Pith Number

pith:YSDI377R

pith:2016:YSDI377RWW4MAAUZKDTT4VZ7GU

not attested not anchored not stored refs pending

The average number of spanning trees in sparse graphs with given degrees

Brendan D. McKay, Catherine Greenhill, Matthew Kwan, Mikhail Isaev

arxiv:1606.01586 v3 · 2016-06-05 · 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{YSDI377RWW4MAAUZKDTT4VZ7GU}

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	2026-05-18T00:50:29.518743Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4868dfff1b5b8c0029950e73e573f3537564364dbb1e32f9ff7760914f41a81

Aliases

arxiv: 1606.01586 · arxiv_version: 1606.01586v3 · doi: 10.48550/arxiv.1606.01586 · pith_short_12: YSDI377RWW4M · pith_short_16: YSDI377RWW4MAAUZ · pith_short_8: YSDI377R

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/YSDI377RWW4MAAUZKDTT4VZ7GU \
  | 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: c4868dfff1b5b8c0029950e73e573f3537564364dbb1e32f9ff7760914f41a81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e60ed1469fc9c35a0c281931dfd3e3cae4b486a2e6a40564ec76b35f28ec46c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-06-05T23:57:22Z",
    "title_canon_sha256": "c2148bd3c6867b268591cce960126564fe27ae9082d3cd62bde95b44e52849aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.01586",
    "kind": "arxiv",
    "version": 3
  }
}