Pith Number

pith:IS43QA26

pith:2011:IS43QA26EDW3DREYOSX5SZKPFN

not attested not anchored not stored refs pending

Negative eigenvalues of two-dimensional Schr\"{o}dinger operators

Alexander Grigor'yan, Nikolai Nadirashvili

arxiv:1112.4986 v2 · 2011-12-21 · math.AP · math-ph · 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{IS43QA26EDW3DREYOSX5SZKPFN}

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	2026-05-18T03:57:36.926365Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

44b9b8035e20edb1c49874afd9654f2b522a72dac03e91bdd82afc4b71f90a07

Aliases

arxiv: 1112.4986 · arxiv_version: 1112.4986v2 · doi: 10.48550/arxiv.1112.4986 · pith_short_12: IS43QA26EDW3 · pith_short_16: IS43QA26EDW3DREY · pith_short_8: IS43QA26

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/IS43QA26EDW3DREYOSX5SZKPFN \
  | 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: 44b9b8035e20edb1c49874afd9654f2b522a72dac03e91bdd82afc4b71f90a07

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "949d9520579ef7f9b1f0bb3369ae14a4224ba37e00967c8268529a4138dca943",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-12-21T10:57:45Z",
    "title_canon_sha256": "062137d78806203f467fd9007719031b59dc9575d3f15ab6378ba3d88bd3c773"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4986",
    "kind": "arxiv",
    "version": 2
  }
}