Pith Number

pith:IIEFVGU7

pith:2012:IIEFVGU7EL4ANUZRHCJRCBQSME

not attested not anchored not stored refs pending

Strong convergence for reduced free products (Remarks on a result by Paul Skoufranis)

Gilles Pisier

arxiv:1203.3186 v3 · 2012-03-14 · 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{IIEFVGU7EL4ANUZRHCJRCBQSME}

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	2026-05-18T00:34:05.474619Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42085a9a9f22f806d33138931106126107bd1374f311fa334881381e7c0b902c

Aliases

arxiv: 1203.3186 · arxiv_version: 1203.3186v3 · doi: 10.48550/arxiv.1203.3186 · pith_short_12: IIEFVGU7EL4A · pith_short_16: IIEFVGU7EL4ANUZR · pith_short_8: IIEFVGU7

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/IIEFVGU7EL4ANUZRHCJRCBQSME \
  | 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: 42085a9a9f22f806d33138931106126107bd1374f311fa334881381e7c0b902c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68b74c45a240f3cd682bd1d03e5495381340e9f0eb8f2845259b0142f8f9e8f2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-03-14T19:50:17Z",
    "title_canon_sha256": "6b98b2a132d6f908c15ffe1a34474f9e71394a21261b546ac08b9d0a7dde1100"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.3186",
    "kind": "arxiv",
    "version": 3
  }
}