Pith Number

pith:W562VUFL

pith:2026:W562VUFL2J3ECK7WKPNEU44M2B

not attested not anchored not stored refs pending

Quantitative propagation of chaos for the Boltzmann equation with moderately soft potentials

An Zhang, Chenguang Liu, Liping Xu

arxiv:2607.13825 v1 · 2026-07-15 · 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{W562VUFL2J3ECK7WKPNEU44M2B}

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	2026-07-16T01:23:08.299901Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b77daad0abd276412bf653da4a738cd04e94818cc4ee23539542ae7b66ca0284

Aliases

arxiv: 2607.13825 · arxiv_version: 2607.13825v1 · doi: 10.48550/arxiv.2607.13825 · pith_short_12: W562VUFL2J3E · pith_short_16: W562VUFL2J3ECK7W · pith_short_8: W562VUFL

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/W562VUFL2J3ECK7WKPNEU44M2B \
  | 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: b77daad0abd276412bf653da4a738cd04e94818cc4ee23539542ae7b66ca0284

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ab008b60465f1ffdf5fd2eab8ca17b9b91a82c8326d2042d4e9c335949d0933",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-15T13:31:04Z",
    "title_canon_sha256": "4d3de556f2d27a67c9d368550a514d7fdecd20f8b99234eef32426a5cb93f691"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.13825",
    "kind": "arxiv",
    "version": 1
  }
}