Pith Number

pith:O3GZXC52

pith:2022:O3GZXC52AGQ642FJ7MDCFCZCHI

not attested not anchored not stored refs pending

Sobolev spaces revisited

Andreas Seeger, Haim Brezis, Jean Van Schaftingen, Po-Lam Yung

arxiv:2202.01410 v1 · 2022-02-03 · 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{O3GZXC52AGQ642FJ7MDCFCZCHI}

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	2026-07-05T05:23:07.834089Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76cd9b8bba01a1ee68a9fb06228b223a0a711370eeb448f0ef603458b8cc5b8f

Aliases

arxiv: 2202.01410 · arxiv_version: 2202.01410v1 · doi: 10.48550/arxiv.2202.01410 · pith_short_12: O3GZXC52AGQ6 · pith_short_16: O3GZXC52AGQ642FJ · pith_short_8: O3GZXC52

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/O3GZXC52AGQ642FJ7MDCFCZCHI \
  | 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: 76cd9b8bba01a1ee68a9fb06228b223a0a711370eeb448f0ef603458b8cc5b8f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac535a1b39ccd3917cbbbf1056116cb77e28b304909b6dae90d3910512670161",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2022-02-03T04:59:58Z",
    "title_canon_sha256": "d41e436721e352bd4886569a33736b1725f5d9dd80b78d0945f755fb84ec4497"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2202.01410",
    "kind": "arxiv",
    "version": 1
  }
}