Pith Number

pith:KII6ZUVC

pith:2010:KII6ZUVCPINU2LBXH5LC6ITMPT

not attested not anchored not stored refs pending

Sharp anisotropic estimates for the Boltzmann collision operator and its entropy production

Philip T. Gressman, Robert M. Strain

arxiv:1007.1276 v3 · 2010-07-08 · math.AP · math-ph · math.CA · 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{KII6ZUVCPINU2LBXH5LC6ITMPT}

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	2026-05-18T01:20:22.644536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5211ecd2a27a1b4d2c373f562f226c7ccd12d97eadf6ed042738ee2baa5a8694

Aliases

arxiv: 1007.1276 · arxiv_version: 1007.1276v3 · doi: 10.48550/arxiv.1007.1276 · pith_short_12: KII6ZUVCPINU · pith_short_16: KII6ZUVCPINU2LBX · pith_short_8: KII6ZUVC

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/KII6ZUVCPINU2LBXH5LC6ITMPT \
  | 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: 5211ecd2a27a1b4d2c373f562f226c7ccd12d97eadf6ed042738ee2baa5a8694

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b4cf2ca024046367a5026ab109bb09be9a95bc55982bc3227c0710ae9a61e40",
    "cross_cats_sorted": [
      "math-ph",
      "math.CA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-07-08T01:53:42Z",
    "title_canon_sha256": "d0c3d592a4c7f73a8d6d63b0b529b0995749312b70a0d8e817dc92f550e13871"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.1276",
    "kind": "arxiv",
    "version": 3
  }
}