Pith Number

pith:5K73PVJW

pith:2026:5K73PVJW5KQQQHQBFCJD65IYR7

not attested not anchored not stored refs pending

Equal probabilities maximize the expected deficit in the siblings of the coupon collector

Aristides V. Doumas, S. Spektor

arxiv:2606.21591 v1 · 2026-06-19 · 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{5K73PVJW5KQQQHQBFCJD65IYR7}

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	2026-06-23T01:13:15.579706Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eabfb7d536eaa1081e0128923f75188fca605cda46a507d8f0e1bdc570c24f19

Aliases

arxiv: 2606.21591 · arxiv_version: 2606.21591v1 · doi: 10.48550/arxiv.2606.21591 · pith_short_12: 5K73PVJW5KQQ · pith_short_16: 5K73PVJW5KQQQHQB · pith_short_8: 5K73PVJW

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/5K73PVJW5KQQQHQBFCJD65IYR7 \
  | 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: eabfb7d536eaa1081e0128923f75188fca605cda46a507d8f0e1bdc570c24f19

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "134a1da44760505927086d1b579092021668eca9d66e4cf95ecf03fdcbcc87f6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-19T16:47:42Z",
    "title_canon_sha256": "3ef88c4564a5c2dad9091813ddf64ba33c012cb1576ef8f33ff32a1e4118a7b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.21591",
    "kind": "arxiv",
    "version": 1
  }
}