Pith Number

pith:WWXTWQB3

pith:2005:WWXTWQB3AJBAEKQNKDLUCQZPBS

not attested not anchored not stored refs pending

Fine properties of the integrated density of states and a quantitative separation property of the Dirichlet eigenvalues

Michael Goldstein, Wilhelm Schlag

arxiv:math-ph/0501005 v2 · 2005-01-02 · math-ph · math.DS · 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{WWXTWQB3AJBAEKQNKDLUCQZPBS}

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	2026-05-18T01:05:30.184304Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5af3b403b0242022a0d50d741432f0cb329718966e39a0c648ec1cd3f735fdf

Aliases

arxiv: math-ph/0501005 · arxiv_version: math-ph/0501005v2 · doi: 10.48550/arxiv.math-ph/0501005 · pith_short_12: WWXTWQB3AJBA · pith_short_16: WWXTWQB3AJBAEKQN · pith_short_8: WWXTWQB3

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/WWXTWQB3AJBAEKQNKDLUCQZPBS \
  | 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: b5af3b403b0242022a0d50d741432f0cb329718966e39a0c648ec1cd3f735fdf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "179734ced0a594389c2a3dc1c602a2f57e830ee52e5f3eeb09b4c578da7891a4",
    "cross_cats_sorted": [
      "math.DS",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2005-01-02T21:11:49Z",
    "title_canon_sha256": "03569a1e05be3011893c643ab8ce59f8e674960fc59949fbaac6b97598d19d8e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0501005",
    "kind": "arxiv",
    "version": 2
  }
}