Pith Number

pith:ANQB3I3N

pith:2025:ANQB3I3NTXDJO56DWNY27HDZAP

not attested not anchored not stored refs pending

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

Guiying Yan, Luyi Li, Ping Li, Qiang Zhou

arxiv:2507.16351 v1 · 2025-07-22 · 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{ANQB3I3NTXDJO56DWNY27HDZAP}

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	2026-07-05T11:41:07.912665Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03601da36d9dc69777c3b371af9c7903f40d83e221e18336dee2e1ab796fc34a

Aliases

arxiv: 2507.16351 · arxiv_version: 2507.16351v1 · doi: 10.48550/arxiv.2507.16351 · pith_short_12: ANQB3I3NTXDJ · pith_short_16: ANQB3I3NTXDJO56D · pith_short_8: ANQB3I3N

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/ANQB3I3NTXDJO56DWNY27HDZAP \
  | 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: 03601da36d9dc69777c3b371af9c7903f40d83e221e18336dee2e1ab796fc34a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bea6cf8bb8bc5199b49d079646f8d3574a2ae53f82dff151cf5b3482fa3c5e25",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-22T08:33:38Z",
    "title_canon_sha256": "d44d44b627d6084f2b506a3bb30a8678847606901463ad539b3a6191eb202b89"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.16351",
    "kind": "arxiv",
    "version": 1
  }
}