Pith Number

pith:CIBZKBKS

pith:2017:CIBZKBKSRMDWGEIR7QELB4GAC3

not attested not anchored not stored refs pending

A Short Proof for a Lower Bound on the Zero Forcing Number

D. Rautenbach, M. F\"urst

arxiv:1705.08365 v1 · 2017-05-23 · 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{CIBZKBKSRMDWGEIR7QELB4GAC3}

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	2026-05-18T00:43:48.460996Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12039505528b07631111fc08b0f0c016d5ac4899a694df30e82b40299a365087

Aliases

arxiv: 1705.08365 · arxiv_version: 1705.08365v1 · doi: 10.48550/arxiv.1705.08365 · pith_short_12: CIBZKBKSRMDW · pith_short_16: CIBZKBKSRMDWGEIR · pith_short_8: CIBZKBKS

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/CIBZKBKSRMDWGEIR7QELB4GAC3 \
  | 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: 12039505528b07631111fc08b0f0c016d5ac4899a694df30e82b40299a365087

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4ce40e55494aaf5287b208f9bbfd7856509132948a4da79e4cb557f9d907a93",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-05-23T15:32:53Z",
    "title_canon_sha256": "86ddcab34a185938d285b9d2ae236a127b8686171ea6e89d996ce1dc4e5673ea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.08365",
    "kind": "arxiv",
    "version": 1
  }
}