Pith Number

pith:U4QHPK3P

pith:2025:U4QHPK3P4OPTN2IOY5U3TU3IZA

not attested not anchored not stored refs pending

Maxmum Size of a Uniform Family with Bounded VC-dimension

Tianchi Yang, Xingxing Yu

arxiv:2508.14334 v1 · 2025-08-20 · 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{U4QHPK3P4OPTN2IOY5U3TU3IZA}

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.

Cited by

2 papers in Pith

A disproof of the uniform witness conjecture

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

Receipt and verification

First computed	2026-07-05T11:56:30.009256Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a72077ab6fe39f36e90ec769b9d368c8068cc16316295d9658105c9df1eaee70

Aliases

arxiv: 2508.14334 · arxiv_version: 2508.14334v1 · doi: 10.48550/arxiv.2508.14334 · pith_short_12: U4QHPK3P4OPT · pith_short_16: U4QHPK3P4OPTN2IO · pith_short_8: U4QHPK3P

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/U4QHPK3P4OPTN2IOY5U3TU3IZA \
  | 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: a72077ab6fe39f36e90ec769b9d368c8068cc16316295d9658105c9df1eaee70

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5831b7d852f1847dd1a9c1460791f556383cdeaaea93fdbb613ec300ed1b2af",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-08-20T01:15:44Z",
    "title_canon_sha256": "55785a7fe567dfe6626daec1d894fd70b7c8aee11c44f3a2cf15ceed29c86aa4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.14334",
    "kind": "arxiv",
    "version": 1
  }
}