Pith Number

pith:PSPW7BWA

pith:2017:PSPW7BWAB3DVY5E5UVNWV6VJ7Z

not attested not anchored not stored refs pending

Lower bounds on matrix factorization ranks via noncommutative polynomial optimization

David de Laat, Monique Laurent, Sander Gribling

arxiv:1708.01573 v3 · 2017-08-04 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PSPW7BWAB3DVY5E5UVNWV6VJ7Z}

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	2026-05-18T00:01:39.068041Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c9f6f86c00ec75c749da55b6afaa9fe6930930d54cc6b2f62626e6e8d01b5ff

Aliases

arxiv: 1708.01573 · arxiv_version: 1708.01573v3 · doi: 10.48550/arxiv.1708.01573 · pith_short_12: PSPW7BWAB3DV · pith_short_16: PSPW7BWAB3DVY5E5 · pith_short_8: PSPW7BWA

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/PSPW7BWAB3DVY5E5UVNWV6VJ7Z \
  | 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: 7c9f6f86c00ec75c749da55b6afaa9fe6930930d54cc6b2f62626e6e8d01b5ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea2ad0bb96a300c11fb2c5199ed4986c036834f7057f34b72f6e1db3465f5c8f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2017-08-04T16:28:23Z",
    "title_canon_sha256": "44e22a8039b33a8a2f34c11f7ad778caa8a3f4adc34be056e5757b43e52513eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.01573",
    "kind": "arxiv",
    "version": 3
  }
}