Pith Number

pith:GXWEK2PP

pith:2015:GXWEK2PPMVVA4YO7EP24VAX7FS

not attested not anchored not stored refs pending

On the optimal paving over MASAs in von Neumann algebras

Sorin Popa, Stefaan Vaes

arxiv:1507.01072 v1 · 2015-07-04 · 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{GXWEK2PPMVVA4YO7EP24VAX7FS}

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	2026-05-18T01:10:18.399955Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35ec4569ef656a0e61df23f5ca82ff2c9d46776471db20050cc62a715a406243

Aliases

arxiv: 1507.01072 · arxiv_version: 1507.01072v1 · doi: 10.48550/arxiv.1507.01072 · pith_short_12: GXWEK2PPMVVA · pith_short_16: GXWEK2PPMVVA4YO7 · pith_short_8: GXWEK2PP

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/GXWEK2PPMVVA4YO7EP24VAX7FS \
  | 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: 35ec4569ef656a0e61df23f5ca82ff2c9d46776471db20050cc62a715a406243

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82b71505157640479f2c317f86cc82b2746ceb02c85e9d040ce081258455b2e8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-07-04T05:50:52Z",
    "title_canon_sha256": "3e25a7ae074fdac486e5efa3007c4220ffc0352d41f3aca82007ce9c6d10dd22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.01072",
    "kind": "arxiv",
    "version": 1
  }
}