Pith Number

pith:3NENGRFR

pith:2014:3NENGRFRJRXHVY3QSIUWSSSHC4

not attested not anchored not stored refs pending

Variable exponent Sobolev spaces associated with Jacobi expansions

A.J. Castro, A. Sanabria, J.J. Betancor, R. Scotto, V. Almeida

arxiv:1410.3642 v2 · 2014-10-14 · 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{3NENGRFRJRXHVY3QSIUWSSSHC4}

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	2026-07-05T07:04:07.446867Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db48d344b14c6e7ae3709229694a471722f1636cee09b7e486612ffda447cf93

Aliases

arxiv: 1410.3642 · arxiv_version: 1410.3642v2 · doi: 10.48550/arxiv.1410.3642 · pith_short_12: 3NENGRFRJRXH · pith_short_16: 3NENGRFRJRXHVY3Q · pith_short_8: 3NENGRFR

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/3NENGRFRJRXHVY3QSIUWSSSHC4 \
  | 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: db48d344b14c6e7ae3709229694a471722f1636cee09b7e486612ffda447cf93

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1bd653d9068248c4cd8a112abc0aa416a9692e60a4906e0c77f1395e9abf43b1",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2014-10-14T10:40:15Z",
    "title_canon_sha256": "59fe023fa59bf292cf64ceae46816f567b3de62b3d9b14a20dbd217749fbf33b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.3642",
    "kind": "arxiv",
    "version": 2
  }
}