Pith Number

pith:GE5X5AZV

pith:2010:GE5X5AZV4MPY23T7P2ORHOQ7PU

not attested not anchored not stored refs pending

Extremal norms of graphs and matrices

Vladimir Nikiforov

arxiv:1007.3947 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{GE5X5AZV4MPY23T7P2ORHOQ7PU}

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	2026-05-18T04:42:36.035964Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

313b7e8335e31f8d6e7f7e9d13ba1f7d29c52867d471d59d46919027f703ca16

Aliases

arxiv: 1007.3947 · arxiv_version: 1007.3947v2 · doi: 10.48550/arxiv.1007.3947 · pith_short_12: GE5X5AZV4MPY · pith_short_16: GE5X5AZV4MPY23T7 · pith_short_8: GE5X5AZV

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/GE5X5AZV4MPY23T7P2ORHOQ7PU \
  | 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: 313b7e8335e31f8d6e7f7e9d13ba1f7d29c52867d471d59d46919027f703ca16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59cafa0aa653dc56fca50db5c874a903e6fee0c194b300779b504f71ddd5e632",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-07-22T17:22:42Z",
    "title_canon_sha256": "74fcfd1a4fb616b6a345b92d7a0e9a7a4d640366168bd9194721eeac01a6a332"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.3947",
    "kind": "arxiv",
    "version": 2
  }
}