Pith Number

pith:LTV7P75Y

pith:2009:LTV7P75YGBYWV5KSBYVPSV57IG

not attested not anchored not stored refs pending

On the number of spanning trees a planar graph can have

Andr\'e Schulz, Kevin Buchin

arxiv:0912.0712 v2 · 2009-12-03 · 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{LTV7P75YGBYWV5KSBYVPSV57IG}

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	2026-05-18T04:41:25.141379Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5cebf7ffb830716af5520e2af957bf4191dd5d72b6211ea2f28b7d9739585f27

Aliases

arxiv: 0912.0712 · arxiv_version: 0912.0712v2 · doi: 10.48550/arxiv.0912.0712 · pith_short_12: LTV7P75YGBYW · pith_short_16: LTV7P75YGBYWV5KS · pith_short_8: LTV7P75Y

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/LTV7P75YGBYWV5KSBYVPSV57IG \
  | 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: 5cebf7ffb830716af5520e2af957bf4191dd5d72b6211ea2f28b7d9739585f27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63b47df20828a13c1844cbdb1e4ad1b162afbb54c606f3f96b3db16b77155763",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-12-03T19:11:39Z",
    "title_canon_sha256": "054d7bfacb68bb795eb9a3d9e8cd6964d94ef5fc99e633abc5a42afd02a62b7a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.0712",
    "kind": "arxiv",
    "version": 2
  }
}