Pith Number

pith:6R3VFMHE

pith:2006:6R3VFMHEQSJDX2BOV2JJWIAY52

not attested not anchored not stored refs pending

Regularity theory for the spatially homogeneous Boltzmann equation with cut-off

C\'edric Villani (UMPA-Ensl), Cl\'ement Mouhot (CEREMADE)

arxiv:math/0607539 v1 · 2006-07-21 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6R3VFMHEQSJDX2BOV2JJWIAY52}

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	2026-05-18T01:08:49.918514Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f47752b0e484923be82eae929b2018ee96db44e737dc10c5dbe083f79c75e2a2

Aliases

arxiv: math/0607539 · arxiv_version: math/0607539v1 · doi: 10.48550/arxiv.math/0607539 · pith_short_12: 6R3VFMHEQSJD · pith_short_16: 6R3VFMHEQSJDX2BO · pith_short_8: 6R3VFMHE

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/6R3VFMHEQSJDX2BOV2JJWIAY52 \
  | 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: f47752b0e484923be82eae929b2018ee96db44e737dc10c5dbe083f79c75e2a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9eceb5cb2f118f3a6d2392d12e56ff530870ecf6effa2df1bc8f25460bb75428",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2006-07-21T14:58:12Z",
    "title_canon_sha256": "2c52bc71eb0e7df687cc16a104e7029a1ea0400ebbc3595febefcef7cd221635"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0607539",
    "kind": "arxiv",
    "version": 1
  }
}