Pith Number

pith:D2E3IGH5

pith:2010:D2E3IGH5RGTPSP3MCVD2QNDV6Q

not attested not anchored not stored refs pending

Complete asymptotic expansion of the integrated density of states of multidimensional almost-periodic Schrodinger operators

Leonid Parnovski, Roman Shterenberg

arxiv:1004.2939 v2 · 2010-04-17 · 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{D2E3IGH5RGTPSP3MCVD2QNDV6Q}

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	2026-05-18T04:41:35.781240Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e89b418fd89a6f93f6c1547a83475f4300c42424c6598ee281ce8b777a79174

Aliases

arxiv: 1004.2939 · arxiv_version: 1004.2939v2 · doi: 10.48550/arxiv.1004.2939 · pith_short_12: D2E3IGH5RGTP · pith_short_16: D2E3IGH5RGTPSP3M · pith_short_8: D2E3IGH5

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/D2E3IGH5RGTPSP3MCVD2QNDV6Q \
  | 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: 1e89b418fd89a6f93f6c1547a83475f4300c42424c6598ee281ce8b777a79174

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "081630ae63cb1fbf7aa1233328f5ef1556ee08c8c7c132fd28b17310ccf644e3",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-04-17T03:05:21Z",
    "title_canon_sha256": "f33c870a095936564275035bc77cf33c6ffb006938da6de39f3620241e5101a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.2939",
    "kind": "arxiv",
    "version": 2
  }
}