Pith Number

pith:VJVAWRSQ

pith:2004:VJVAWRSQL4I3H2YMSHA5YU62EX

not attested not anchored not stored refs pending

The border rank of the multiplication of two by two matrices is seven

J.M. Landsberg

arxiv:math/0407224 v3 · 2004-07-13 · math.AG · cs.NA · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VJVAWRSQL4I3H2YMSHA5YU62EX}

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	2026-06-03T22:06:15.444782Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa6a0b46505f11b3eb0c91c1dc53da25e2dc6ad5ff8299de3c0c973c69feb563

Aliases

arxiv: math/0407224 · arxiv_version: math/0407224v3 · doi: 10.48550/arxiv.math/0407224 · pith_short_12: VJVAWRSQL4I3 · pith_short_16: VJVAWRSQL4I3H2YM · pith_short_8: VJVAWRSQ

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/VJVAWRSQL4I3H2YMSHA5YU62EX \
  | 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: aa6a0b46505f11b3eb0c91c1dc53da25e2dc6ad5ff8299de3c0c973c69feb563

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca2ef8413887c49ef807052ac33ff57fae6823761be6eadcc16f4a56a24b1f38",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2004-07-13T19:28:25Z",
    "title_canon_sha256": "0dc4c508d1d139e9b82663060ebdd288693bef4ddb1f72e50fb75b6e156fabc3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0407224",
    "kind": "arxiv",
    "version": 3
  }
}