Pith Number

pith:UTCW5YK4

pith:2014:UTCW5YK4RBYC5UFMDHMORTXUPZ

not attested not anchored not stored refs pending

On the density of certain languages with $p^2$ letters

Carlos Segovia, Monika Winklmeier

arxiv:1409.2067 v2 · 2014-09-06 · math.CO · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UTCW5YK4RBYC5UFMDHMORTXUPZ}

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	2026-05-18T01:35:40.205162Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4c56ee15c88702ed0ac19d8e8cef47e4dc0def3d2b04c3a3eaa87f76be02f5c

Aliases

arxiv: 1409.2067 · arxiv_version: 1409.2067v2 · doi: 10.48550/arxiv.1409.2067 · pith_short_12: UTCW5YK4RBYC · pith_short_16: UTCW5YK4RBYC5UFM · pith_short_8: UTCW5YK4

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/UTCW5YK4RBYC5UFMDHMORTXUPZ \
  | 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: a4c56ee15c88702ed0ac19d8e8cef47e4dc0def3d2b04c3a3eaa87f76be02f5c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a9144fa8e47e9d1e3ebdfc0d55d41b394f9b272a60a2e45ee9b52e963d925443",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-09-06T23:17:14Z",
    "title_canon_sha256": "874c119bcd7962f74ea0507c144b3f82a98233fbf1d580bb8bb1b6084d157fc5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.2067",
    "kind": "arxiv",
    "version": 2
  }
}