Pith Number

pith:CP3LIK4M

pith:2025:CP3LIK4MK2LUCUIP6457D5QMP4

not attested not anchored not stored refs pending

Exact Tur\'{a}n densities in triple systems

Caihong Yang, Hongbin Zhao, Nannan Chen, Yuzhen Qi

arxiv:2507.07360 v1 · 2025-07-10 · 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{CP3LIK4MK2LUCUIP6457D5QMP4}

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	2026-07-05T11:34:56.519906Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13f6b42b8c569741510ff73bf1f60c7f1f328c6a37afb8e01ee86dd9373435ad

Aliases

arxiv: 2507.07360 · arxiv_version: 2507.07360v1 · doi: 10.48550/arxiv.2507.07360 · pith_short_12: CP3LIK4MK2LU · pith_short_16: CP3LIK4MK2LUCUIP · pith_short_8: CP3LIK4M

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/CP3LIK4MK2LUCUIP6457D5QMP4 \
  | 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: 13f6b42b8c569741510ff73bf1f60c7f1f328c6a37afb8e01ee86dd9373435ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7acc21183841636c5c011799b2458aa5f0c93d1eb43be06c0b9ed43b9953d154",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-10T00:59:12Z",
    "title_canon_sha256": "05cca7aeea566aa5aeb4e4c22b88af1f24c1fb897780f358da220399923a9a21"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.07360",
    "kind": "arxiv",
    "version": 1
  }
}