Pith Number

pith:FEXUZVCU

pith:2024:FEXUZVCUHQSCGXKPQG7AUZM4J6

not attested not anchored not stored refs pending

Rate of convergence of the Kac particle system for the Boltzmann equation with hard potentials

An Zhang, Chenguang Liu, Liping Xu

arxiv:2409.04031 v1 · 2024-09-06 · math.PR · math-ph · math.AP · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FEXUZVCUHQSCGXKPQG7AUZM4J6}

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	2026-07-05T09:04:41.199679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

292f4cd4543c24235d4f81be0a659c4f97a755ade74466731e3679c0ca4cb37f

Aliases

arxiv: 2409.04031 · arxiv_version: 2409.04031v1 · doi: 10.48550/arxiv.2409.04031 · pith_short_12: FEXUZVCUHQSC · pith_short_16: FEXUZVCUHQSCGXKP · pith_short_8: FEXUZVCU

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/FEXUZVCUHQSCGXKPQG7AUZM4J6 \
  | 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: 292f4cd4543c24235d4f81be0a659c4f97a755ade74466731e3679c0ca4cb37f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad6caf92314ca5cee5c261128e6f12f3083b5eb711e201fc28bb74a033aa1c47",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2024-09-06T05:33:20Z",
    "title_canon_sha256": "e3a9a07cf0bc0e19dab54c934f35d02152f762892d57620d1b0d04e3b1634dd1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.04031",
    "kind": "arxiv",
    "version": 1
  }
}