Pith Number

pith:35TCHGIA

pith:2016:35TCHGIAMMM3MU22X6VVJ6NFIR

not attested not anchored not stored refs pending

Lebesgue decomposition of functionals and unique preduals for commutants modulo normed ideals

Dan-Virgil Voiculescu

arxiv:1608.07228 v1 · 2016-08-25 · math.OA · 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{35TCHGIAMMM3MU22X6VVJ6NFIR}

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	2026-05-18T01:07:54.526232Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df662399006319b6535abfab54f9a5445a19bed3c7feb8cab0d7a67ae45ba127

Aliases

arxiv: 1608.07228 · arxiv_version: 1608.07228v1 · doi: 10.48550/arxiv.1608.07228 · pith_short_12: 35TCHGIAMMM3 · pith_short_16: 35TCHGIAMMM3MU22 · pith_short_8: 35TCHGIA

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/35TCHGIAMMM3MU22X6VVJ6NFIR \
  | 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: df662399006319b6535abfab54f9a5445a19bed3c7feb8cab0d7a67ae45ba127

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f59cbb823e01238fde0ce2e12617bac7ae27c0ca0ab91fff213e072791647ad",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2016-08-25T17:33:33Z",
    "title_canon_sha256": "0a61a35da6c4a5b60e381fd0ecd8f0e958f0ca0f67ed527b191ba9fba87e1715"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.07228",
    "kind": "arxiv",
    "version": 1
  }
}