Pith Number

pith:HDDNU2AI

pith:2012:HDDNU2AISIKPZILIMYOXCRRMDJ

not attested not anchored not stored refs pending

The Number of Spanning Trees of an Infinite Family of Outerplanar, Small-World and Self-Similar Graphs

Alicia Miralles, Francesc Comellas, Hongxiao Liu, Zhongzhi Zhang

arxiv:1210.0092 v2 · 2012-09-29 · math.CO · cs.DM

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HDDNU2AISIKPZILIMYOXCRRMDJ}

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	2026-05-18T01:54:12.548759Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

38c6da68089214fca168661d71462c1a623ee54e995416f105313d36e151619b

Aliases

arxiv: 1210.0092 · arxiv_version: 1210.0092v2 · doi: 10.48550/arxiv.1210.0092 · pith_short_12: HDDNU2AISIKP · pith_short_16: HDDNU2AISIKPZILI · pith_short_8: HDDNU2AI

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/HDDNU2AISIKPZILIMYOXCRRMDJ \
  | 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: 38c6da68089214fca168661d71462c1a623ee54e995416f105313d36e151619b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c71c0836429eecf8d98571de2d450ce5ddfbf4bc0be99418459530d931bfd55",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-09-29T10:43:06Z",
    "title_canon_sha256": "e0b503e637a29f0b1304b77439cb7d3980c86cef8e19f10a2134f96274a44a3f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.0092",
    "kind": "arxiv",
    "version": 2
  }
}