Pith Number

pith:4N5WCWMP

pith:2016:4N5WCWMPH723TC6N77ZKCQQ5E3

not attested not anchored not stored refs pending

A $2n^2-log(n)-1$ lower bound for the border rank of matrix multiplication

J.M. Landsberg, Mateusz Micha{\l}ek

arxiv:1608.07486 v1 · 2016-08-26 · cs.CC · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4N5WCWMPH723TC6N77ZKCQQ5E3}

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	2026-05-18T01:07:52.911646Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e37b61598f3ff5b98bcdfff2a1421d26e6e82f8a77d2a17a61d83df4639df50a

Aliases

arxiv: 1608.07486 · arxiv_version: 1608.07486v1 · doi: 10.48550/arxiv.1608.07486 · pith_short_12: 4N5WCWMPH723 · pith_short_16: 4N5WCWMPH723TC6N · pith_short_8: 4N5WCWMP

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/4N5WCWMPH723TC6N77ZKCQQ5E3 \
  | 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: e37b61598f3ff5b98bcdfff2a1421d26e6e82f8a77d2a17a61d83df4639df50a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a3585e812998cba256cb47f4cf0c58521819e5e0e4efe94731d360c615b0869d",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2016-08-26T15:06:53Z",
    "title_canon_sha256": "5dd8126cce583f1b328834024d0d81ec15a6d920e4533132784d29db285b65e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.07486",
    "kind": "arxiv",
    "version": 1
  }
}