Pith Number

pith:AUFFECSW

pith:2018:AUFFECSWSN4ZPKJPOG5HD6COLQ

not attested not anchored not stored refs pending

The sparse circular law under minimal assumptions

Konstantin Tikhomirov, Mark Rudelson

arxiv:1807.08085 v3 · 2018-07-21 · 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{AUFFECSWSN4ZPKJPOG5HD6COLQ}

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	2026-05-17T23:52:15.851574Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

050a520a56937997a92f71ba71f84e5c2fd717328f1b705f8fd6cc39fba64b1a

Aliases

arxiv: 1807.08085 · arxiv_version: 1807.08085v3 · doi: 10.48550/arxiv.1807.08085 · pith_short_12: AUFFECSWSN4Z · pith_short_16: AUFFECSWSN4ZPKJP · pith_short_8: AUFFECSW

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/AUFFECSWSN4ZPKJPOG5HD6COLQ \
  | 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: 050a520a56937997a92f71ba71f84e5c2fd717328f1b705f8fd6cc39fba64b1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af6f7639490dcb1fbc7d3914c5a03396fb3613c2eeb360ccec8d59e5cc35395b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-07-21T05:04:06Z",
    "title_canon_sha256": "477e334e343ebc424483a4d27c8f234f7faac991317569a8df90c03349ae31c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.08085",
    "kind": "arxiv",
    "version": 3
  }
}