Pith Number

pith:4N4DEHI3

pith:2012:4N4DEHI3IPMOJEPF3YDB5MUVND

not attested not anchored not stored refs pending

Automated Counting of Towers (\`A La Bordelaise) [Or: Footnote to p. 81 of the Flajolet-Sedgewick Chef-d'{\oe}vre]

Doron Zeilberger, Shalosh B. Ekhad

arxiv:1212.4105 v1 · 2012-12-17 · 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{4N4DEHI3IPMOJEPF3YDB5MUVND}

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	2026-05-18T03:38:14.798262Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e378321d1b43d8e491e5de061eb29568df7918a0319960696fc022089889dc64

Aliases

arxiv: 1212.4105 · arxiv_version: 1212.4105v1 · doi: 10.48550/arxiv.1212.4105 · pith_short_12: 4N4DEHI3IPMO · pith_short_16: 4N4DEHI3IPMOJEPF · pith_short_8: 4N4DEHI3

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/4N4DEHI3IPMOJEPF3YDB5MUVND \
  | 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: e378321d1b43d8e491e5de061eb29568df7918a0319960696fc022089889dc64

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "497fc173138365e57d0068a76a937a385518265ec743827c7cc74e6d9a5663c8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-12-17T19:15:04Z",
    "title_canon_sha256": "21654e83cab5d8e60c25f17b318d7f3208b794d38986c6628bba3e1371b46f76"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.4105",
    "kind": "arxiv",
    "version": 1
  }
}