Pith Number

pith:6VPHSFYU

pith:2014:6VPHSFYUFCUJIIY5HBXGPDEWAO

not attested not anchored not stored refs pending

Harmonic functions on multiplicative graphs and inverse Pitman transform on infinite random paths

C\'edric Lecouvey (LMPT), Emmanuel Lesigne (LMPT), Marc Peign\'e

arxiv:1409.2334 v3 · 2014-09-08 · math.CO · math.PR · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6VPHSFYUFCUJIIY5HBXGPDEWAO}

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	2026-05-18T02:26:31.592405Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f55e79171428a894231d386e678c96038b8d56963643fea679bf8e9639327dd2

Aliases

arxiv: 1409.2334 · arxiv_version: 1409.2334v3 · doi: 10.48550/arxiv.1409.2334 · pith_short_12: 6VPHSFYUFCUJ · pith_short_16: 6VPHSFYUFCUJIIY5 · pith_short_8: 6VPHSFYU

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/6VPHSFYUFCUJIIY5HBXGPDEWAO \
  | 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: f55e79171428a894231d386e678c96038b8d56963643fea679bf8e9639327dd2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4ac4d6dc911179921e7a71567c26cb8b5798fd434be0fa11d4142dec756627e",
    "cross_cats_sorted": [
      "math.PR",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-09-08T13:26:45Z",
    "title_canon_sha256": "0b432f76fc7af8146ccdfbe61d9b9c368de2b1255cd9ccc8859255eb14038045"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.2334",
    "kind": "arxiv",
    "version": 3
  }
}