Pith Number

pith:ZPN76FH4

pith:2014:ZPN76FH4OUFQETYVNDYZFZHBJK

not attested not anchored not stored refs pending

On martingale tail sums for the path length in random trees

Henning Sulzbach

arxiv:1412.3508 v3 · 2014-12-11 · math.PR · cs.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{ZPN76FH4OUFQETYVNDYZFZHBJK}

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	2026-05-18T01:18:47.947523Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbdbff14fc750b024f1568f192e4e14aac7c74312047c325f4e3c18d866e1314

Aliases

arxiv: 1412.3508 · arxiv_version: 1412.3508v3 · doi: 10.48550/arxiv.1412.3508 · pith_short_12: ZPN76FH4OUFQ · pith_short_16: ZPN76FH4OUFQETYV · pith_short_8: ZPN76FH4

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/ZPN76FH4OUFQETYVNDYZFZHBJK \
  | 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: cbdbff14fc750b024f1568f192e4e14aac7c74312047c325f4e3c18d866e1314

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e7960ad2d17aab934ef46a3a30d48144f45bbe7a2d0aac4f59a58bb7d1b6e0a",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-12-11T00:36:31Z",
    "title_canon_sha256": "977f77502e823a935e82051429b9a5b8b0ebb3e4dac27880dbea31d62dec0c47"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.3508",
    "kind": "arxiv",
    "version": 3
  }
}