Pith Number

pith:I4FFLUOM

pith:2025:I4FFLUOMWCFTXL5NH3KVGIVGGA

not attested not anchored not stored refs pending

Planar Tur\'{a}n numbers of three configurations

Ping Li, Xuqing Bai, Zhipeng Gao

arxiv:2509.06131 v2 · 2025-09-07 · 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{I4FFLUOMWCFTXL5NH3KVGIVGGA}

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	2026-07-05T12:11:20.518429Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

470a55d1ccb08b3bafad3ed55322a63038e7911aa05aec58c73d7a9ce9578085

Aliases

arxiv: 2509.06131 · arxiv_version: 2509.06131v2 · doi: 10.48550/arxiv.2509.06131 · pith_short_12: I4FFLUOMWCFT · pith_short_16: I4FFLUOMWCFTXL5N · pith_short_8: I4FFLUOM

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/I4FFLUOMWCFTXL5NH3KVGIVGGA \
  | 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: 470a55d1ccb08b3bafad3ed55322a63038e7911aa05aec58c73d7a9ce9578085

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8babfbe5990ace2f5b02d44a5514774a01bb016aecb3fed0e1f0fede3d3596d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-09-07T16:38:46Z",
    "title_canon_sha256": "dddd98278a4d457af6706e426af13bd7e6563a829f5c9c7e497780a89aa4d23b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.06131",
    "kind": "arxiv",
    "version": 2
  }
}