Pith Number

pith:ZXZOCTTG

pith:2026:ZXZOCTTGFS6HP46BDILNIU5ZUV

not attested not anchored not stored refs pending

A congruence obstruction to Roman's bound for Zarankiewicz numbers

Ankan Sadhu

arxiv:2608.07607 v1 · 2026-08-06 · 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{ZXZOCTTGFS6HP46BDILNIU5ZUV}

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	2026-08-11T00:15:28.775548Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdf2e14e662cbc77f3c11a16d453b9a552eaf57a677b80fd6ccebc9ec37e64d6

Aliases

arxiv: 2608.07607 · arxiv_version: 2608.07607v1 · doi: 10.48550/arxiv.2608.07607 · pith_short_12: ZXZOCTTGFS6H · pith_short_16: ZXZOCTTGFS6HP46B · pith_short_8: ZXZOCTTG

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/ZXZOCTTGFS6HP46BDILNIU5ZUV \
  | 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: cdf2e14e662cbc77f3c11a16d453b9a552eaf57a677b80fd6ccebc9ec37e64d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43fbf43880a88c4604539074e5b0f771dd90c0bea4933f91de9185408476d4c1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-08-06T20:20:47Z",
    "title_canon_sha256": "1846f9e0c3143a6eae8f1380522566eb48ba3765f15b4778d082482146592d78"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.07607",
    "kind": "arxiv",
    "version": 1
  }
}