Pith Number

pith:M67RERYK

pith:2025:M67RERYK7K4DY47JEZG543NN26

not attested not anchored not stored refs pending

The number of primes not in a numerical semigroup

Hui Zhu, Yong-Gao Chen

arxiv:2506.03625 v2 · 2025-06-04 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M67RERYK7K4DY47JEZG543NN26}

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	2026-07-05T11:22:41.377899Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67bf12470afab83c73e9264dde6dadd7abca443ca12dcf392e28419e2fd7c758

Aliases

arxiv: 2506.03625 · arxiv_version: 2506.03625v2 · doi: 10.48550/arxiv.2506.03625 · pith_short_12: M67RERYK7K4D · pith_short_16: M67RERYK7K4DY47J · pith_short_8: M67RERYK

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/M67RERYK7K4DY47JEZG543NN26 \
  | 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: 67bf12470afab83c73e9264dde6dadd7abca443ca12dcf392e28419e2fd7c758

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cefd0deb023b9e371c94577ab7819c506753e548a50cf7befead76f31b3cdf5e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-06-04T07:08:29Z",
    "title_canon_sha256": "e6e1527c24c4eae9d2ac10ed1026f07cd922fd171a1cae883441874758044963"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.03625",
    "kind": "arxiv",
    "version": 2
  }
}