Pith Number

pith:2B7DUZM2

pith:2010:2B7DUZM2FUFQK7F5RVKVPYG4ZX

not attested not anchored not stored refs pending

Burkholder's function via Monge--Amp\`ere equation

Alexander Volberg, Vasily Vasyunin

arxiv:1006.2633 v2 · 2010-06-14 · math.AP · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2B7DUZM2FUFQK7F5RVKVPYG4ZX}

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	2026-05-18T04:31:59.982610Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d07e3a659a2d0b057cbd8d5557e0dccde6fce5566478212f9301bfce8f90a1ef

Aliases

arxiv: 1006.2633 · arxiv_version: 1006.2633v2 · doi: 10.48550/arxiv.1006.2633 · pith_short_12: 2B7DUZM2FUFQ · pith_short_16: 2B7DUZM2FUFQK7F5 · pith_short_8: 2B7DUZM2

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/2B7DUZM2FUFQK7F5RVKVPYG4ZX \
  | 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: d07e3a659a2d0b057cbd8d5557e0dccde6fce5566478212f9301bfce8f90a1ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4b14463f22909cf3cbd0b5130e50b91bd2410b1aac56016ee969ac7ded2b9d6",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-06-14T08:31:57Z",
    "title_canon_sha256": "5088a6249d4a9d4436db7988080c61c1659d5c78ca93d9db9583f3d8765a43c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.2633",
    "kind": "arxiv",
    "version": 2
  }
}