Pith Number

pith:WOD7SATJ

pith:2007:WOD7SATJ6BVLYW3THFBX2G5LE5

not attested not anchored not stored refs pending

On higher real and stable ranks for CCR C*-algebras

Lawrence G. Brown

arxiv:0708.3072 v1 · 2007-08-22 · 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{WOD7SATJ6BVLYW3THFBX2G5LE5}

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	2026-05-18T00:42:49.382683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b387f90269f06abc5b7339437d1bab275716b185679c0aa0c1120025c987f3d6

Aliases

arxiv: 0708.3072 · arxiv_version: 0708.3072v1 · doi: 10.48550/arxiv.0708.3072 · pith_short_12: WOD7SATJ6BVL · pith_short_16: WOD7SATJ6BVLYW3T · pith_short_8: WOD7SATJ

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/WOD7SATJ6BVLYW3THFBX2G5LE5 \
  | 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: b387f90269f06abc5b7339437d1bab275716b185679c0aa0c1120025c987f3d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1bc445d1819d9ee34fa3ce847754e13399c178c80ea129d699b72732bb7abb46",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2007-08-22T19:14:17Z",
    "title_canon_sha256": "bed58bb47f9e8ccabdca385d05fc28fd0b733f9a0b4c8d9769d3726d7a76c2ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0708.3072",
    "kind": "arxiv",
    "version": 1
  }
}