Pith Number

pith:O3JNPD65

pith:2026:O3JNPD65RIIUWVEXAAAQ3COLM7

not attested not anchored not stored refs pending

Recursive lower bounds for uniform set systems of bounded VC-dimension

Gennian Ge, Xiaochen Zhao

arxiv:2606.22064 v1 · 2026-06-20 · math.CO · math.ST · stat.TH

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O3JNPD65RIIUWVEXAAAQ3COLM7}

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

1 paper in Pith

A disproof of the uniform witness conjecture

Receipt and verification

First computed	2026-06-23T02:13:06.781854Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76d2d78fdd8a114b549700010d89cb67f4253a1842ba6153fa75c2d16f6b5962

Aliases

arxiv: 2606.22064 · arxiv_version: 2606.22064v1 · doi: 10.48550/arxiv.2606.22064 · pith_short_12: O3JNPD65RIIU · pith_short_16: O3JNPD65RIIUWVEX · pith_short_8: O3JNPD65

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/O3JNPD65RIIUWVEXAAAQ3COLM7 \
  | 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: 76d2d78fdd8a114b549700010d89cb67f4253a1842ba6153fa75c2d16f6b5962

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb93b3b61df660017c474d29531ac8b13d9f2a70c0cc515eaf250c1b52526122",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-20T14:26:23Z",
    "title_canon_sha256": "7db93955649dba89b2e11fb0bd77480d01ac903905cb00da9cb56668c7d391d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.22064",
    "kind": "arxiv",
    "version": 1
  }
}