Pith Number

pith:ZLG4DCPH

pith:2012:ZLG4DCPH2CAE6JMTBBYOFC45MH

not attested not anchored not stored refs pending

Composition in ultradifferentiable classes

Armin Rainer, Gerhard Schindl

arxiv:1210.5102 v3 · 2012-10-18 · math.FA · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZLG4DCPH2CAE6JMTBBYOFC45MH}

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	2026-05-18T01:19:44.984212Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cacdc189e7d0804f25930870e28b9d61d5ee265c99f5bd68e994438cfacc7322

Aliases

arxiv: 1210.5102 · arxiv_version: 1210.5102v3 · doi: 10.48550/arxiv.1210.5102 · pith_short_12: ZLG4DCPH2CAE · pith_short_16: ZLG4DCPH2CAE6JMT · pith_short_8: ZLG4DCPH

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/ZLG4DCPH2CAE6JMTBBYOFC45MH \
  | 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: cacdc189e7d0804f25930870e28b9d61d5ee265c99f5bd68e994438cfacc7322

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02c453f77584999b8bf1e39d3496e041d88758a9ce422558c0194d87fcbc6083",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-10-18T11:44:36Z",
    "title_canon_sha256": "6b943a118aa06fe4ff31790305ec4d755c34d1e0ac3819636682108b129abd37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5102",
    "kind": "arxiv",
    "version": 3
  }
}