Pith Number

pith:VBAU5PX2

pith:2009:VBAU5PX2Z4IEAEH6UBENUN3MJI

not attested not anchored not stored refs pending

Concave majorant of stochastic processes and Burgers turbulence

Raphael Lachieze-Rey

arxiv:0909.1088 v3 · 2009-09-06 · 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{VBAU5PX2Z4IEAEH6UBENUN3MJI}

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	2026-05-18T04:27:15.183011Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8414ebefacf104010fea048da376c4a1251e76e07d1b381df381ba44d38c886

Aliases

arxiv: 0909.1088 · arxiv_version: 0909.1088v3 · doi: 10.48550/arxiv.0909.1088 · pith_short_12: VBAU5PX2Z4IE · pith_short_16: VBAU5PX2Z4IEAEH6 · pith_short_8: VBAU5PX2

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/VBAU5PX2Z4IEAEH6UBENUN3MJI \
  | 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: a8414ebefacf104010fea048da376c4a1251e76e07d1b381df381ba44d38c886

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1be7a574cbf6fb3442826ff9bc66d4b846a3b268c476a668648becfb100413b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-09-06T15:40:42Z",
    "title_canon_sha256": "d8fb910f85dc6d51de0e270e5dae6fcae0770b9c0df0bbf39ba9e522fbcad7ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.1088",
    "kind": "arxiv",
    "version": 3
  }
}