Pith Number

pith:CNXSE4CD

pith:2015:CNXSE4CDIKIVXIOU7Z56CQFGXS

not attested not anchored not stored refs pending

The number of trees in a graph

Dhruv Mubayi, Jacques Verstraete

arxiv:1511.07274 v1 · 2015-11-23 · 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{CNXSE4CDIKIVXIOU7Z56CQFGXS}

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	2026-05-18T01:26:11.776614Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

136f22704342915ba1d4fe7be140a6bca22c1358c03ac4cbcebc759bfb4d117c

Aliases

arxiv: 1511.07274 · arxiv_version: 1511.07274v1 · doi: 10.48550/arxiv.1511.07274 · pith_short_12: CNXSE4CDIKIV · pith_short_16: CNXSE4CDIKIVXIOU · pith_short_8: CNXSE4CD

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/CNXSE4CDIKIVXIOU7Z56CQFGXS \
  | 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: 136f22704342915ba1d4fe7be140a6bca22c1358c03ac4cbcebc759bfb4d117c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46c4926ec5de13ccefcc267b582b826248fbdc1cfa73abcefb83df8daa7d5848",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-11-23T15:31:31Z",
    "title_canon_sha256": "ab9c466e52b481d42318e9a1f20de85b878b7c0afab209b0e3bf4d83c9843b80"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.07274",
    "kind": "arxiv",
    "version": 1
  }
}