Pith Number

pith:JXJ3ST57

pith:2012:JXJ3ST57J22NHIVBVIJBOLH2TW

not attested not anchored not stored refs pending

On the Fourier Expansion of Word Maps

Gili Schul, Ori Parzanchevski

arxiv:1207.0453 v1 · 2012-07-02 · math.GR · 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{JXJ3ST57J22NHIVBVIJBOLH2TW}

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	2026-05-18T02:55:39.414566Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4dd3b94fbf4eb4d3a2a1aa12172cfa9db3921e8b60f4297fb25e72ec18fd2318

Aliases

arxiv: 1207.0453 · arxiv_version: 1207.0453v1 · doi: 10.48550/arxiv.1207.0453 · pith_short_12: JXJ3ST57J22N · pith_short_16: JXJ3ST57J22NHIVB · pith_short_8: JXJ3ST57

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/JXJ3ST57J22NHIVBVIJBOLH2TW \
  | 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: 4dd3b94fbf4eb4d3a2a1aa12172cfa9db3921e8b60f4297fb25e72ec18fd2318

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d927440a48abea82d0826afe0a9f0c6c02faa7c912d608538aa3e2e95369c584",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-07-02T17:47:33Z",
    "title_canon_sha256": "a752d980b29ae07818da6758071e196b1c3db7e708ae59ec3bbaeb427e034c67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.0453",
    "kind": "arxiv",
    "version": 1
  }
}