Pith Number

pith:LXGXDDXF

pith:2016:LXGXDDXFI4EZEJRS3REFOL36F3

not attested not anchored not stored refs pending

Local circular law for the product of a deterministic matrix with a random matrix

Fan Yang, Haokai Xi, Jun Yin

arxiv:1603.04066 v2 · 2016-03-13 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LXGXDDXFI4EZEJRS3REFOL36F3}

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	2026-05-18T00:03:20.049675Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5dcd718ee54709922632dc48572f7e2ed13d3374eb88ee655a88da89581f9dd5

Aliases

arxiv: 1603.04066 · arxiv_version: 1603.04066v2 · doi: 10.48550/arxiv.1603.04066 · pith_short_12: LXGXDDXFI4EZ · pith_short_16: LXGXDDXFI4EZEJRS · pith_short_8: LXGXDDXF

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/LXGXDDXFI4EZEJRS3REFOL36F3 \
  | 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: 5dcd718ee54709922632dc48572f7e2ed13d3374eb88ee655a88da89581f9dd5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48901efbdac0773bbec6195ac2a3896131dbcd95da8d85c9fbd10e43bd645247",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-03-13T19:11:25Z",
    "title_canon_sha256": "fbf5723e8a67c0bf130dabe89bffef59c719a6039193c30e61f473a4a89f185c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.04066",
    "kind": "arxiv",
    "version": 2
  }
}