Pith Number

pith:UCJFOBM5

pith:2010:UCJFOBM55EZEBA3AP6AIPIUOUR

not attested not anchored not stored refs pending

Rubio de Francia's extrapolation theory: estimates for the distribution function

Javier Soria, Mar\'ia J. Carro, Rodolfo H. Torres

arxiv:1011.2032 v1 · 2010-11-09 · math.CA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UCJFOBM55EZEBA3AP6AIPIUOUR}

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	2026-05-18T02:58:01.507488Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a09257059de9324083607f8087a28ea466bd9e710785fd7542c06e61716ad8fa

Aliases

arxiv: 1011.2032 · arxiv_version: 1011.2032v1 · doi: 10.48550/arxiv.1011.2032 · pith_short_12: UCJFOBM55EZE · pith_short_16: UCJFOBM55EZEBA3A · pith_short_8: UCJFOBM5

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/UCJFOBM55EZEBA3AP6AIPIUOUR \
  | 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: a09257059de9324083607f8087a28ea466bd9e710785fd7542c06e61716ad8fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d85dba7dd9ca1c3d74039889f434cbd4168a9652c267f407638ef8855cad8ebe",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-11-09T10:43:32Z",
    "title_canon_sha256": "61cbb79eae7284b18ac1ebbbad6d592b7dc23a33eedb15a447ea1493309372e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2032",
    "kind": "arxiv",
    "version": 1
  }
}