Pith Number

pith:WJKXFIUH

pith:2003:WJKXFIUHGE2MLELBXGG4CDHL5I

not attested not anchored not stored refs pending

A group-theoretic approach to fast matrix multiplication

Christopher Umans, Henry Cohn

arxiv:math/0307321 v2 · 2003-07-24 · math.GR · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WJKXFIUHGE2MLELBXGG4CDHL5I}

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	2026-05-18T04:00:02.987506Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b25572a2873134c59161b98dc10cebea0dee8bd817daef6d6a08a1d43af7adf4

Aliases

arxiv: math/0307321 · arxiv_version: math/0307321v2 · doi: 10.48550/arxiv.math/0307321 · pith_short_12: WJKXFIUHGE2M · pith_short_16: WJKXFIUHGE2MLELB · pith_short_8: WJKXFIUH

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/WJKXFIUHGE2MLELBXGG4CDHL5I \
  | 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: b25572a2873134c59161b98dc10cebea0dee8bd817daef6d6a08a1d43af7adf4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c8437de7a00272b51b58668b2e96285fc7a3ad88fe1b476e532a1dfbe118a0e",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2003-07-24T04:37:11Z",
    "title_canon_sha256": "a6f7a423f8e65ac3763e550767f9fd8cc403f6d93e44c00facb8ff1743e14061"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0307321",
    "kind": "arxiv",
    "version": 2
  }
}