Pith Number

pith:CE3UNNUO

pith:2012:CE3UNNUOYLDQYKUPA5QGOLD3TG

not attested not anchored not stored refs pending

Selfsimilarity in the Birkhoff sum of the cotangent function

Oliver Knill

arxiv:1206.5458 v1 · 2012-06-24 · math.DS · 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{CE3UNNUOYLDQYKUPA5QGOLD3TG}

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	2026-05-18T03:52:40.043365Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

113746b68ec2c70c2a8f0760672c7b99949440523157e5ecfd1980213a40e4d1

Aliases

arxiv: 1206.5458 · arxiv_version: 1206.5458v1 · doi: 10.48550/arxiv.1206.5458 · pith_short_12: CE3UNNUOYLDQ · pith_short_16: CE3UNNUOYLDQYKUP · pith_short_8: CE3UNNUO

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/CE3UNNUOYLDQYKUPA5QGOLD3TG \
  | 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: 113746b68ec2c70c2a8f0760672c7b99949440523157e5ecfd1980213a40e4d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ce0cfd8cfc30b08529db95ed40c76b1f6117244597b671b73282e36642483e0",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-06-24T02:14:30Z",
    "title_canon_sha256": "ee2127aaf22c2b0fe63bddffe669d2aade9873222e5b22edda2ed1511d4ca8a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.5458",
    "kind": "arxiv",
    "version": 1
  }
}