Pith Number

pith:ILRPNOQ6

pith:2011:ILRPNOQ64Z5KBMAHNMYKRAZL6B

not attested not anchored not stored refs pending

A CLT for Information-theoretic statistics of Non-centered Gram random matrices

Jack W. Silverstein, Jamal Najim, Malika Kharouf, Walid Hachem

arxiv:1107.0145 v1 · 2011-07-01 · math.PR · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ILRPNOQ64Z5KBMAHNMYKRAZL6B}

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	2026-05-18T04:19:02.585975Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42e2f6ba1ee67aa0b0076b30a8832bf045bdda1dc2810be7c4b0d33db0302fef

Aliases

arxiv: 1107.0145 · arxiv_version: 1107.0145v1 · doi: 10.48550/arxiv.1107.0145 · pith_short_12: ILRPNOQ64Z5K · pith_short_16: ILRPNOQ64Z5KBMAH · pith_short_8: ILRPNOQ6

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/ILRPNOQ64Z5KBMAHNMYKRAZL6B \
  | 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: 42e2f6ba1ee67aa0b0076b30a8832bf045bdda1dc2810be7c4b0d33db0302fef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c484efc3c241e7336b7d656c509956c9c0982f387a200b0f0ddfb079c1a2497a",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-07-01T08:36:05Z",
    "title_canon_sha256": "625eeab1035572e6902dce73b22b941768b4f090874b75ea3ea97263e5a891d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.0145",
    "kind": "arxiv",
    "version": 1
  }
}