Pith Number

pith:4NT4DCQI

pith:2000:4NT4DCQIRO2ZPBDN25IVKJEI7T

not attested not anchored not stored refs pending

The Density of States and the Spectral Shift Density of Random Schroedinger Operators

Robert Schrader, Vadim Kostrykin

arxiv:math-ph/0011033 v1 · 2000-11-18 · math-ph · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4NT4DCQIRO2ZPBDN25IVKJEI7T}

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	2026-07-04T14:33:37.234294Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e367c18a088bb597846dd751552488fcd9f8ad9b53fe9a536749aedffb25fc91

Aliases

arxiv: math-ph/0011033 · arxiv_version: math-ph/0011033v1 · doi: 10.48550/arxiv.math-ph/0011033 · pith_short_12: 4NT4DCQIRO2Z · pith_short_16: 4NT4DCQIRO2ZPBDN · pith_short_8: 4NT4DCQI

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/4NT4DCQIRO2ZPBDN25IVKJEI7T \
  | 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: e367c18a088bb597846dd751552488fcd9f8ad9b53fe9a536749aedffb25fc91

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5dbc34eb2d9c0f387a5984430e06f6b903a8db9e383a6653b2a6043fbec23f53",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2000-11-18T22:33:40Z",
    "title_canon_sha256": "aa788d6054de63e1bd3a1dd9a48a216e7cf97e26f539d9bce9c58047e9385f9e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0011033",
    "kind": "arxiv",
    "version": 1
  }
}