Pith Number

pith:BJM3WGZJ

pith:2013:BJM3WGZJO5L5OTTJCW2EGCF5DC

not attested not anchored not stored refs pending

A II$_1$ factor approach to the Kadison-Singer problem

Sorin Popa

arxiv:1303.1424 v3 · 2013-03-06 · 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{BJM3WGZJO5L5OTTJCW2EGCF5DC}

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	2026-05-18T01:51:16.122781Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a59bb1b297757d74e6915b44308bd18af160e7bdf91d6f55ff6b8560f5b2bbd

Aliases

arxiv: 1303.1424 · arxiv_version: 1303.1424v3 · doi: 10.48550/arxiv.1303.1424 · pith_short_12: BJM3WGZJO5L5 · pith_short_16: BJM3WGZJO5L5OTTJ · pith_short_8: BJM3WGZJ

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/BJM3WGZJO5L5OTTJCW2EGCF5DC \
  | 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: 0a59bb1b297757d74e6915b44308bd18af160e7bdf91d6f55ff6b8560f5b2bbd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b1115e1a574548cc34330f00f4e551e5c057bc493855846b7623bbab310f526",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2013-03-06T19:00:04Z",
    "title_canon_sha256": "f77c39ef4e9429ed2bffde6644ba85ebf06e0c398b26c179aced2bf5c24a705a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.1424",
    "kind": "arxiv",
    "version": 3
  }
}