Pith Number

pith:GRTPUG2M

pith:2013:GRTPUG2MNBAFCRZMUQRE7Y7TO7

not attested not anchored not stored refs pending

On moment indeterminacy of the Benini income distribution

Christian Kleiber

arxiv:1306.0364 v1 · 2013-06-03 · stat.OT · 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{GRTPUG2MNBAFCRZMUQRE7Y7TO7}

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	2026-05-18T01:08:32.765675Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3466fa1b4c684051472ca4224fe3f377f8577127fda49682ff4564dd48dc77f8

Aliases

arxiv: 1306.0364 · arxiv_version: 1306.0364v1 · doi: 10.48550/arxiv.1306.0364 · pith_short_12: GRTPUG2MNBAF · pith_short_16: GRTPUG2MNBAFCRZM · pith_short_8: GRTPUG2M

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/GRTPUG2MNBAFCRZMUQRE7Y7TO7 \
  | 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: 3466fa1b4c684051472ca4224fe3f377f8577127fda49682ff4564dd48dc77f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0120f332ffb80545697fbf74198ce609d643a1393565e956ad53c1e0035fd414",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "stat.OT",
    "submitted_at": "2013-06-03T11:37:35Z",
    "title_canon_sha256": "d3f2949721ad5a963342af86aa08afb8fce4be23f92bea1ac60b1317cb694541"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0364",
    "kind": "arxiv",
    "version": 1
  }
}