Pith Number

pith:FOJQ53JU

pith:2008:FOJQ53JUPL4YJYFBQPDTWZDE7C

not attested not anchored not stored refs pending

On Strong Convergence to Equilibrium for the Boltzmann Equation with Soft Potentials

Eric A. Carlen, Maria C. Carvalho, Xuguang Lu

arxiv:0808.1064 v2 · 2008-08-07 · math-ph · math.FA · 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{FOJQ53JUPL4YJYFBQPDTWZDE7C}

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	2026-05-18T02:15:43.785045Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b930eed347af984e0a183c73b6464f8a70234d5144308f77d01f9babb602fe6

Aliases

arxiv: 0808.1064 · arxiv_version: 0808.1064v2 · doi: 10.48550/arxiv.0808.1064 · pith_short_12: FOJQ53JUPL4Y · pith_short_16: FOJQ53JUPL4YJYFB · pith_short_8: FOJQ53JU

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/FOJQ53JUPL4YJYFBQPDTWZDE7C \
  | 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: 2b930eed347af984e0a183c73b6464f8a70234d5144308f77d01f9babb602fe6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4cf16a7d1238fa24b44975ff609adaead292159ff1c279426ef395688204fc39",
    "cross_cats_sorted": [
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2008-08-07T16:17:23Z",
    "title_canon_sha256": "b4a52a285d943e27a507197d1347d2a409b1a424eb0629a1ce9445ead8e51fc2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0808.1064",
    "kind": "arxiv",
    "version": 2
  }
}