Pith Number

pith:XDXEF4WK

pith:2010:XDXEF4WKRIHDTFSGXAZIVWRMVB

not attested not anchored not stored refs pending

Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics

John von Neumann

arxiv:1003.2133 v2 · 2010-03-10 · physics.hist-ph · cond-mat.stat-mech · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XDXEF4WKRIHDTFSGXAZIVWRMVB}

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.

Cited by

3 papers in Pith

Nature abhors a vacuum: A simple rigorous example of thermalization in an isolated macroscopic quantum system

Macroscopic Irreversibility in Quantum Systems: Free Expansion in a Fermion Chain

Grand-Canonical Typicality

Receipt and verification

First computed	2026-05-18T04:34:19.524102Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8ee42f2ca8a0e399646b8328ada2ca876f0dc24f6c91de573b7a9d69b3d2cc5

Aliases

arxiv: 1003.2133 · arxiv_version: 1003.2133v2 · doi: 10.48550/arxiv.1003.2133 · pith_short_12: XDXEF4WKRIHD · pith_short_16: XDXEF4WKRIHDTFSG · pith_short_8: XDXEF4WK

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/XDXEF4WKRIHDTFSGXAZIVWRMVB \
  | 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: b8ee42f2ca8a0e399646b8328ada2ca876f0dc24f6c91de573b7a9d69b3d2cc5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1783f4c8dd17a46277e75b3cfacf0ea1342c81f0ae9035c624532ed4c69545f5",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.hist-ph",
    "submitted_at": "2010-03-10T15:49:48Z",
    "title_canon_sha256": "d575d4bba016abc43fff8188c5e02240890e0e19b965862650853f7e639a1ca0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.2133",
    "kind": "arxiv",
    "version": 2
  }
}