZTWDNDWROAYDT

not attested not anchored not stored refs pending

Product and puzzle formulae for GL_n Belkale-Kumar coefficients

Allen Knutson, Kevin Purbhoo

arxiv:1008.4979 v2 · 2010-08-30 · 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{5ZAC4W6PHO4LOZTWDNDWROAYDT}

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	2026-05-18T04:39:58.978502Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee402e5bcf3bb8b766761b4768b8181cf3561e8f6b354d78e072212c623e65d8

Aliases

arxiv: 1008.4979 · arxiv_version: 1008.4979v2 · doi: 10.48550/arxiv.1008.4979 · pith_short_12: 5ZAC4W6PHO4L · pith_short_16: 5ZAC4W6PHO4LOZTW · pith_short_8: 5ZAC4W6P

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/5ZAC4W6PHO4LOZTWDNDWROAYDT \
  | 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: ee402e5bcf3bb8b766761b4768b8181cf3561e8f6b354d78e072212c623e65d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de4e7a8a0a30c9fa4919f8f314cf16877d8f03d4c40372a59761f6ebf4df6591",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-08-30T01:10:39Z",
    "title_canon_sha256": "c7e8add41b2fc093d61b6bc91a0910421d23cd094ef63d9cc0232b60daef7d42"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.4979",
    "kind": "arxiv",
    "version": 2
  }
}