Pith Number

pith:KZSKCPOP

pith:2011:KZSKCPOPJZTYG73V7PITNAV5AI

not attested not anchored not stored refs pending

On approximation numbers of composition operators

Daniel Li (LML), Herv\'e Queff\'elec (LPP), Luis Rodriguez-Piazza

arxiv:1104.4451 v1 · 2011-04-22 · 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{KZSKCPOPJZTYG73V7PITNAV5AI}

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	2026-05-18T04:23:34.575734Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5664a13dcf4e67837f75fbd13682bd0219aea0c32c56934c882a5d81c3085b9b

Aliases

arxiv: 1104.4451 · arxiv_version: 1104.4451v1 · doi: 10.48550/arxiv.1104.4451 · pith_short_12: KZSKCPOPJZTY · pith_short_16: KZSKCPOPJZTYG73V · pith_short_8: KZSKCPOP

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/KZSKCPOPJZTYG73V7PITNAV5AI \
  | 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: 5664a13dcf4e67837f75fbd13682bd0219aea0c32c56934c882a5d81c3085b9b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82b336e5d5ac21b21624f800369e086828a01900fb7e18a69a0700667afa0b0a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-04-22T14:36:19Z",
    "title_canon_sha256": "caf924e8e932737fe586b4f9645eab816c6951e8bbaa6ac196b62f5f63ec4901"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.4451",
    "kind": "arxiv",
    "version": 1
  }
}