Pith Number

pith:4WKJWL5G

pith:2011:4WKJWL5GPACAPEU5IZAMGY4O7L

not attested not anchored not stored refs pending

Higher matrix-tree theorems

Anastasia Trofimova, Andrey Ploskonosov, Yurii Burman

arxiv:1109.6625 v1 · 2011-09-29 · 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{4WKJWL5GPACAPEU5IZAMGY4O7L}

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	2026-05-18T04:12:01.222755Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5949b2fa6780407929d4640c3638efaf237581464430ca2082f35320084571e

Aliases

arxiv: 1109.6625 · arxiv_version: 1109.6625v1 · doi: 10.48550/arxiv.1109.6625 · pith_short_12: 4WKJWL5GPACA · pith_short_16: 4WKJWL5GPACAPEU5 · pith_short_8: 4WKJWL5G

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/4WKJWL5GPACAPEU5IZAMGY4O7L \
  | 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: e5949b2fa6780407929d4640c3638efaf237581464430ca2082f35320084571e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "28e0ec73e5468d78ff9aca7733d989110593f7822cad676f4852cb83b7626cec",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-09-29T19:13:07Z",
    "title_canon_sha256": "71b13aea0b1f017627327ec28dfddc447e158d034641711dae134fc433de4c47"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.6625",
    "kind": "arxiv",
    "version": 1
  }
}