Pith Number

pith:MAQSIDPI

pith:2013:MAQSIDPITZTA75ZHFD5IXZ4PZY

not attested not anchored not stored refs pending

The Brownian motion as the limit of a deterministic system of hard-spheres

Isabelle Gallagher, Laure Saint-Raymond, Thierry Bodineau

arxiv:1305.3397 v2 · 2013-05-15 · math.AP · math-ph · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MAQSIDPITZTA75ZHFD5IXZ4PZY}

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	2026-05-18T02:25:49.333206Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6021240de89e660ff72728fa8be78fce14253013a978b50ead7bc0a4a05fd035

Aliases

arxiv: 1305.3397 · arxiv_version: 1305.3397v2 · doi: 10.48550/arxiv.1305.3397 · pith_short_12: MAQSIDPITZTA · pith_short_16: MAQSIDPITZTA75ZH · pith_short_8: MAQSIDPI

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/MAQSIDPITZTA75ZHFD5IXZ4PZY \
  | 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: 6021240de89e660ff72728fa8be78fce14253013a978b50ead7bc0a4a05fd035

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e21373df35f71bbd76e73a705b5ffe5312b77eb59cf4ce7553246c5562e06155",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-05-15T09:12:54Z",
    "title_canon_sha256": "f2757a911462309f090923f28fe5bfbd494d0d1f994209af03b805f3a566f26b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.3397",
    "kind": "arxiv",
    "version": 2
  }
}