Pith Number

pith:ZFZMKQ4X

pith:2010:ZFZMKQ4XNMY5TLZ7TSIMTQGNIC

not attested not anchored not stored refs pending

On the Boltzmann-Grad limit for the two dimensional periodic Lorentz gas

Emanuele Caglioti, Fran\c{c}ois Golse

arxiv:1002.1463 v3 · 2010-02-07 · math.AP · math-ph · 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{ZFZMKQ4XNMY5TLZ7TSIMTQGNIC}

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	2026-05-18T03:50:11.196212Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c972c543976b31d9af3f9c90c9c0cd40adc594faf93cbae11b887b7c7ab8e2fb

Aliases

arxiv: 1002.1463 · arxiv_version: 1002.1463v3 · doi: 10.48550/arxiv.1002.1463 · pith_short_12: ZFZMKQ4XNMY5 · pith_short_16: ZFZMKQ4XNMY5TLZ7 · pith_short_8: ZFZMKQ4X

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/ZFZMKQ4XNMY5TLZ7TSIMTQGNIC \
  | 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: c972c543976b31d9af3f9c90c9c0cd40adc594faf93cbae11b887b7c7ab8e2fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b564a6d0ce900bd50e151781231a984029be5edf9c72b44ff9008e36055a891",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-02-07T16:00:06Z",
    "title_canon_sha256": "95e05f486092be4d3c94b00b9c5d15453abf97fcdf4eca11695d07bdd821b126"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.1463",
    "kind": "arxiv",
    "version": 3
  }
}