Pith Number

pith:57RWA6RI

pith:2010:57RWA6RI62QB7ZWLVQCZ2QMYGJ

not attested not anchored not stored refs pending

On the sum of k largest singular values of graphs and matrices

Vladimir Nikiforov

arxiv:1007.3949 v2 · 2010-07-22 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{57RWA6RI62QB7ZWLVQCZ2QMYGJ}

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	2026-05-18T04:42:36.029509Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efe3607a28f6a01fe6cbac059d41983273d90918685c291aee07af79d13347c5

Aliases

arxiv: 1007.3949 · arxiv_version: 1007.3949v2 · doi: 10.48550/arxiv.1007.3949 · pith_short_12: 57RWA6RI62QB · pith_short_16: 57RWA6RI62QB7ZWL · pith_short_8: 57RWA6RI

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/57RWA6RI62QB7ZWLVQCZ2QMYGJ \
  | 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: efe3607a28f6a01fe6cbac059d41983273d90918685c291aee07af79d13347c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4bae7ca3b008657e4101201d9f8e6293fc3ee27ef822b28096c796c66c34b7af",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-07-22T17:26:37Z",
    "title_canon_sha256": "904de715dbe847b7e24694b921b1b6fe3024177ad80eee50b5175fb02e3a15c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.3949",
    "kind": "arxiv",
    "version": 2
  }
}