Pith Number

pith:4N2SPQHB

pith:2026:4N2SPQHB3AAXHCBKECVN6FIYFP

not attested not anchored not stored refs pending

An Improved Upper Bound on the Zarankiewicz Number z(43;2)

Ankan Sadhu

arxiv:2608.01606 v1 · 2026-08-03 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4N2SPQHB3AAXHCBKECVN6FIYFP}

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	2026-08-04T02:06:06.972483Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e37527c0e1d80173882a20aadf15182bfef0d46ab6e9c0f0a67964f1e5f090f4

Aliases

arxiv: 2608.01606 · arxiv_version: 2608.01606v1 · doi: 10.48550/arxiv.2608.01606 · pith_short_12: 4N2SPQHB3AAX · pith_short_16: 4N2SPQHB3AAXHCBK · pith_short_8: 4N2SPQHB

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/4N2SPQHB3AAXHCBKECVN6FIYFP \
  | 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: e37527c0e1d80173882a20aadf15182bfef0d46ab6e9c0f0a67964f1e5f090f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41d1ac9d184823b9796efabd26642a6f13af9e2821ee62624aaad967d52993b9",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-08-03T02:29:12Z",
    "title_canon_sha256": "7a1510f8c138caf6a3e3edc76acb4e1cbc83f3dd5e604c26801cbfeea5b5d209"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.01606",
    "kind": "arxiv",
    "version": 1
  }
}