Pith Number

pith:3CMZLXJR

pith:2008:3CMZLXJR6MPYGG33PH6ZJMS56E

not attested not anchored not stored refs pending

Uniform convergence for complex $[\mathbf{0,1}]$-martingales

Beno\^it Mandelbrot, Julien Barral, Xiong Jin

arxiv:0812.4556 v3 · 2008-12-24 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3CMZLXJR6MPYGG33PH6ZJMS56E}

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	2026-05-18T01:09:24.331275Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d89995dd31f31f831b7b79fd94b25df102328510e85ec1daf8df38a900f043e0

Aliases

arxiv: 0812.4556 · arxiv_version: 0812.4556v3 · doi: 10.48550/arxiv.0812.4556 · pith_short_12: 3CMZLXJR6MPY · pith_short_16: 3CMZLXJR6MPYGG33 · pith_short_8: 3CMZLXJR

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/3CMZLXJR6MPYGG33PH6ZJMS56E \
  | 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: d89995dd31f31f831b7b79fd94b25df102328510e85ec1daf8df38a900f043e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "722059d08e2db38c5b7e7685e88178d19fa2c08cc8b95f8d2921d16959ffe54d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-12-24T17:38:25Z",
    "title_canon_sha256": "c08439d438ed79093304aef6a213ba4cfffc9d011c90f4017a129fb844255fc3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.4556",
    "kind": "arxiv",
    "version": 3
  }
}