Pith Number

pith:4R6RTXSP

pith:2017:4R6RTXSP4JCZKSTNZ7FJY3O4WI

not attested not anchored not stored refs pending

On the number of types in sparse graphs

Micha{\l} Pilipczuk, Sebastian Siebertz, Szymon Toru\'nczyk

arxiv:1705.09336 v2 · 2017-05-25 · cs.DM · 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{4R6RTXSP4JCZKSTNZ7FJY3O4WI}

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	2026-05-18T00:31:19.369584Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e47d19de4fe245954a6dcfca9c6ddcb20998324611a046340de6eac442811f0a

Aliases

arxiv: 1705.09336 · arxiv_version: 1705.09336v2 · doi: 10.48550/arxiv.1705.09336 · pith_short_12: 4R6RTXSP4JCZ · pith_short_16: 4R6RTXSP4JCZKSTN · pith_short_8: 4R6RTXSP

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/4R6RTXSP4JCZKSTNZ7FJY3O4WI \
  | 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: e47d19de4fe245954a6dcfca9c6ddcb20998324611a046340de6eac442811f0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "356c93adabbb7b50dedebe649d5ad8433ea4aa2467589f467d38683637e5baec",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2017-05-25T19:22:25Z",
    "title_canon_sha256": "58bff59b80e40c4a423f540306d3e862e8377b7df0faba5eb51729df7c41d0ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.09336",
    "kind": "arxiv",
    "version": 2
  }
}