Pith Number

pith:VUMUAJEW

pith:2015:VUMUAJEWNAIW37WOQ3LGATE66R

not attested not anchored not stored refs pending

No-gaps delocalization for general random matrices

Mark Rudelson, Roman Vershynin

arxiv:1506.04012 v1 · 2015-06-12 · 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{VUMUAJEWNAIW37WOQ3LGATE66R}

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	2026-05-18T00:54:11.011626Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad1940249668116dfece86d6604c9ef475bc8c0a645c138a8fc73c0740b813a8

Aliases

arxiv: 1506.04012 · arxiv_version: 1506.04012v1 · doi: 10.48550/arxiv.1506.04012 · pith_short_12: VUMUAJEWNAIW · pith_short_16: VUMUAJEWNAIW37WO · pith_short_8: VUMUAJEW

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/VUMUAJEWNAIW37WOQ3LGATE66R \
  | 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: ad1940249668116dfece86d6604c9ef475bc8c0a645c138a8fc73c0740b813a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f28943c02175d4ff53ecfbccc1d5aae22d7d0d3deae90d2e9b2b4dffb3120967",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-06-12T13:13:14Z",
    "title_canon_sha256": "a091296a6bf2fc9acb9ace2d2fefd7cadd3eb184713e510ae1b5de84c7b975f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.04012",
    "kind": "arxiv",
    "version": 1
  }
}