Pith Number

pith:I3L2IIPS

pith:2026:I3L2IIPS5JHHW55C4ZA6OJNIMK

not attested not anchored not stored refs pending

A Single-Exponential Erd\H{o}s--Hajnal Bound for Graphs of Bounded VC-Dimension

Jiasheng Zeng, Shuang Sun, Yan Wang

arxiv:2607.09049 v1 · 2026-07-10 · 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{I3L2IIPS5JHHW55C4ZA6OJNIMK}

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	2026-07-13T00:17:37.691105Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46d7a421f2ea4e7b77a2e641e725a862977c0d4bb5dbe681d9b49716ceb40917

Aliases

arxiv: 2607.09049 · arxiv_version: 2607.09049v1 · doi: 10.48550/arxiv.2607.09049 · pith_short_12: I3L2IIPS5JHH · pith_short_16: I3L2IIPS5JHHW55C · pith_short_8: I3L2IIPS

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/I3L2IIPS5JHHW55C4ZA6OJNIMK \
  | 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: 46d7a421f2ea4e7b77a2e641e725a862977c0d4bb5dbe681d9b49716ceb40917

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "295121e78bc590adb33e3f5aaa29d1e67aec10861b7c47f3ab9ab50da43ee01d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-10T02:38:07Z",
    "title_canon_sha256": "4abaef3b00e8d6a50cdef67339784bfb64612bb18b0c86ef37f6f5db534effe3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.09049",
    "kind": "arxiv",
    "version": 1
  }
}