Pith Number

pith:T746IGN4

pith:2007:T746IGN4HBJ7SEMWPICISQMRQI

not attested not anchored not stored refs pending

The Boltzmann-Grad limit of the periodic Lorentz gas in two space dimensions

Emanuele Caglioti, Fran\c{c}ois Golse (CMLS-EcolePolytechnique, LJLL)

arxiv:0710.0716 v2 · 2007-10-03 · math.DS · 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{T746IGN4HBJ7SEMWPICISQMRQI}

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	2026-05-18T03:14:30.727725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ff9e419bc3853f911967a04894191820f13975aa6421ab754fa2910098be625

Aliases

arxiv: 0710.0716 · arxiv_version: 0710.0716v2 · doi: 10.48550/arxiv.0710.0716 · pith_short_12: T746IGN4HBJ7 · pith_short_16: T746IGN4HBJ7SEMW · pith_short_8: T746IGN4

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/T746IGN4HBJ7SEMWPICISQMRQI \
  | 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: 9ff9e419bc3853f911967a04894191820f13975aa6421ab754fa2910098be625

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a7a5ab4fbbd94dcc414b392583c0c71fc35b200c761ade0ea1dc006932361b9",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2007-10-03T06:57:55Z",
    "title_canon_sha256": "15a65b23dc4b4c60713202c9b520e3740ec892fe28782f92341a383fdd536324"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.0716",
    "kind": "arxiv",
    "version": 2
  }
}