Pith Number

pith:4MDTO35R

pith:2012:4MDTO35RQU3TKELBKNZD2JZ5W4

not attested not anchored not stored refs pending

Ergodicity breaking in geometric Brownian motion

Ole Peters, William Klein

arxiv:1209.4517 v3 · 2012-09-20 · math-ph · math.MP · q-fin.RM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4MDTO35RQU3TKELBKNZD2JZ5W4}

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	2026-05-18T03:30:55.308359Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e307376fb1853735116153723d273db72f5aef315afa7cdb00317275c9dc550a

Aliases

arxiv: 1209.4517 · arxiv_version: 1209.4517v3 · doi: 10.48550/arxiv.1209.4517 · pith_short_12: 4MDTO35RQU3T · pith_short_16: 4MDTO35RQU3TKELB · pith_short_8: 4MDTO35R

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/4MDTO35RQU3TKELBKNZD2JZ5W4 \
  | 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: e307376fb1853735116153723d273db72f5aef315afa7cdb00317275c9dc550a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd4de8609fa253a3254cc93743ac6c8682a7687bf9f431890d45e05e023d0cfa",
    "cross_cats_sorted": [
      "math.MP",
      "q-fin.RM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-09-20T12:56:32Z",
    "title_canon_sha256": "2938fe0e2844fc1ee7b58398e713e3445bbf3bb50ddc8dc92818d2e96d3f686c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.4517",
    "kind": "arxiv",
    "version": 3
  }
}