Pith Number

pith:4RAR3KLV

pith:2019:4RAR3KLVCPPRH5TPI6TQWPFAUC

not attested not anchored not stored refs pending

Frobenius-Perron theory for projective schemes

E. Wicks, H. Zhu, J. J. Zhang, J.M. Chen, X-.H. Zhang, Z.B. Gao

arxiv:1907.02221 v3 · 2019-07-04 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4RAR3KLVCPPRH5TPI6TQWPFAUC}

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	2026-07-05T03:41:22.083488Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4411da97513df13f66f47a70b3ca0a09ab9a3aedb22e091d8c55c16a519463f

Aliases

arxiv: 1907.02221 · arxiv_version: 1907.02221v3 · doi: 10.48550/arxiv.1907.02221 · pith_short_12: 4RAR3KLVCPPR · pith_short_16: 4RAR3KLVCPPRH5TP · pith_short_8: 4RAR3KLV

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/4RAR3KLVCPPRH5TPI6TQWPFAUC \
  | 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: e4411da97513df13f66f47a70b3ca0a09ab9a3aedb22e091d8c55c16a519463f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3eb5ea2689fd770b2dedc0fd7184477c44151e5b696d2748e73986392ee86e23",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2019-07-04T05:22:08Z",
    "title_canon_sha256": "0cbf4144940c01067f9a438eff8abaf97c1a43be092a372570fd8977e7d7c366"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.02221",
    "kind": "arxiv",
    "version": 3
  }
}