Pith Number

pith:WA6YPUHY

pith:2022:WA6YPUHYIS7JCG5HCBF3NRK5LW

not attested not anchored not stored refs pending

An improved lower bound for the planar Tur\'an number of cycles

Yongxin Lan, Zi-Xia Song

arxiv:2209.01312 v1 · 2022-09-03 · 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{WA6YPUHYIS7JCG5HCBF3NRK5LW}

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

Planar Tur\'an number of disjoint union of $C_3$ and $C_5$

Receipt and verification

First computed	2026-07-05T04:54:27.861925Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b03d87d0f844be911ba7104bb6c55d5daea265a62d37f0d546092469c6f1909b

Aliases

arxiv: 2209.01312 · arxiv_version: 2209.01312v1 · doi: 10.48550/arxiv.2209.01312 · pith_short_12: WA6YPUHYIS7J · pith_short_16: WA6YPUHYIS7JCG5H · pith_short_8: WA6YPUHY

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/WA6YPUHYIS7JCG5HCBF3NRK5LW \
  | 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: b03d87d0f844be911ba7104bb6c55d5daea265a62d37f0d546092469c6f1909b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb7f476f1f431983ba79b3405d2f2f8dc86c0323950e7053a3dc0bc70d22f17e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2022-09-03T02:34:37Z",
    "title_canon_sha256": "919027f996b8afada4af90d0bb1b1f4e770125f908fb495ae5291a1eb6b679e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2209.01312",
    "kind": "arxiv",
    "version": 1
  }
}