Pith Number

pith:HPBAFLWN

pith:2019:HPBAFLWNB6XPK5B2LKQOJGWHVN

not attested not anchored not stored refs pending

Graphs with a unique maximum open packing

Bo\v{s}tjan Bre\v{s}ar, Douglas F. Rall, Kirsti Kuenzel

arxiv:1901.09859 v1 · 2019-01-28 · 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{HPBAFLWNB6XPK5B2LKQOJGWHVN}

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	2026-05-17T23:55:23.648634Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3bc202aecd0faef5743a5aa0e49ac7ab4a0ebc420732409bd6930799f6ce5eff

Aliases

arxiv: 1901.09859 · arxiv_version: 1901.09859v1 · doi: 10.48550/arxiv.1901.09859 · pith_short_12: HPBAFLWNB6XP · pith_short_16: HPBAFLWNB6XPK5B2 · pith_short_8: HPBAFLWN

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/HPBAFLWNB6XPK5B2LKQOJGWHVN \
  | 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: 3bc202aecd0faef5743a5aa0e49ac7ab4a0ebc420732409bd6930799f6ce5eff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ada0186441361d517aa3e91b31cc8faadcff8021c5e9671a640ac8de2b656a70",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-01-28T18:04:31Z",
    "title_canon_sha256": "5dc4fbd08bffe845459ba449a2ff161800a47c9a63265f5166e1d6e1eb17f8f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1901.09859",
    "kind": "arxiv",
    "version": 1
  }
}