Pith Number

pith:AW4QX74Y

pith:2010:AW4QX74YWFXWQY64NJEDP45BON

not attested not anchored not stored refs pending

Boltzmann equation without angular cutoff in the whole space: I, Global existence for soft potential

Chao-Jiang Xu (LMRS), IRENAV), Radjesvarane Alexandre (IRENAV, Seiji Ukai (Mr.), Tong Yang, Yoshinori Morimoto

arxiv:1007.0304 v2 · 2010-07-02 · 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{AW4QX74YWFXWQY64NJEDP45BON}

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	2026-05-18T04:38:16.856549Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05b90bff98b16f6863dc6a4837f3a173712bf7d7da78b6012019e2cba5e289d0

Aliases

arxiv: 1007.0304 · arxiv_version: 1007.0304v2 · doi: 10.48550/arxiv.1007.0304 · pith_short_12: AW4QX74YWFXW · pith_short_16: AW4QX74YWFXWQY64 · pith_short_8: AW4QX74Y

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/AW4QX74YWFXWQY64NJEDP45BON \
  | 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: 05b90bff98b16f6863dc6a4837f3a173712bf7d7da78b6012019e2cba5e289d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09d748623b1732b7b48157b873033d021877c992591e61952629fd0670c3cb61",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-07-02T06:47:34Z",
    "title_canon_sha256": "59b615f76fce98f27c4a4a5533d7bad5dfb63dcf99b1fd6ee208f7be4518d56d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.0304",
    "kind": "arxiv",
    "version": 2
  }
}