Pith Number

pith:ZR4DPUH6

pith:2013:ZR4DPUH6PARIWGRUZH7CCL3OY4

not attested not anchored not stored refs pending

A generalization of Combinatorial Nullstellensatz

Micha{\l} Laso\'n

arxiv:1302.4647 v1 · 2013-02-19 · 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{ZR4DPUH6PARIWGRUZH7CCL3OY4}

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.

Cited by

1 paper in Pith

On converse invariant trees of diameter four

Receipt and verification

First computed	2026-07-05T03:37:35.698890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc7837d0fe78228b1a34c9fe212f6ec7392735a6b805fb483aee3edb584473e4

Aliases

arxiv: 1302.4647 · arxiv_version: 1302.4647v1 · doi: 10.48550/arxiv.1302.4647 · pith_short_12: ZR4DPUH6PARI · pith_short_16: ZR4DPUH6PARIWGRU · pith_short_8: ZR4DPUH6

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/ZR4DPUH6PARIWGRUZH7CCL3OY4 \
  | 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: cc7837d0fe78228b1a34c9fe212f6ec7392735a6b805fb483aee3edb584473e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8a887ddf1740b9d5968c64647b2d641b6a9beaf3b5e99ec756eb319587ba826",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-02-19T15:40:45Z",
    "title_canon_sha256": "49a31cf80ae58f70cdfc171261800a202d11c580e3f8732109e5fac006afd4fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.4647",
    "kind": "arxiv",
    "version": 1
  }
}