Pith Number

pith:QQJ7NS7A

pith:2026:QQJ7NS7ANJL4SSJEKBH46TJM3G

not attested not anchored not stored refs pending

Beating the Ahlswede--Khachatrian bound for the Erd\H{o}s--Frankl--Pach problem

Tuan Tran, Zixiang Xu

arxiv:2606.23469 v1 · 2026-06-22 · 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{QQJ7NS7ANJL4SSJEKBH46TJM3G}

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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

A disproof of the uniform witness conjecture

Receipt and verification

First computed	2026-06-23T03:14:20.749891Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8413f6cbe06a57c94924504fcf4d2cd9a919423d765028f7c2bf892a41e7501a

Aliases

arxiv: 2606.23469 · arxiv_version: 2606.23469v1 · doi: 10.48550/arxiv.2606.23469 · pith_short_12: QQJ7NS7ANJL4 · pith_short_16: QQJ7NS7ANJL4SSJE · pith_short_8: QQJ7NS7A

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/QQJ7NS7ANJL4SSJEKBH46TJM3G \
  | 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: 8413f6cbe06a57c94924504fcf4d2cd9a919423d765028f7c2bf892a41e7501a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "673f803c320c200c5a704786343812192a242bf3dc6ce9be929fe847e56a5e5b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-22T15:16:37Z",
    "title_canon_sha256": "f3c9dcc9e22d29ad0592b81b066fc983a7a3a3df13b55ccb0b173600c8ea47f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.23469",
    "kind": "arxiv",
    "version": 1
  }
}