Pith Number

pith:CBKNWK3K

pith:2010:CBKNWK3KYU562NQEW4RQZAYOFU

not attested not anchored not stored refs pending

Fixed points of the smoothing transform: Two-sided solutions

Gerold Alsmeyer, Matthias Meiners

arxiv:1009.2412 v2 · 2010-09-13 · 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{CBKNWK3KYU562NQEW4RQZAYOFU}

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	2026-05-18T04:06:33.392837Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1054db2b6ac53bed3604b7230c830e2d396c0d63b365bec63dd12293cd244712

Aliases

arxiv: 1009.2412 · arxiv_version: 1009.2412v2 · doi: 10.48550/arxiv.1009.2412 · pith_short_12: CBKNWK3KYU56 · pith_short_16: CBKNWK3KYU562NQE · pith_short_8: CBKNWK3K

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/CBKNWK3KYU562NQEW4RQZAYOFU \
  | 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: 1054db2b6ac53bed3604b7230c830e2d396c0d63b365bec63dd12293cd244712

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e2bbdac02b74360b2b4996a8fcc549a36dd4d717b369642301779355bf016c0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-09-13T15:05:37Z",
    "title_canon_sha256": "742c18a507ec3adee63d90846d15c1c0c4864118a35a4752f8e865b0d32ba493"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.2412",
    "kind": "arxiv",
    "version": 2
  }
}