Pith Number

pith:WTPC5YYK

pith:2016:WTPC5YYKPQX5ADP3ANYRRB2DHQ

not attested not anchored not stored refs pending

Packing minor-closed families of graphs into complete graphs

Mathias Schacht, Silvia Messuti, Vojt\v{e}ch R\"odl

arxiv:1602.06780 v2 · 2016-02-22 · 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{WTPC5YYKPQX5ADP3ANYRRB2DHQ}

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	2026-05-18T01:16:54.473860Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b4de2ee30a7c2fd00dfb03711887433c0356364f433546492891e0095fdfff5f

Aliases

arxiv: 1602.06780 · arxiv_version: 1602.06780v2 · doi: 10.48550/arxiv.1602.06780 · pith_short_12: WTPC5YYKPQX5 · pith_short_16: WTPC5YYKPQX5ADP3 · pith_short_8: WTPC5YYK

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/WTPC5YYKPQX5ADP3ANYRRB2DHQ \
  | 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: b4de2ee30a7c2fd00dfb03711887433c0356364f433546492891e0095fdfff5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b2ee5f2c2758700711a2ede489ef717bea2b640f6b90ccb77a96d5891d66294c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-02-22T14:10:31Z",
    "title_canon_sha256": "c114909827595d7efa9d02fdac161176a6ea73ecc93d3318493f93bd718ed2cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.06780",
    "kind": "arxiv",
    "version": 2
  }
}