Pith Number

pith:Z5KS2C6B

pith:2026:Z5KS2C6BHRGC4L3JAD3UH2IW4I

not attested not anchored not stored refs pending

The frog model with death and drift on free products of complete graphs

\'Elcio Lebensztayn, Jaime Utria, Nancy Garcia

arxiv:2606.10165 v1 · 2026-06-08 · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z5KS2C6BHRGC4L3JAD3UH2IW4I}

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	2026-06-10T01:08:57.733254Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf552d0bc13c4c2e2f6900f743e916e229e048422c7d1e759e5860e44a08b0d9

Aliases

arxiv: 2606.10165 · arxiv_version: 2606.10165v1 · doi: 10.48550/arxiv.2606.10165 · pith_short_12: Z5KS2C6BHRGC · pith_short_16: Z5KS2C6BHRGC4L3J · pith_short_8: Z5KS2C6B

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/Z5KS2C6BHRGC4L3JAD3UH2IW4I \
  | 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: cf552d0bc13c4c2e2f6900f743e916e229e048422c7d1e759e5860e44a08b0d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23a9f380ac2b51b7e68eb6bdb3188ff7fe35f3e5661b63ed9b42f3aaf5d061c7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-08T20:48:42Z",
    "title_canon_sha256": "62a3d57c6ed83434d16272c7b0446e3212cf4b9763fcfd89ba4571885e963375"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.10165",
    "kind": "arxiv",
    "version": 1
  }
}