Pith Number

pith:762UCCKG

pith:2016:762UCCKGZQPX6BQERIYEZD3GZU

not attested not anchored not stored refs pending

Local inhomogeneous circular law

Johannes Alt, Laszlo Erdos, Torben Kr\"uger

arxiv:1612.07776 v3 · 2016-12-22 · math.PR · 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{762UCCKGZQPX6BQERIYEZD3GZU}

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	2026-05-18T00:46:26.184704Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffb5410946cc1f7f06048a304c8f66cd177e637e50e40051ab392746f163b163

Aliases

arxiv: 1612.07776 · arxiv_version: 1612.07776v3 · doi: 10.48550/arxiv.1612.07776 · pith_short_12: 762UCCKGZQPX · pith_short_16: 762UCCKGZQPX6BQE · pith_short_8: 762UCCKG

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/762UCCKGZQPX6BQERIYEZD3GZU \
  | 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: ffb5410946cc1f7f06048a304c8f66cd177e637e50e40051ab392746f163b163

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6354fd0a2b0bffa3f653021b45fce7e8966479cfaa0973606a332b62d676197f",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-12-22T20:24:40Z",
    "title_canon_sha256": "87899389cdbc12acc7821a65a18602f48c7eb74a1f229cfcea1f869079ec9e7c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.07776",
    "kind": "arxiv",
    "version": 3
  }
}