Pith Number

pith:AO65EC6Y

pith:2013:AO65EC6Y2GCNVI5PNG4CCBLR25

not attested not anchored not stored refs pending

Approximating Mills ratio

Armengol Gasull, Frederic Utzet

arxiv:1307.3433 v1 · 2013-07-12 · 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{AO65EC6Y2GCNVI5PNG4CCBLR25}

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	2026-05-18T03:18:39.168752Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03bdd20bd8d184daa3af69b8210571d7620f8dce6a753189b6d22f5923b81c67

Aliases

arxiv: 1307.3433 · arxiv_version: 1307.3433v1 · doi: 10.48550/arxiv.1307.3433 · pith_short_12: AO65EC6Y2GCN · pith_short_16: AO65EC6Y2GCNVI5P · pith_short_8: AO65EC6Y

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/AO65EC6Y2GCNVI5PNG4CCBLR25 \
  | 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: 03bdd20bd8d184daa3af69b8210571d7620f8dce6a753189b6d22f5923b81c67

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "996a43c3d8a6cb73c937ce037f2693bb08104b001b38c04248e86cddb77ea675",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-07-12T12:23:56Z",
    "title_canon_sha256": "e1c3e6102e33bf54c7482dc7f47cd8b9fe283e30870652fc3bbbbb22e745f613"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.3433",
    "kind": "arxiv",
    "version": 1
  }
}