Pith Number

pith:GYQXPCRG

pith:2012:GYQXPCRGCZXW2PEBZEQHT5XYGN

not attested not anchored not stored refs pending

Kotani-Last problem and Hardy spaces on surfaces of Widom type

A. Volberg, P. Yuditskii

arxiv:1210.7069 v1 · 2012-10-26 · math-ph · math.CV · 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{GYQXPCRGCZXW2PEBZEQHT5XYGN}

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	2026-05-18T03:42:12.865279Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3621778a26166f6d3c81c92079f6f8337fad2add992d0304955cc604a828073e

Aliases

arxiv: 1210.7069 · arxiv_version: 1210.7069v1 · doi: 10.48550/arxiv.1210.7069 · pith_short_12: GYQXPCRGCZXW · pith_short_16: GYQXPCRGCZXW2PEB · pith_short_8: GYQXPCRG

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/GYQXPCRGCZXW2PEBZEQHT5XYGN \
  | 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: 3621778a26166f6d3c81c92079f6f8337fad2add992d0304955cc604a828073e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02f6bf71d6c81813b3a4d61ec9c2e8753e554ec438dc8112af9a8ac0e3e24d6a",
    "cross_cats_sorted": [
      "math.CV",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-10-26T08:59:58Z",
    "title_canon_sha256": "9794a1d78cff22e48ae07eb252d2958ed6eb14b076792287e025826c9775f795"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.7069",
    "kind": "arxiv",
    "version": 1
  }
}