Pith Number

pith:5V6X45BK

pith:2001:5V6X45BKEGLYXJ7FGMRKPR4T7P

not attested not anchored not stored refs pending

Spectral gap of doubly stochastic matrices generated from equidistributed unitary matrices

G.Berkolaiko (Weizmann Institute, Israel)

arxiv:nlin/0104009 v2 · 2001-04-04 · nlin.CD

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5V6X45BKEGLYXJ7FGMRKPR4T7P}

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	2026-05-18T04:10:47.298956Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed7d7e742a21978ba7e53322a7c793fbd495e5cc48b78953ce47a37059069854

Aliases

arxiv: nlin/0104009 · arxiv_version: nlin/0104009v2 · doi: 10.48550/arxiv.nlin/0104009 · pith_short_12: 5V6X45BKEGLY · pith_short_16: 5V6X45BKEGLYXJ7F · pith_short_8: 5V6X45BK

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/5V6X45BKEGLYXJ7FGMRKPR4T7P \
  | 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: ed7d7e742a21978ba7e53322a7c793fbd495e5cc48b78953ce47a37059069854

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0817c4c308f63b6f56a7bbe48d6d5f4c55216802f25e8bcb384c31e33b894433",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "nlin.CD",
    "submitted_at": "2001-04-04T15:41:40Z",
    "title_canon_sha256": "9a042cd4548a9fed82008537b7963d3b0591f5462616502561e32546195f3f50"
  },
  "schema_version": "1.0",
  "source": {
    "id": "nlin/0104009",
    "kind": "arxiv",
    "version": 2
  }
}