Pith Number

pith:BGL2VW5H

pith:2009:BGL2VW5H6TT35UPGXT4JQTQNE5

not attested not anchored not stored refs pending

The grazing collision limit of Kac caricature of Bose-Einstein particles

Giuseppe Toscani, Thibaut Allemand (DMA)

arxiv:0903.2739 v3 · 2009-03-16 · 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{BGL2VW5H6TT35UPGXT4JQTQNE5}

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	2026-05-18T04:23:11.794936Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0997aadba7f4e7bed1e6bcf8984e0d27606ca6ff9c40aabf37a0a36279bd4568

Aliases

arxiv: 0903.2739 · arxiv_version: 0903.2739v3 · doi: 10.48550/arxiv.0903.2739 · pith_short_12: BGL2VW5H6TT3 · pith_short_16: BGL2VW5H6TT35UPG · pith_short_8: BGL2VW5H

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/BGL2VW5H6TT35UPGXT4JQTQNE5 \
  | 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: 0997aadba7f4e7bed1e6bcf8984e0d27606ca6ff9c40aabf37a0a36279bd4568

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1994a719d1d4d42057d0862b86eeecef7562acadc8cdc62b8a1767cc23cc4417",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2009-03-16T12:51:18Z",
    "title_canon_sha256": "66c6158edaa73b97c172d9f39d2b919cbb396f8e9468cf02ae1c273776cbd971"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.2739",
    "kind": "arxiv",
    "version": 3
  }
}