Pith Number

pith:PZURMBVK

pith:2016:PZURMBVKPQXKMWMFGX4RHUKXMW

not attested not anchored not stored refs pending

Probability that product of real random matrices have all eigenvalues real tend to 1

Tulasi Ram Reddy

arxiv:1606.07581 v1 · 2016-06-24 · 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{PZURMBVKPQXKMWMFGX4RHUKXMW}

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	2026-05-18T00:52:34.241044Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e691606aa7c2ea6598535f913d1576592a261ba60203e36ce58b4e5c63d57ba

Aliases

arxiv: 1606.07581 · arxiv_version: 1606.07581v1 · doi: 10.48550/arxiv.1606.07581 · pith_short_12: PZURMBVKPQXK · pith_short_16: PZURMBVKPQXKMWMF · pith_short_8: PZURMBVK

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/PZURMBVKPQXKMWMFGX4RHUKXMW \
  | 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: 7e691606aa7c2ea6598535f913d1576592a261ba60203e36ce58b4e5c63d57ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba01c9b6ca5f0480b0423560d1a90e927c7ded98c2cbdcf11b91e2e5d1cf9079",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-06-24T06:42:38Z",
    "title_canon_sha256": "cfa188d8882192da17ee2fa02013ef6fc16a7417a060e0ec36fc2e287e1c0b41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.07581",
    "kind": "arxiv",
    "version": 1
  }
}