Pith Number

pith:O3U45HVW

pith:2016:O3U45HVWVRRZZOANA3HMJ52T6H

not attested not anchored not stored refs pending

Brushing Number and Zero-Forcing Number of Graphs and their Line Graphs

Aras Erzurumluoglu, David Pike, Karen Meagher

arxiv:1609.05854 v1 · 2016-09-19 · 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{O3U45HVWVRRZZOANA3HMJ52T6H}

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	2026-07-05T01:28:57.407290Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76e9ce9eb6ac639cb80d06cec4f753f1d0ec9c2de5079d697de6d4004aadcac9

Aliases

arxiv: 1609.05854 · arxiv_version: 1609.05854v1 · doi: 10.48550/arxiv.1609.05854 · pith_short_12: O3U45HVWVRRZ · pith_short_16: O3U45HVWVRRZZOAN · pith_short_8: O3U45HVW

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/O3U45HVWVRRZZOANA3HMJ52T6H \
  | 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: 76e9ce9eb6ac639cb80d06cec4f753f1d0ec9c2de5079d697de6d4004aadcac9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72517f5df8adbe1b7abc66a487bf4e74c31284ef6dcacfa5308c203d17259b68",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-09-19T18:44:46Z",
    "title_canon_sha256": "6c14cf92c80e467e44c90e31488ae1834cc0144707d99525a705b091a372a441"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.05854",
    "kind": "arxiv",
    "version": 1
  }
}