Pith Number

pith:3CQPIFYI

pith:2010:3CQPIFYIJ54ENMFFJIC4PCEDTF

not attested not anchored not stored refs pending

A new characterization of Sobolev spaces on $\mathbb{R}^n$

Joan Mateu, Joan Verdera, Roc Alabern

arxiv:1011.0667 v2 · 2010-11-02 · math.CA · math.AP · 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{3CQPIFYIJ54ENMFFJIC4PCEDTF}

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	2026-05-18T04:34:37.995854Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d8a0f417084f7846b0a54a05c788839973330dbb0148257c031544321b3dec46

Aliases

arxiv: 1011.0667 · arxiv_version: 1011.0667v2 · doi: 10.48550/arxiv.1011.0667 · pith_short_12: 3CQPIFYIJ54E · pith_short_16: 3CQPIFYIJ54ENMFF · pith_short_8: 3CQPIFYI

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/3CQPIFYIJ54ENMFFJIC4PCEDTF \
  | 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: d8a0f417084f7846b0a54a05c788839973330dbb0148257c031544321b3dec46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97eedb40b56889659d6185d75ad341969e8a3fbdf98f02e91ecaa21e06d0b4b9",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-11-02T16:37:17Z",
    "title_canon_sha256": "a4536236c8a6afc42a20942b477bef8bd5268f27948d09f9532d51e1095e5339"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.0667",
    "kind": "arxiv",
    "version": 2
  }
}