Pith Number

pith:FBWLND6O

pith:2012:FBWLND6O2GJ73RMIZ4XEZTXAEE

not attested not anchored not stored refs pending

Amalgamated free product type III factors with at most one Cartan subalgebra

Cyril Houdayer, R\'emi Boutonnet, Sven Raum

arxiv:1212.4994 v2 · 2012-12-20 · math.OA · math.DS · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FBWLND6O2GJ73RMIZ4XEZTXAEE}

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	2026-05-17T23:53:35.926579Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

286cb68fced193fdc588cf2e4ccee0211a97001a2723bed2c9392ee9036f2bfa

Aliases

arxiv: 1212.4994 · arxiv_version: 1212.4994v2 · doi: 10.48550/arxiv.1212.4994 · pith_short_12: FBWLND6O2GJ7 · pith_short_16: FBWLND6O2GJ73RMI · pith_short_8: FBWLND6O

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/FBWLND6O2GJ73RMIZ4XEZTXAEE \
  | 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: 286cb68fced193fdc588cf2e4ccee0211a97001a2723bed2c9392ee9036f2bfa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a7ccc96a0a6957330b149496d61392e33f4e57b431713d064b5c3ee4dbdce89",
    "cross_cats_sorted": [
      "math.DS",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-12-20T11:53:55Z",
    "title_canon_sha256": "2c15590eafa8532ab01b84bbe9113dbd02fb6c80df52801aec6f3ba04ef0ef04"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.4994",
    "kind": "arxiv",
    "version": 2
  }
}