Pith Number

pith:MIYNJVHY

pith:2012:MIYNJVHY6W5POSTK76BRXS5UAD

not attested not anchored not stored refs pending

A quantitative version of the commutator theorem for zero trace matrices

Gideon Schechtman, Narutaka Ozawa, William B. Johnson

arxiv:1202.0986 v2 · 2012-02-05 · 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{MIYNJVHY6W5POSTK76BRXS5UAD}

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	2026-05-18T02:57:15.177153Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6230d4d4f8f5baf74a6aff831bcbb400fcbd0ddeca9d1d9354e5eaf0066e69ed

Aliases

arxiv: 1202.0986 · arxiv_version: 1202.0986v2 · doi: 10.48550/arxiv.1202.0986 · pith_short_12: MIYNJVHY6W5P · pith_short_16: MIYNJVHY6W5POSTK · pith_short_8: MIYNJVHY

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/MIYNJVHY6W5POSTK76BRXS5UAD \
  | 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: 6230d4d4f8f5baf74a6aff831bcbb400fcbd0ddeca9d1d9354e5eaf0066e69ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f64566e8254c31a91cc5ed040c59bba4bc6f392d1577aebbcc237ccf5268572c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-02-05T18:16:14Z",
    "title_canon_sha256": "67c5d8044b94b7436a950379ffb12107c95b4914ec2dda0c16ea336a548387d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.0986",
    "kind": "arxiv",
    "version": 2
  }
}