Pith Number

pith:WCFGLAKS

pith:2016:WCFGLAKS6TC4UK5GQULLUWDS6O

not attested not anchored not stored refs pending

The Bernstein homomorphism via Aguiar-Bergeron-Sottile universality

Darij Grinberg

arxiv:1604.02969 v2 · 2016-04-11 · math.CO · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WCFGLAKS6TC4UK5GQULLUWDS6O}

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	2026-05-18T01:16:54.399524Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b08a658152f4c5ca2ba68516ba5872f3aaf1040aeedf6356f906a4e08622fbaa

Aliases

arxiv: 1604.02969 · arxiv_version: 1604.02969v2 · doi: 10.48550/arxiv.1604.02969 · pith_short_12: WCFGLAKS6TC4 · pith_short_16: WCFGLAKS6TC4UK5G · pith_short_8: WCFGLAKS

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/WCFGLAKS6TC4UK5GQULLUWDS6O \
  | 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: b08a658152f4c5ca2ba68516ba5872f3aaf1040aeedf6356f906a4e08622fbaa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20b193ddb4e4e21ae87f5b6ebe116bed0a1f2dd4532f62478e58ca8b44b349d2",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-04-11T14:13:29Z",
    "title_canon_sha256": "2becc5d32d7d8bcb24c277af9d659b07ccbeb70f368e92277e68a681843ef4a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.02969",
    "kind": "arxiv",
    "version": 2
  }
}