Pith Number

pith:NT5GSGCZ

pith:2008:NT5GSGCZSFDL6AZXGTQRAFL7B3

not attested not anchored not stored refs pending

On the Joint Distribution of Energy Levels of Random Schroedinger Operators

Michael Aizenman, Simone Warzel

arxiv:0804.4231 v2 · 2008-04-26 · 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{NT5GSGCZSFDL6AZXGTQRAFL7B3}

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	2026-05-18T04:38:51.037934Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6cfa6918599146bf033734e110157f0ec3f16c27c9a0439a6048d36a1921bd23

Aliases

arxiv: 0804.4231 · arxiv_version: 0804.4231v2 · doi: 10.48550/arxiv.0804.4231 · pith_short_12: NT5GSGCZSFDL · pith_short_16: NT5GSGCZSFDL6AZX · pith_short_8: NT5GSGCZ

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/NT5GSGCZSFDL6AZXGTQRAFL7B3 \
  | 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: 6cfa6918599146bf033734e110157f0ec3f16c27c9a0439a6048d36a1921bd23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a671ebbd03c6789726de719c0abf223a875ea90c2fbb18ee06f921d0826a41b",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2008-04-26T15:23:01Z",
    "title_canon_sha256": "63715880b2442a34f6e007e92842b6856ef517dc5fd89c0fc7b2f69aa139c5b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0804.4231",
    "kind": "arxiv",
    "version": 2
  }
}