Pith Number

pith:M73V2QTL

pith:2012:M73V2QTLW2I3T2TLNJQYS32S3L

not attested not anchored not stored refs pending

The Number of Spanning Trees in Apollonian Networks

Bin Wu, Francesc Comellas, Zhongzhi Zhang

arxiv:1210.0090 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{M73V2QTLW2I3T2TLNJQYS32S3L}

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	2026-05-18T03:01:47.012353Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67f75d426bb691b9ea6b6a61896f52dad359784a7550afcb2103583664b759c5

Aliases

arxiv: 1210.0090 · arxiv_version: 1210.0090v2 · doi: 10.48550/arxiv.1210.0090 · pith_short_12: M73V2QTLW2I3 · pith_short_16: M73V2QTLW2I3T2TL · pith_short_8: M73V2QTL

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/M73V2QTLW2I3T2TLNJQYS32S3L \
  | 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: 67f75d426bb691b9ea6b6a61896f52dad359784a7550afcb2103583664b759c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e70cbb76074e0b35a1914e9c10be60665c7368b4d6b542bdfae8942d8fcc204f",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-09-29T10:06:05Z",
    "title_canon_sha256": "3cb71919226dbb8ec3aa43ee4ee3657a026231aeee68932d69605cbd7f063255"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.0090",
    "kind": "arxiv",
    "version": 2
  }
}