Pith Number

pith:NP4S4BMD

pith:2010:NP4S4BMDDRQSQHDWSHHTN2DFTU

not attested not anchored not stored refs pending

Spectral methods for the non cut-off Boltzmann equation and numerical grazing collision limit

C\'edric Villani, Giuseppe Toscani, Lorenzo Pareschi

arxiv:1009.5589 v1 · 2010-09-28 · math.NA · cond-mat.stat-mech · physics.plasm-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NP4S4BMDDRQSQHDWSHHTN2DFTU}

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	2026-05-18T04:40:09.790966Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6bf92e05831c61281c7691cf36e8659d1652022aea98bf74ec30cc57845ef83f

Aliases

arxiv: 1009.5589 · arxiv_version: 1009.5589v1 · doi: 10.48550/arxiv.1009.5589 · pith_short_12: NP4S4BMDDRQS · pith_short_16: NP4S4BMDDRQSQHDW · pith_short_8: NP4S4BMD

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/NP4S4BMDDRQSQHDWSHHTN2DFTU \
  | 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: 6bf92e05831c61281c7691cf36e8659d1652022aea98bf74ec30cc57845ef83f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e359f37fd3f8c747bfb29bb5410e63fe7cb9a3aa905569744c846440e4e1f284",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "physics.plasm-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2010-09-28T14:44:47Z",
    "title_canon_sha256": "9263c6e7a36786933c66b89fdb9f1d572440afaf3c92e1cdc296bbb367da05fc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.5589",
    "kind": "arxiv",
    "version": 1
  }
}