Pith Number

pith:5573LW34

pith:2012:5573LW34F6UP553D7D2CV7HXHE

not attested not anchored not stored refs pending

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

Leonid Parnovski, Roman Shterenberg, Sergey Morozov

arxiv:1204.1076 v1 · 2012-04-04 · 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{5573LW34F6UP553D7D2CV7HXHE}

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	2026-05-18T02:26:53.186069Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef7fb5db7c2fa8fef763f8f42afcf7391e9e2a8c143678e943dc0214eaf142b8

Aliases

arxiv: 1204.1076 · arxiv_version: 1204.1076v1 · doi: 10.48550/arxiv.1204.1076 · pith_short_12: 5573LW34F6UP · pith_short_16: 5573LW34F6UP553D · pith_short_8: 5573LW34

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/5573LW34F6UP553D7D2CV7HXHE \
  | 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: ef7fb5db7c2fa8fef763f8f42afcf7391e9e2a8c143678e943dc0214eaf142b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89af1f63e5dd4744bc408a8256776fa360826d1930549e78bdb53cfdff2d90ff",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-04-04T21:04:07Z",
    "title_canon_sha256": "4994259f39deb012037dab98076a349f5d052dff56a1fa1d15e4d08c2ec89de2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.1076",
    "kind": "arxiv",
    "version": 1
  }
}