Pith Number

pith:MTW6F7VA

pith:2021:MTW6F7VAZGUXFTZJAZMM7DUJBF

not attested not anchored not stored refs pending

Spaces of Besov-Sobolev type and a problem on nonlinear approximation

Andreas Seeger, Brian Street, Jean Van Schaftingen, \'Oscar Dom\'inguez, Po-Lam Yung

arxiv:2112.05539 v2 · 2021-12-10 · math.FA · cs.NA · math.CA · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MTW6F7VAZGUXFTZJAZMM7DUJBF}

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	2026-07-05T05:23:07.519834Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

64ede2fea0c9a972cf290658cf8e89097a075ef9949d8bbe48d2e80389b57d9b

Aliases

arxiv: 2112.05539 · arxiv_version: 2112.05539v2 · doi: 10.48550/arxiv.2112.05539 · pith_short_12: MTW6F7VAZGUX · pith_short_16: MTW6F7VAZGUXFTZJ · pith_short_8: MTW6F7VA

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/MTW6F7VAZGUXFTZJAZMM7DUJBF \
  | 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: 64ede2fea0c9a972cf290658cf8e89097a075ef9949d8bbe48d2e80389b57d9b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "53b6f943f47f24edb6c7cdd75d0ec9a8600f0fa836d531ebc6ece0b20d975b46",
    "cross_cats_sorted": [
      "cs.NA",
      "math.CA",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2021-12-10T13:45:40Z",
    "title_canon_sha256": "5356ac82c8498ec1823f83edb2a8728f390f19294bda9a845cef4e6f22410851"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.05539",
    "kind": "arxiv",
    "version": 2
  }
}