Pith Number

pith:5EDXKBH6

pith:2011:5EDXKBH62F642HZODAZNQFNM5N

not attested not anchored not stored refs pending

Smoothing effect of weak solutions for the spatially homogeneous Boltzmann Equation without angular cutoff

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

arxiv:1104.5648 v1 · 2011-04-29 · 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{5EDXKBH62F642HZODAZNQFNM5N}

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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	2026-05-18T02:29:25.598439Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9077504fed17dcd1f2e1832d815aceb5b463327279f1734ba4ae4dd23d462d3

Aliases

arxiv: 1104.5648 · arxiv_version: 1104.5648v1 · doi: 10.48550/arxiv.1104.5648 · pith_short_12: 5EDXKBH62F64 · pith_short_16: 5EDXKBH62F642HZO · pith_short_8: 5EDXKBH6

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/5EDXKBH62F642HZODAZNQFNM5N \
  | 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: e9077504fed17dcd1f2e1832d815aceb5b463327279f1734ba4ae4dd23d462d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3cd73de9c76ac16d4e326f9e10a1191dc3ef83a5f2f0e154ae7c413ef405bd23",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-04-29T15:04:47Z",
    "title_canon_sha256": "10418b39ae4cfbb7afad87d518447feff82aaeb973744516a0ff90cd3c9cf59e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.5648",
    "kind": "arxiv",
    "version": 1
  }
}