Pith Number

pith:5PBE3Q77

pith:2012:5PBE3Q77JK7KSXFLLXQ5SCP773

not attested not anchored not stored refs pending

Contractive multipliers from Hardy space to weighted Hardy space

Joseph A. Ball, Vladimir Bolotnikov

arxiv:1209.3690 v1 · 2012-09-17 · 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{5PBE3Q77JK7KSXFLLXQ5SCP773}

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	2026-05-18T03:45:23.695681Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebc24dc3ff4abea95cab5de1d909fffedcdb600ef62d61ffc38e62da94fb0846

Aliases

arxiv: 1209.3690 · arxiv_version: 1209.3690v1 · doi: 10.48550/arxiv.1209.3690 · pith_short_12: 5PBE3Q77JK7K · pith_short_16: 5PBE3Q77JK7KSXFL · pith_short_8: 5PBE3Q77

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/5PBE3Q77JK7KSXFLLXQ5SCP773 \
  | 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: ebc24dc3ff4abea95cab5de1d909fffedcdb600ef62d61ffc38e62da94fb0846

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69977c178295724f13f7b2abf8f042d0daf0817b5c6cbbee248aaf17c002602e",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-09-17T15:28:18Z",
    "title_canon_sha256": "949d235ac5cc40e2c9bc016e443d810570e056235f7b0718b7774cf968a09e71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3690",
    "kind": "arxiv",
    "version": 1
  }
}