Pith Number

pith:2J2OBMDF

pith:2010:2J2OBMDFUE5TOH3Q3DYOHC4GAH

not attested not anchored not stored refs pending

The Boltzmann equation without angular cutoff in the whole space: III, Qualitative properties of solutions

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

arxiv:1008.3442 v2 · 2010-08-20 · 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{2J2OBMDFUE5TOH3Q3DYOHC4GAH}

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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	2026-05-18T02:05:44.455182Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d274e0b065a13b371f70d8f0e38b8601d28533056ff421f99856526ac8c8e67f

Aliases

arxiv: 1008.3442 · arxiv_version: 1008.3442v2 · doi: 10.48550/arxiv.1008.3442 · pith_short_12: 2J2OBMDFUE5T · pith_short_16: 2J2OBMDFUE5TOH3Q · pith_short_8: 2J2OBMDF

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/2J2OBMDFUE5TOH3Q3DYOHC4GAH \
  | 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: d274e0b065a13b371f70d8f0e38b8601d28533056ff421f99856526ac8c8e67f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eee444aa4c6f30d2a651ddaa2ae7b7c934c1a0070c100998cbd7c656b1f3840d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-08-20T06:45:59Z",
    "title_canon_sha256": "7ea779b8c6aa77c26a728c9a2b140cb7daaf07c0f1dfa58ed88a0f1da606db2d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.3442",
    "kind": "arxiv",
    "version": 2
  }
}