Pith Number

pith:WLVRYGUF

pith:2012:WLVRYGUFSKQFTDPIIKLLHCDBIZ

not attested not anchored not stored refs pending

Spectral theoretic characterization of the massless Dirac operator

Dmitri Vassiliev, Olga Chervova, Robert J. Downes

arxiv:1209.3510 v2 · 2012-09-16 · math.SP · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WLVRYGUFSKQFTDPIIKLLHCDBIZ}

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	2026-05-18T02:17:12.689015Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2eb1c1a8592a0598de84296b3886146499bcd0c7d0ef0c2e9e3eec785656bf6

Aliases

arxiv: 1209.3510 · arxiv_version: 1209.3510v2 · doi: 10.48550/arxiv.1209.3510 · pith_short_12: WLVRYGUFSKQF · pith_short_16: WLVRYGUFSKQFTDPI · pith_short_8: WLVRYGUF

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/WLVRYGUFSKQFTDPIIKLLHCDBIZ \
  | 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: b2eb1c1a8592a0598de84296b3886146499bcd0c7d0ef0c2e9e3eec785656bf6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2979426ed0dd0644302be22f0e5abbcac44399023d6bb5552c761ef6667acea5",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2012-09-16T18:25:34Z",
    "title_canon_sha256": "a193e0a8b8136cd053a1a04afabd220f2fe485b3f8096626d78c36461ba270d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3510",
    "kind": "arxiv",
    "version": 2
  }
}