Pith Number

pith:TN53KHWI

pith:2009:TN53KHWIU3SHBYSJLLB7Y3IWEJ

not attested not anchored not stored refs pending

Path count asymptotics and Stirling numbers

A. Varchenko, K. Petersen

arxiv:0911.1970 v2 · 2009-11-10 · math.CO · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TN53KHWIU3SHBYSJLLB7Y3IWEJ}

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	2026-05-18T04:27:58.292247Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b7bb51ec8a6e470e2495ac3fc6d16224bbd2b346d6498ff072bb4f2eaa32a78

Aliases

arxiv: 0911.1970 · arxiv_version: 0911.1970v2 · doi: 10.48550/arxiv.0911.1970 · pith_short_12: TN53KHWIU3SH · pith_short_16: TN53KHWIU3SHBYSJ · pith_short_8: TN53KHWI

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/TN53KHWIU3SHBYSJLLB7Y3IWEJ \
  | 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: 9b7bb51ec8a6e470e2495ac3fc6d16224bbd2b346d6498ff072bb4f2eaa32a78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "791c2181e553c0982d195d5656960feb81d761d1ae7150cc77280dcf94bfb18a",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-11-10T18:56:24Z",
    "title_canon_sha256": "4e2377e5590fd40270209cdc447f323f39aced36ba68ad02fd1cdcf3d3540ca2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.1970",
    "kind": "arxiv",
    "version": 2
  }
}