Pith Number

pith:OZOUAIAQ

pith:2015:OZOUAIAQQP2TA2IVJTSV2XDYF5

not attested not anchored not stored refs pending

Arithmetic in Metamath, Case Study: Bertrand's Postulate

Mario Carneiro

arxiv:1503.02349 v2 · 2015-03-09 · math.LO · cs.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OZOUAIAQQP2TA2IVJTSV2XDYF5}

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	2026-05-18T02:17:11.079150Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

765d40201083f53069154ce55d5c782f7a0627240cd24cd15e97ef1e2b18dfa4

Aliases

arxiv: 1503.02349 · arxiv_version: 1503.02349v2 · doi: 10.48550/arxiv.1503.02349 · pith_short_12: OZOUAIAQQP2T · pith_short_16: OZOUAIAQQP2TA2IV · pith_short_8: OZOUAIAQ

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/OZOUAIAQQP2TA2IVJTSV2XDYF5 \
  | 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: 765d40201083f53069154ce55d5c782f7a0627240cd24cd15e97ef1e2b18dfa4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "796bae31f9553c6bb6ddfddc1beccd91085cba47f31f69fbe915c230636823d2",
    "cross_cats_sorted": [
      "cs.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2015-03-09T00:46:46Z",
    "title_canon_sha256": "e8ef5e3669b3404d70338c0e7a6f28b08d291094387e1151d6c5fd73630c6c72"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.02349",
    "kind": "arxiv",
    "version": 2
  }
}