Pith Number

pith:ZVR7TX7D

pith:2021:ZVR7TX7DXIPBUPDYNAF7D2WTFW

not attested not anchored not stored refs pending

Critical probabilistic characteristics of the Cram\'er model for primes and arithmetical properties

Michel Weber

arxiv:2105.11020 v1 · 2021-05-23 · 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{ZVR7TX7DXIPBUPDYNAF7D2WTFW}

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	2026-05-22T01:03:38.414280Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd63f9dfe3ba1e1a3c78680bf1ead32d8a64fd52e97aa8d98bb869b97f8dd729

Aliases

arxiv: 2105.11020 · arxiv_version: 2105.11020v1 · doi: 10.48550/arxiv.2105.11020 · pith_short_12: ZVR7TX7DXIPB · pith_short_16: ZVR7TX7DXIPBUPDY · pith_short_8: ZVR7TX7D

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/ZVR7TX7DXIPBUPDYNAF7D2WTFW \
  | 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: cd63f9dfe3ba1e1a3c78680bf1ead32d8a64fd52e97aa8d98bb869b97f8dd729

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68230e6e49b0c4fc2da6fa909f2507c6275d10a6bdfcd732037ab9a19b1b4386",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-05-23T21:13:10Z",
    "title_canon_sha256": "db031d063cde745965a9a605d2d289c64214aa4ab1d36e40be0ecd0fb00a6eee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2105.11020",
    "kind": "arxiv",
    "version": 1
  }
}