Pith Number

pith:VKRQGZTA

pith:2016:VKRQGZTAKV4QAQXE3J7EMCJ3W4

not attested not anchored not stored refs pending

Minimum rank and zero forcing number for butterfly networks

Cyriac Grigorious, Daniela Ferrero, Joe Ryan, Sudeep Stephen, Thomas Kalinowski

arxiv:1607.07522 v3 · 2016-07-26 · math.CO · cs.DM

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VKRQGZTAKV4QAQXE3J7EMCJ3W4}

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	2026-05-17T23:50:07.639593Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aaa303666055790042e4da7e46093bb71682b95719a2f46eff5b547bdbf0ecba

Aliases

arxiv: 1607.07522 · arxiv_version: 1607.07522v3 · doi: 10.48550/arxiv.1607.07522 · pith_short_12: VKRQGZTAKV4Q · pith_short_16: VKRQGZTAKV4QAQXE · pith_short_8: VKRQGZTA

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/VKRQGZTAKV4QAQXE3J7EMCJ3W4 \
  | 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: aaa303666055790042e4da7e46093bb71682b95719a2f46eff5b547bdbf0ecba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39569a8865cfa8d5e74c1a8711a465f38b183e4655e3f87956e0de8405a1620b",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-07-26T02:19:45Z",
    "title_canon_sha256": "8e6c94ca3bb20788016f3cd8d37f89f402e2558018bc0efcc74334bce3020f6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.07522",
    "kind": "arxiv",
    "version": 3
  }
}