Pith Number

pith:RGBP7DYT

pith:2011:RGBP7DYTPKZBKCPEWWYC4QISDG

not attested not anchored not stored refs pending

New lower bounds for the border rank of matrix multiplication

Giorgio Ottaviani, J. M. Landsberg

arxiv:1112.6007 v3 · 2011-12-27 · 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{RGBP7DYTPKZBKCPEWWYC4QISDG}

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	2026-05-18T03:22:06.333149Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8982ff8f137ab21509e4b5b02e4112198c6f24dbe0f3275174a6a1fdd64031c0

Aliases

arxiv: 1112.6007 · arxiv_version: 1112.6007v3 · doi: 10.48550/arxiv.1112.6007 · pith_short_12: RGBP7DYTPKZB · pith_short_16: RGBP7DYTPKZBKCPE · pith_short_8: RGBP7DYT

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/RGBP7DYTPKZBKCPEWWYC4QISDG \
  | 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: 8982ff8f137ab21509e4b5b02e4112198c6f24dbe0f3275174a6a1fdd64031c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d801a6441894c106f884b36cafb606cd6131838ea3a6c53f7168b25b777b30a0",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2011-12-27T19:24:57Z",
    "title_canon_sha256": "9d5c31fb56e5e3749565d4f0fad8da572a65f37d74baa16dd7823bddd716be87"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.6007",
    "kind": "arxiv",
    "version": 3
  }
}