Pith Number

pith:UZZHMM4V

pith:2012:UZZHMM4VVXUBQBE3CSRTEJTYB2

not attested not anchored not stored refs pending

Pascal triangle, Stirling numbers and the unique invariance of the Euler characteristic

Ana Luz\'on, Manuel A. Mor\'on

arxiv:1202.0663 v1 · 2012-02-03 · 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{UZZHMM4VVXUBQBE3CSRTEJTYB2}

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	2026-05-18T04:03:08.291481Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a672763395ade818049b14a33226780eb8b7c33ee46b8a71717b4c55f82a7cb6

Aliases

arxiv: 1202.0663 · arxiv_version: 1202.0663v1 · doi: 10.48550/arxiv.1202.0663 · pith_short_12: UZZHMM4VVXUB · pith_short_16: UZZHMM4VVXUBQBE3 · pith_short_8: UZZHMM4V

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/UZZHMM4VVXUBQBE3CSRTEJTYB2 \
  | 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: a672763395ade818049b14a33226780eb8b7c33ee46b8a71717b4c55f82a7cb6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36b1383fa5c516d11da7e74f6f2728487668fe86aef665bbd03e2760e9ca5b94",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-02-03T11:14:21Z",
    "title_canon_sha256": "194794e38888ece5f4ce80d3a5dbe380a540650b6f853245cdbad497fd90cf02"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.0663",
    "kind": "arxiv",
    "version": 1
  }
}