Pith Number

pith:XIQ2XFA2

pith:2011:XIQ2XFA2TBSEKQUGKZGBGJOTBU

not attested not anchored not stored refs pending

Cram\'er's theorem for asymptotically decoupled fields

Pierre Petit, Rapha\"el Cerf

arxiv:1103.4415 v1 · 2011-03-22 · 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{XIQ2XFA2TBSEKQUGKZGBGJOTBU}

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	2026-05-18T04:26:02.110763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba21ab941a9864454286564c1325d30d145af2ac0c99c2e47e2d72b998fe514e

Aliases

arxiv: 1103.4415 · arxiv_version: 1103.4415v1 · doi: 10.48550/arxiv.1103.4415 · pith_short_12: XIQ2XFA2TBSE · pith_short_16: XIQ2XFA2TBSEKQUG · pith_short_8: XIQ2XFA2

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/XIQ2XFA2TBSEKQUGKZGBGJOTBU \
  | 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: ba21ab941a9864454286564c1325d30d145af2ac0c99c2e47e2d72b998fe514e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66b94679f898a4e84dccda610625122276e62fde523f97c21f7af3a45b79fde3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-03-22T23:35:45Z",
    "title_canon_sha256": "6c3bf8482ded9a58ae8e6e73ff056daef03a9b04d51505092ef6ba0f76126569"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.4415",
    "kind": "arxiv",
    "version": 1
  }
}