Pith Number

pith:5URONA6R

pith:2007:5URONA6RRXCHGX6YIZNOQ2Y3DV

not attested not anchored not stored refs pending

Optimal Wegner estimates for random Schroedinger operators on metric graphs

Ivan Veselic, Mario Helm, Michael J. Gruber

arxiv:0711.1953 v2 · 2007-11-13 · math.SP · math-ph · math.FA · 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{5URONA6RRXCHGX6YIZNOQ2Y3DV}

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	2026-05-18T04:31:12.412843Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed22e683d18dc4735fd8465ae86b1b1d603d676f282563d423e68581fc6c9ad6

Aliases

arxiv: 0711.1953 · arxiv_version: 0711.1953v2 · doi: 10.48550/arxiv.0711.1953 · pith_short_12: 5URONA6RRXCH · pith_short_16: 5URONA6RRXCHGX6Y · pith_short_8: 5URONA6R

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/5URONA6RRXCHGX6YIZNOQ2Y3DV \
  | 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: ed22e683d18dc4735fd8465ae86b1b1d603d676f282563d423e68581fc6c9ad6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8522526ea74ea374b569cd7943150da3ab0349cec58d129a79df479c23a43a11",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.SP",
    "submitted_at": "2007-11-13T11:48:29Z",
    "title_canon_sha256": "3a4507cf223a6837064c3c17f5dafd15e351bd1123cb5517e13f9cc3b5cf050d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0711.1953",
    "kind": "arxiv",
    "version": 2
  }
}