Pith Number

pith:7KNN4JJ5

pith:2014:7KNN4JJ5MNKBDNIYYRG7SORFKC

not attested not anchored not stored refs pending

Equivalence of stability properties for ultradifferentiable function classes

Armin Rainer, Gerhard Schindl

arxiv:1407.6673 v2 · 2014-07-24 · 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{7KNN4JJ5MNKBDNIYYRG7SORFKC}

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	2026-05-18T01:19:44.788511Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa9ade253d635411b518c44df93a2550b43bd8a37f98dcc6415781c93af074ad

Aliases

arxiv: 1407.6673 · arxiv_version: 1407.6673v2 · doi: 10.48550/arxiv.1407.6673 · pith_short_12: 7KNN4JJ5MNKB · pith_short_16: 7KNN4JJ5MNKBDNIY · pith_short_8: 7KNN4JJ5

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/7KNN4JJ5MNKBDNIYYRG7SORFKC \
  | 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: fa9ade253d635411b518c44df93a2550b43bd8a37f98dcc6415781c93af074ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d52f2d86bc3e281f30fdf960e5434977c8b9ce545234d5e0857a49b1b8c9a3d8",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2014-07-24T18:11:25Z",
    "title_canon_sha256": "60625e4a9b60a01c173d31c23adfc4bcc6986e484b8815796b0314de72e1ceed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.6673",
    "kind": "arxiv",
    "version": 2
  }
}