Pith Number

pith:WKZNMA7A

pith:2010:WKZNMA7AAXGLJGXOQRHBGGBYTP

not attested not anchored not stored refs pending

Permutations and beta-shifts

Sergi Elizalde

arxiv:1008.4167 v1 · 2010-08-24 · 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{WKZNMA7AAXGLJGXOQRHBGGBYTP}

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	2026-05-18T04:41:53.559225Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2b2d603e005ccb49aee844e1318389bfd3e0eb7b17c607d63670eda208341cb

Aliases

arxiv: 1008.4167 · arxiv_version: 1008.4167v1 · doi: 10.48550/arxiv.1008.4167 · pith_short_12: WKZNMA7AAXGL · pith_short_16: WKZNMA7AAXGLJGXO · pith_short_8: WKZNMA7A

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/WKZNMA7AAXGLJGXOQRHBGGBYTP \
  | 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: b2b2d603e005ccb49aee844e1318389bfd3e0eb7b17c607d63670eda208341cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7df6f931ca67370f72994e5fafdfbf8b1f88c2afa9959b3b97be341e1a65c45",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-08-24T22:16:42Z",
    "title_canon_sha256": "b85592816b9e61d3b690eb5307651ccd7e1247400505e3d3daf2ca0ee22bfddb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.4167",
    "kind": "arxiv",
    "version": 1
  }
}