Pith Number

pith:HFMZ7VJD

pith:2012:HFMZ7VJD7WMTYRSTLQ7DSSNWC5

not attested not anchored not stored refs pending

The local circular law II: the edge case

Horng-Tzer Yau, Jun Yin, Paul Bourgade

arxiv:1206.3187 v3 · 2012-06-14 · 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{HFMZ7VJD7WMTYRSTLQ7DSSNWC5}

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	2026-05-18T03:05:35.838451Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39599fd523fd993c46535c3e3949b61757db3cd3788bc12b7dbbab16aed9c77e

Aliases

arxiv: 1206.3187 · arxiv_version: 1206.3187v3 · doi: 10.48550/arxiv.1206.3187 · pith_short_12: HFMZ7VJD7WMT · pith_short_16: HFMZ7VJD7WMTYRST · pith_short_8: HFMZ7VJD

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/HFMZ7VJD7WMTYRSTLQ7DSSNWC5 \
  | 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: 39599fd523fd993c46535c3e3949b61757db3cd3788bc12b7dbbab16aed9c77e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e401f14c175d13eefd4fe5ea979fb2532e63c370bd1d0005cfc042bd1f7cab3",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-06-14T17:17:57Z",
    "title_canon_sha256": "b14fa5262c0c5fa6d0bf604baf01246cd19e98d46aaf8b25f3cb9b844986a11b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.3187",
    "kind": "arxiv",
    "version": 3
  }
}