Pith Number

pith:VZ7O5D6L

pith:2012:VZ7O5D6LUQXGTSYADLYH44Z2PQ

not attested not anchored not stored refs pending

Two Brownian Particles with Rank-Based Characteristics and Skew-Elastic Collisions

E. Robert Fernholz, Ioannis Karatzas, Tomoyuki Ichiba

arxiv:1206.4350 v2 · 2012-06-19 · 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{VZ7O5D6LUQXGTSYADLYH44Z2PQ}

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	2026-05-18T03:48:13.220578Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae7eee8fcba42e69cb001af07e733a7c1654112d46ad1d43c198cf06acc9fe35

Aliases

arxiv: 1206.4350 · arxiv_version: 1206.4350v2 · doi: 10.48550/arxiv.1206.4350 · pith_short_12: VZ7O5D6LUQXG · pith_short_16: VZ7O5D6LUQXGTSYA · pith_short_8: VZ7O5D6L

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/VZ7O5D6LUQXGTSYADLYH44Z2PQ \
  | 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: ae7eee8fcba42e69cb001af07e733a7c1654112d46ad1d43c198cf06acc9fe35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "106afcaa9efce92beea44990aa373dda2fc57d09eaa1be94bbf1f0a961685d7f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-06-19T22:20:56Z",
    "title_canon_sha256": "59754b9b608019bc88e46677bdf65bc237191a831e7966dd154eb357a7dc939b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.4350",
    "kind": "arxiv",
    "version": 2
  }
}