Pith Number

pith:VLXMG4JL

pith:2023:VLXMG4JL3MBIM3KPDAHLPN6BLD

not attested not anchored not stored refs pending

The sparse circular law, revisited

Ashwin Sah, Julian Sahasrabudhe, Mehtaab Sawhney

arxiv:2310.17600 v2 · 2023-10-26 · 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{VLXMG4JL3MBIM3KPDAHLPN6BLD}

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

Spectral radii of sparse non-Hermitian random matrices

Receipt and verification

First computed	2026-07-05T09:58:17.119646Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aaeec3712bdb02866d4f180eb7b7c158ff6bda97f9d01610086639a10ca80664

Aliases

arxiv: 2310.17600 · arxiv_version: 2310.17600v2 · doi: 10.48550/arxiv.2310.17600 · pith_short_12: VLXMG4JL3MBI · pith_short_16: VLXMG4JL3MBIM3KP · pith_short_8: VLXMG4JL

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/VLXMG4JL3MBIM3KPDAHLPN6BLD \
  | 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: aaeec3712bdb02866d4f180eb7b7c158ff6bda97f9d01610086639a10ca80664

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9b817eed35047e87ca3165cb776b588872ce1571fb027cb196536651e01f56b",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2023-10-26T17:23:35Z",
    "title_canon_sha256": "9cabe3f5a8fd6e389f70b8266f19f8de199984d9b1238bc70155e8ef35582420"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2310.17600",
    "kind": "arxiv",
    "version": 2
  }
}