Pith Number

pith:I2FOPCNQ

pith:2004:I2FOPCNQP4ABGONK2H2ZPKKRMU

not attested not anchored not stored refs pending

A noncommutative version of the John-Nirenberg theorem

Magdalena Musat, Marius Junge

arxiv:math/0410121 v2 · 2004-10-05 · math.FA · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I2FOPCNQP4ABGONK2H2ZPKKRMU}

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	2026-07-04T14:50:07.719336Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

468ae789b07f001339aad1f597a9516512757e81fe87aee15f96b2fa3bacfca6

Aliases

arxiv: math/0410121 · arxiv_version: math/0410121v2 · doi: 10.48550/arxiv.math/0410121 · pith_short_12: I2FOPCNQP4AB · pith_short_16: I2FOPCNQP4ABGONK · pith_short_8: I2FOPCNQ

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/I2FOPCNQP4ABGONK2H2ZPKKRMU \
  | 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: 468ae789b07f001339aad1f597a9516512757e81fe87aee15f96b2fa3bacfca6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dabdd00eb5bb37604ce632799ea69af1221c4f45dac1d0afcaa3c446908a5b23",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2004-10-05T21:08:20Z",
    "title_canon_sha256": "f05fa757aa5e1b2ea1ce4076a073d6a5badda52557d009f212d0e60a0d7c13b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0410121",
    "kind": "arxiv",
    "version": 2
  }
}