Pith Number

pith:PKJRW6AG

pith:2016:PKJRW6AGF36E6TJJJNQFEGQKKC

not attested not anchored not stored refs pending

A lower bound on the zero forcing number

Randy Davila, Sudeep Stephen, Thomas Kalinowski

arxiv:1611.06557 v4 · 2016-11-20 · 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{PKJRW6AGF36E6TJJJNQFEGQKKC}

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	2026-05-18T00:01:49.204653Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a931b78062efc4f4d294b60521a0a50ab22819fc6a16e3b14d34102d27d83bb

Aliases

arxiv: 1611.06557 · arxiv_version: 1611.06557v4 · doi: 10.48550/arxiv.1611.06557 · pith_short_12: PKJRW6AGF36E · pith_short_16: PKJRW6AGF36E6TJJ · pith_short_8: PKJRW6AG

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/PKJRW6AGF36E6TJJJNQFEGQKKC \
  | 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: 7a931b78062efc4f4d294b60521a0a50ab22819fc6a16e3b14d34102d27d83bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2aedc8b3bf01be4dc8e8538e549a5e3c24faf1850f3d6e887dde8f8c01de6cfa",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-11-20T18:09:51Z",
    "title_canon_sha256": "33479707be12ca069aaa4e9badfe97a44f153b87b6012cf2088d5d5f3455abdd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.06557",
    "kind": "arxiv",
    "version": 4
  }
}