Pith Number

pith:FK25W5XL

pith:2025:FK25W5XLFDZFQ7HIBP7CE7OS53

not attested not anchored not stored refs pending

Loop clusters on complete graphs

Yves Le Jan

arxiv:2504.16976 v2 · 2025-04-23 · 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{FK25W5XLFDZFQ7HIBP7CE7OS53}

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	2026-07-05T11:55:18.927159Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ab5db76eb28f2587ce80bfe227dd2eecdaabc4276caf6f725cfcca6cf362952

Aliases

arxiv: 2504.16976 · arxiv_version: 2504.16976v2 · doi: 10.48550/arxiv.2504.16976 · pith_short_12: FK25W5XLFDZF · pith_short_16: FK25W5XLFDZFQ7HI · pith_short_8: FK25W5XL

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/FK25W5XLFDZFQ7HIBP7CE7OS53 \
  | 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: 2ab5db76eb28f2587ce80bfe227dd2eecdaabc4276caf6f725cfcca6cf362952

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea100d82744015ba6c2434f4f18df06bb6e134aa236894f760d912c873cd3369",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-04-23T17:21:31Z",
    "title_canon_sha256": "d0d8fe9fdb9d6c8299b5b386e9e94a06a9a4c0a423b7f1f46b47d1b3bb9c5aba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2504.16976",
    "kind": "arxiv",
    "version": 2
  }
}