Pith Number

pith:P75V6NQM

pith:2013:P75V6NQMZ3GJX5WSPCT3CM7CKS

not attested not anchored not stored refs pending

Mean Dimension, Mean Rank, and von Neumann-L\"uck Rank

Bingbing Liang, Hanfeng Li

arxiv:1307.5471 v3 · 2013-07-20 · math.DS · math.AT · math.FA · math.GR · 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{P75V6NQMZ3GJX5WSPCT3CM7CKS}

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	2026-05-18T00:12:01.326712Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ffb5f360ccecc9bf6d278a7b133e2548cc0ea6e817f8aa862059f5ae44aa39e

Aliases

arxiv: 1307.5471 · arxiv_version: 1307.5471v3 · doi: 10.48550/arxiv.1307.5471 · pith_short_12: P75V6NQMZ3GJ · pith_short_16: P75V6NQMZ3GJX5WS · pith_short_8: P75V6NQM

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/P75V6NQMZ3GJX5WSPCT3CM7CKS \
  | 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: 7ffb5f360ccecc9bf6d278a7b133e2548cc0ea6e817f8aa862059f5ae44aa39e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b147185e4b90a2ed6a8ca0e786ddfab0bffc0f97719081e42256ffbb145e8dee",
    "cross_cats_sorted": [
      "math.AT",
      "math.FA",
      "math.GR",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-07-20T22:34:04Z",
    "title_canon_sha256": "d65dc904e3c3fcff2819a330044c6ea6139505588e16ae9a037ce073f62d14c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.5471",
    "kind": "arxiv",
    "version": 3
  }
}