Pith Number

pith:5AA2WRYA

pith:2011:5AA2WRYAKBSWKWM7V522GGSOMT

not attested not anchored not stored refs pending

Rational Functions with a Unique Critical Point

Xander Faber

arxiv:1102.1433 v2 · 2011-02-07 · math.NT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5AA2WRYAKBSWKWM7V522GGSOMT}

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	2026-05-18T04:21:52.727749Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e801ab4700506565599faf75a31a4e64cdc9b54df02a5aad8a5208025640b4df

Aliases

arxiv: 1102.1433 · arxiv_version: 1102.1433v2 · doi: 10.48550/arxiv.1102.1433 · pith_short_12: 5AA2WRYAKBSW · pith_short_16: 5AA2WRYAKBSWKWM7 · pith_short_8: 5AA2WRYA

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/5AA2WRYAKBSWKWM7V522GGSOMT \
  | 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: e801ab4700506565599faf75a31a4e64cdc9b54df02a5aad8a5208025640b4df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69617852246e4d6c0823f02e9e52b6d504c599ec98439307ad7ef802c0786444",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-02-07T21:01:23Z",
    "title_canon_sha256": "5cc8139a3ba11fbc4550298aab9614dca4b432e55e89f0a885e23c8391462bd9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.1433",
    "kind": "arxiv",
    "version": 2
  }
}