Pith Number

pith:BDKA57F2

pith:2011:BDKA57F2NJ7OCOH5L7EU6X7HYE

not attested not anchored not stored refs pending

MF-traces and a Lower Bound for the Topological Free Entropy Dimension in Unital C*-algebras

Don Hadwin, Junhao Shen, Qihui Li, Weihua Li

arxiv:1109.0673 v1 · 2011-09-04 · 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{BDKA57F2NJ7OCOH5L7EU6X7HYE}

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	2026-05-18T04:14:07.065951Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

08d40efcba6a7ee138fd5fc94f5fe7c13c0f49ed04a5ce212e6cbcf08a2dd78a

Aliases

arxiv: 1109.0673 · arxiv_version: 1109.0673v1 · doi: 10.48550/arxiv.1109.0673 · pith_short_12: BDKA57F2NJ7O · pith_short_16: BDKA57F2NJ7OCOH5 · pith_short_8: BDKA57F2

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/BDKA57F2NJ7OCOH5L7EU6X7HYE \
  | 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: 08d40efcba6a7ee138fd5fc94f5fe7c13c0f49ed04a5ce212e6cbcf08a2dd78a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4a3582c8d0d0fd2ac7a03a593d80f8e472f1dea27411118bab5c3ecd66fb334",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2011-09-04T05:34:11Z",
    "title_canon_sha256": "ec1661347d38f433937ab36573a78f4a4dea2513def97acf668ec633f0c8085d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.0673",
    "kind": "arxiv",
    "version": 1
  }
}