Pith Number

pith:HVMCHLSA

pith:2016:HVMCHLSAWIVU4QLYODG6DGCI67

not attested not anchored not stored refs pending

On cap sets and the group-theoretic approach to matrix multiplication

Chris Umans, Eric Naslund, Henry Cohn, Jonah Blasiak, Joshua A. Grochow, Thomas Church, William F. Sawin

arxiv:1605.06702 v4 · 2016-05-21 · math.CO · cs.DS · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HVMCHLSAWIVU4QLYODG6DGCI67}

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	2026-05-18T00:52:50.224737Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3d5823ae40b22b4e417870cde19848f7c96f6c5d7a89f0bf20bcafb6574b8352

Aliases

arxiv: 1605.06702 · arxiv_version: 1605.06702v4 · doi: 10.48550/arxiv.1605.06702 · pith_short_12: HVMCHLSAWIVU · pith_short_16: HVMCHLSAWIVU4QLY · pith_short_8: HVMCHLSA

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/HVMCHLSAWIVU4QLYODG6DGCI67 \
  | 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: 3d5823ae40b22b4e417870cde19848f7c96f6c5d7a89f0bf20bcafb6574b8352

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8ad466f6a78314bbbdbaaeee53dc38646cc434de80a5ded2c4e6d3080868c6e",
    "cross_cats_sorted": [
      "cs.DS",
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-05-21T21:28:27Z",
    "title_canon_sha256": "2d38e23545e5854774f7c4e1961110bc2a871e8b6857e84a0c6cd56e712f56d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.06702",
    "kind": "arxiv",
    "version": 4
  }
}