Pith Number

pith:OWN25KCS

pith:2026:OWN25KCSBJMKWF5GBL7HXXVTRS

not attested not anchored not stored refs pending

Strong counterexamples to Mubayi's supersaturation conjecture in every uniformity

Heng Li, Hong Liu, Jing Wang, Xizhi Liu

arxiv:2606.26735 v1 · 2026-06-25 · 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{OWN25KCSBJMKWF5GBL7HXXVTRS}

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	2026-06-26T01:15:58.375449Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

759baea8520a58ab17a60afe7bdeb38cbb58b293b7c2f03500b3cc8dafc6beab

Aliases

arxiv: 2606.26735 · arxiv_version: 2606.26735v1 · doi: 10.48550/arxiv.2606.26735 · pith_short_12: OWN25KCSBJMK · pith_short_16: OWN25KCSBJMKWF5G · pith_short_8: OWN25KCS

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/OWN25KCSBJMKWF5GBL7HXXVTRS \
  | 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: 759baea8520a58ab17a60afe7bdeb38cbb58b293b7c2f03500b3cc8dafc6beab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ced0c15e60db74caa91bc34be62e38a54991b7498b2d69664785bd2e122da95e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-25T08:16:56Z",
    "title_canon_sha256": "1c3cbc2fdecd36d56be0d231d751288578689fc5e1cc93ea1874ebfd269fe875"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.26735",
    "kind": "arxiv",
    "version": 1
  }
}