Pith Number

pith:H4LFR7PC

pith:2026:H4LFR7PCM33MJJTJQHGDAI43CT

not attested not anchored not stored refs pending

Strong counterexamples to a supersaturation question of Ma-Yuan

Long-tu Yuan, Wanfang Chen

arxiv:2606.09518 v1 · 2026-06-08 · 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{H4LFR7PCM33MJJTJQHGDAI43CT}

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	2026-06-09T02:08:53.038181Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3f1658fde266f6c4a66981cc30239b14e80376dc68a115fee96eb35aa0e11aef

Aliases

arxiv: 2606.09518 · arxiv_version: 2606.09518v1 · doi: 10.48550/arxiv.2606.09518 · pith_short_12: H4LFR7PCM33M · pith_short_16: H4LFR7PCM33MJJTJ · pith_short_8: H4LFR7PC

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/H4LFR7PCM33MJJTJQHGDAI43CT \
  | 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: 3f1658fde266f6c4a66981cc30239b14e80376dc68a115fee96eb35aa0e11aef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "005c147ba311b3e6631cdd06560003f1d2e367a74d1cc0466423318ad59537f7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-08T14:08:27Z",
    "title_canon_sha256": "16d7f40441e03287636f653121b118c569b5fc3974220cf0be1a7d083322f159"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.09518",
    "kind": "arxiv",
    "version": 1
  }
}