Pith Number

pith:457AOA2X

pith:2001:457AOA2XVT3JZMQ3MVL6HUJN2A

not attested not anchored not stored refs pending

Random unistochastic matrices

H.-J. Sommers, K. Zyczkowski, M. Kus, W. Slomczynski

arxiv:nlin/0112036 v3 · 2001-12-20 · 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{457AOA2XVT3JZMQ3MVL6HUJN2A}

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

The Born Representation Theorem and the Unistochastic Theorem

Receipt and verification

First computed	2026-07-04T16:28:23.635855Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e77e070357acf69cb21b6557e3d12dd03cf65b3eadd27e89f060af2caef872b7

Aliases

arxiv: nlin/0112036 · arxiv_version: nlin/0112036v3 · doi: 10.48550/arxiv.nlin/0112036 · pith_short_12: 457AOA2XVT3J · pith_short_16: 457AOA2XVT3JZMQ3 · pith_short_8: 457AOA2X

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/457AOA2XVT3JZMQ3MVL6HUJN2A \
  | 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: e77e070357acf69cb21b6557e3d12dd03cf65b3eadd27e89f060af2caef872b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc4474b2746a93119139d89333c620219d2e943fe6f7b3c45762edcfa85f7d6e",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "nlin.CD",
    "submitted_at": "2001-12-20T13:44:52Z",
    "title_canon_sha256": "aa414e0e93fcb3576400c77918fb08970c53d2a93bc00ff6bb68b1333677bb9b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "nlin/0112036",
    "kind": "arxiv",
    "version": 3
  }
}