Pith Number

pith:GVQGRMET

pith:2013:GVQGRMETQATHYZLT3HPLN5ZZS2

not attested not anchored not stored refs pending

A Combinatorial Formula for Principal Minors of a Matrix with Tree-metric Exponents and Its Applications

Akihiro Yabe, Hiroshi Hirai

arxiv:1311.7238 v2 · 2013-11-28 · 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{GVQGRMETQATHYZLT3HPLN5ZZS2}

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	2026-05-18T02:35:52.262921Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

356068b09380267c6573d9deb6f7399696aa90e606985dd9a97b61d07163698a

Aliases

arxiv: 1311.7238 · arxiv_version: 1311.7238v2 · doi: 10.48550/arxiv.1311.7238 · pith_short_12: GVQGRMETQATH · pith_short_16: GVQGRMETQATHYZLT · pith_short_8: GVQGRMET

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/GVQGRMETQATHYZLT3HPLN5ZZS2 \
  | 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: 356068b09380267c6573d9deb6f7399696aa90e606985dd9a97b61d07163698a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94c6e9fa28950153d9345a94ff57497b261f34e5d188b2a82e06f39c1cd55536",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-11-28T08:27:42Z",
    "title_canon_sha256": "b01e92022a111f7dbc09b45d9fedb42ac29e7da26e43faeebc2faef405a654c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.7238",
    "kind": "arxiv",
    "version": 2
  }
}