Pith Number

pith:FAPJCKGV

pith:2009:FAPJCKGVD3H6INGCV62O4JDUNK

not attested not anchored not stored refs pending

Margulis numbers and number fields

Peter B. Shalen

arxiv:0902.1011 v2 · 2009-02-06 · math.DG · math.GT · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FAPJCKGVD3H6INGCV62O4JDUNK}

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	2026-05-18T04:15:48.227641Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

281e9128d51ecfe434c2afb4ee24746aa56e6ff21ed7cd063e8abca6ce1d26d0

Aliases

arxiv: 0902.1011 · arxiv_version: 0902.1011v2 · doi: 10.48550/arxiv.0902.1011 · pith_short_12: FAPJCKGVD3H6 · pith_short_16: FAPJCKGVD3H6INGC · pith_short_8: FAPJCKGV

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/FAPJCKGVD3H6INGCV62O4JDUNK \
  | 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: 281e9128d51ecfe434c2afb4ee24746aa56e6ff21ed7cd063e8abca6ce1d26d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "305521732cf01927579a6ce756aabd1a7043c03b91e77c19e4d753828be3a3af",
    "cross_cats_sorted": [
      "math.GT",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2009-02-06T04:23:12Z",
    "title_canon_sha256": "4f5452d777eb3fe096db45f65dc6753516d313cb75ea4639d16c47c6ad28d8bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0902.1011",
    "kind": "arxiv",
    "version": 2
  }
}