Pith Number

pith:57PUSUHC

pith:2012:57PUSUHC6TQNOF5MEKI7J5Z47C

not attested not anchored not stored refs pending

Compact composition operators on the Dirichlet space and capacity of sets of contact points

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

arxiv:1207.1232 v1 · 2012-07-05 · 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{57PUSUHC6TQNOF5MEKI7J5Z47C}

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	2026-05-18T03:51:46.580882Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

efdf4950e2f4e0d717ac2291f4f73cf8bfa424efbffea04b7715af6c9be9fa56

Aliases

arxiv: 1207.1232 · arxiv_version: 1207.1232v1 · doi: 10.48550/arxiv.1207.1232 · pith_short_12: 57PUSUHC6TQN · pith_short_16: 57PUSUHC6TQNOF5M · pith_short_8: 57PUSUHC

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/57PUSUHC6TQNOF5MEKI7J5Z47C \
  | 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: efdf4950e2f4e0d717ac2291f4f73cf8bfa424efbffea04b7715af6c9be9fa56

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f031836fae47d58d96da397124890b59c414b56527b5b974309ec3d36729c13c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-07-05T11:54:38Z",
    "title_canon_sha256": "38cd66a67944532ab2a606d650886ed4f7864a615354bfb8c21b1992f898c6b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.1232",
    "kind": "arxiv",
    "version": 1
  }
}