Pith Number

pith:WHTO7RWE

pith:2010:WHTO7RWE5VB2VDZFKYDOFEEOWT

not attested not anchored not stored refs pending

Finite dimensional Hopf algebras over the dual group algebra of the symmetric group in three letters

C. Vay, N. Andruskiewitsch

arxiv:1010.5953 v2 · 2010-10-28 · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WHTO7RWE5VB2VDZFKYDOFEEOWT}

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	2026-05-18T03:39:14.795760Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1e6efc6c4ed43aa8f255606e2908eb4f3924cde5bb93d1f745a20f998ac6a63

Aliases

arxiv: 1010.5953 · arxiv_version: 1010.5953v2 · doi: 10.48550/arxiv.1010.5953 · pith_short_12: WHTO7RWE5VB2 · pith_short_16: WHTO7RWE5VB2VDZF · pith_short_8: WHTO7RWE

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/WHTO7RWE5VB2VDZFKYDOFEEOWT \
  | 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: b1e6efc6c4ed43aa8f255606e2908eb4f3924cde5bb93d1f745a20f998ac6a63

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86f1da73575aff086a2227d63abe2871a59c9f2dc2cd68d102571808919359f5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2010-10-28T13:08:40Z",
    "title_canon_sha256": "dfb28167ece64a2d4c0095f265d1e1ffb5adebfcaccfe958c5a0b7ae5fe1c3a4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.5953",
    "kind": "arxiv",
    "version": 2
  }
}