Pith Number

pith:ARHTHCWY

pith:2026:ARHTHCWYWHJWHRJRF6N7CHREVA

not attested not anchored not stored refs pending

Upper Bounds on Tur\'an Densities via Extremal Set Theory

Ningyuan Yang, Tianming Zhu, Xizhi Liu, Yaobin Chen

arxiv:2606.02135 v1 · 2026-06-01 · 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{ARHTHCWYWHJWHRJRF6N7CHREVA}

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	2026-06-02T02:05:07.442010Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

044f338ad8b1d363c5312f9bf11e24a811afcf2caaeba8df16ee5f8ecf491a30

Aliases

arxiv: 2606.02135 · arxiv_version: 2606.02135v1 · doi: 10.48550/arxiv.2606.02135 · pith_short_12: ARHTHCWYWHJW · pith_short_16: ARHTHCWYWHJWHRJR · pith_short_8: ARHTHCWY

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/ARHTHCWYWHJWHRJRF6N7CHREVA \
  | 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: 044f338ad8b1d363c5312f9bf11e24a811afcf2caaeba8df16ee5f8ecf491a30

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26e305cd5f0978caa1fe750bfc7cca675fb6cf2fb22cf616e20ea08348ba5ff8",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-01T12:02:15Z",
    "title_canon_sha256": "9bd87be7b0315c1ec3fd65d3437951e542a8a250d17ef2bb155d468b07482630"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.02135",
    "kind": "arxiv",
    "version": 1
  }
}