Pith Number

pith:IDUMZDLK

pith:2011:IDUMZDLK6TO7OW642XGJNXRCAF

not attested not anchored not stored refs pending

Bounds on the density of states for Schr\" odinger operators

Abel Klein, Jean Bourgain

arxiv:1112.1716 v3 · 2011-12-07 · 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{IDUMZDLK6TO7OW642XGJNXRCAF}

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	2026-05-18T03:37:41.589515Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

40e8cc8d6af4ddf75bdcd5cc96de2201486c5ae67d813257c638d2f9b3387a49

Aliases

arxiv: 1112.1716 · arxiv_version: 1112.1716v3 · doi: 10.48550/arxiv.1112.1716 · pith_short_12: IDUMZDLK6TO7 · pith_short_16: IDUMZDLK6TO7OW64 · pith_short_8: IDUMZDLK

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/IDUMZDLK6TO7OW642XGJNXRCAF \
  | 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: 40e8cc8d6af4ddf75bdcd5cc96de2201486c5ae67d813257c638d2f9b3387a49

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "833421a7efea00de14ae10f12f2bffa8d782be2fe3e3a8d4c1e07f3f7c0a9972",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-12-07T22:11:02Z",
    "title_canon_sha256": "67f8b1301ceda22269b599fdf9b2f71f5298f39ba7e0f6fd50a35593e78e73ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.1716",
    "kind": "arxiv",
    "version": 3
  }
}