Pith Number

pith:4XG5GCRZ

pith:2013:4XG5GCRZO52XSMH4YZCTBCSXIN

not attested not anchored not stored refs pending

Boolean Witt vectors and an integral Edrei-Thoma theorem

Darij Grinberg, James Borger

arxiv:1311.5031 v4 · 2013-11-20 · math.CO · math.NT · 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{4XG5GCRZO52XSMH4YZCTBCSXIN}

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	2026-05-18T00:39:14.108343Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5cdd30a3977757930fcc645308a57434a72f70c626e534cf5f33e8d44dbf1af

Aliases

arxiv: 1311.5031 · arxiv_version: 1311.5031v4 · doi: 10.48550/arxiv.1311.5031 · pith_short_12: 4XG5GCRZO52X · pith_short_16: 4XG5GCRZO52XSMH4 · pith_short_8: 4XG5GCRZ

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/4XG5GCRZO52XSMH4YZCTBCSXIN \
  | 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: e5cdd30a3977757930fcc645308a57434a72f70c626e534cf5f33e8d44dbf1af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b5ee144c7072b37c2a69125d2dae535dfdec1316d07c00dfdc433075d807a4e",
    "cross_cats_sorted": [
      "math.NT",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-11-20T12:14:17Z",
    "title_canon_sha256": "de20771f2dc9fc8bd1f6ebe224741604f11ca0bec765bdfa8539f0c3e4a10a7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.5031",
    "kind": "arxiv",
    "version": 4
  }
}