Pith Number

pith:W7BCZT3T

pith:2019:W7BCZT3TXZUOH3G2O36E5WRHCL

not attested not anchored not stored refs pending

The strong circular law: a combinatorial view

Vishesh Jain

arxiv:1904.11108 v3 · 2019-04-25 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W7BCZT3TXZUOH3G2O36E5WRHCL}

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.

Cited by

1 paper in Pith

Quantitative invertibility of random matrices: a combinatorial perspective

Receipt and verification

First computed	2026-07-05T01:06:47.502184Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7c22ccf73be68e3ecda76fc4eda2712c2ca1789bbc36fc549c420e9a54b3a23

Aliases

arxiv: 1904.11108 · arxiv_version: 1904.11108v3 · doi: 10.48550/arxiv.1904.11108 · pith_short_12: W7BCZT3TXZUO · pith_short_16: W7BCZT3TXZUOH3G2 · pith_short_8: W7BCZT3T

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/W7BCZT3TXZUOH3G2O36E5WRHCL \
  | 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: b7c22ccf73be68e3ecda76fc4eda2712c2ca1789bbc36fc549c420e9a54b3a23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11caad178b5659572bba2a9800553bed390c13dd6ec5a4397d1f6499d5ab71f6",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-04-25T00:58:21Z",
    "title_canon_sha256": "9abbe908497f1b3b59e6186bc7b227fcc394c1a10a65b3db188c3b9baf41920e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.11108",
    "kind": "arxiv",
    "version": 3
  }
}