Pith Number

pith:4HYTTJMU

pith:2018:4HYTTJMUK5IZD7GQF42J75KQ6P

not attested not anchored not stored refs pending

Cut-and-join equation for monotone Hurwitz numbers revisited

Alexandr Popolitov, Petr Dunin-Barkowski, Reinier Kramer, Sergey Shadrin

arxiv:1807.04197 v2 · 2018-07-11 · math.AG · 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{4HYTTJMUK5IZD7GQF42J75KQ6P}

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	2026-05-17T23:46:09.619864Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1f139a594575191fcd02f349ff550f3fc845331de6f1a1f3ff1632b071a9374

Aliases

arxiv: 1807.04197 · arxiv_version: 1807.04197v2 · doi: 10.48550/arxiv.1807.04197 · pith_short_12: 4HYTTJMUK5IZ · pith_short_16: 4HYTTJMUK5IZD7GQ · pith_short_8: 4HYTTJMU

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/4HYTTJMUK5IZD7GQF42J75KQ6P \
  | 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: e1f139a594575191fcd02f349ff550f3fc845331de6f1a1f3ff1632b071a9374

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da50e7edcb8a16572b49f71ea768959f1fdaa484c45124b3d650f4f1f966f5e1",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2018-07-11T15:33:32Z",
    "title_canon_sha256": "c4f991487df63bf0879ff2f4ba073e74348b4b8391577088c909929998983b32"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.04197",
    "kind": "arxiv",
    "version": 2
  }
}