Pith Number

pith:JTBL7ZIV

pith:2012:JTBL7ZIVNQ5D62YZNHCLHKJNPU

not attested not anchored not stored refs pending

Counting graphs with different numbers of spanning trees through the counting of prime partitions

Jernej Azarija

arxiv:1210.5704 v2 · 2012-10-21 · 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{JTBL7ZIVNQ5D62YZNHCLHKJNPU}

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	2026-05-18T03:42:33.496127Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4cc2bfe5156c3a3f6b1969c4b3a92d7d13bccd3f024e38fb346f1d63ce2d6ff0

Aliases

arxiv: 1210.5704 · arxiv_version: 1210.5704v2 · doi: 10.48550/arxiv.1210.5704 · pith_short_12: JTBL7ZIVNQ5D · pith_short_16: JTBL7ZIVNQ5D62YZ · pith_short_8: JTBL7ZIV

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/JTBL7ZIVNQ5D62YZNHCLHKJNPU \
  | 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: 4cc2bfe5156c3a3f6b1969c4b3a92d7d13bccd3f024e38fb346f1d63ce2d6ff0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e7f7c5b0300fb816cef358ed6d998c9c74044247ade70f6e76790c8ec236a57",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-10-21T08:43:54Z",
    "title_canon_sha256": "b50c0e8c193665f0eb03fdb17d1c77c223da65e91f2d6af2b6edc7c6971e384c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5704",
    "kind": "arxiv",
    "version": 2
  }
}