Pith Number

pith:GTH2MO47

pith:2016:GTH2MO47K4MB22SFWYBQC6AVX6

not attested not anchored not stored refs pending

From Chio Pivotal Condensation to the Matrix-Tree theorem

Anya Zhang, Darij Grinberg, Karthik Karnik

arxiv:1606.08193 v1 · 2016-06-27 · 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{GTH2MO47K4MB22SFWYBQC6AVX6}

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	2026-05-18T01:11:52.589945Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34cfa63b9f57181d6a45b603017815bfbe4f55f3d0cb5c7bf11b19d5b86f0ee1

Aliases

arxiv: 1606.08193 · arxiv_version: 1606.08193v1 · doi: 10.48550/arxiv.1606.08193 · pith_short_12: GTH2MO47K4MB · pith_short_16: GTH2MO47K4MB22SF · pith_short_8: GTH2MO47

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/GTH2MO47K4MB22SFWYBQC6AVX6 \
  | 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: 34cfa63b9f57181d6a45b603017815bfbe4f55f3d0cb5c7bf11b19d5b86f0ee1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8faacc57446956de3fde7201b4c547ee219064cd25930e8384ff6f7b262b38f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-06-27T10:14:52Z",
    "title_canon_sha256": "55f6adcbab917e7de59dcd873705f1e93a27815ba23d67750ff6782fb469bdc2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.08193",
    "kind": "arxiv",
    "version": 1
  }
}