Pith Number

pith:C3UVK4CU

pith:2014:C3UVK4CUS2UMLERZSBUDNLA4KE

not attested not anchored not stored refs pending

Lebesgue and Hardy Spaces for Symmetric Norms II: A Vector-Valued Beurling Theorem

Don Hadwin, Yanni Chen, Ye Zhang

arxiv:1408.1117 v1 · 2014-08-05 · math.FA · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{C3UVK4CUS2UMLERZSBUDNLA4KE}

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	2026-05-18T02:45:48.190611Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

16e955705496a8c59239906836ac1c513952c0b83d4508ab427569949565e674

Aliases

arxiv: 1408.1117 · arxiv_version: 1408.1117v1 · doi: 10.48550/arxiv.1408.1117 · pith_short_12: C3UVK4CUS2UM · pith_short_16: C3UVK4CUS2UMLERZ · pith_short_8: C3UVK4CU

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/C3UVK4CUS2UMLERZSBUDNLA4KE \
  | 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: 16e955705496a8c59239906836ac1c513952c0b83d4508ab427569949565e674

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b0303215d2552db634c2ee8b8ba6cbb4f0f1977ea29bbe2aae07f16a4e5c46e",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-08-05T21:13:19Z",
    "title_canon_sha256": "cb241df518f0228aa377a305188074a7cee7624e218e79f1a7691d7fff549b12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.1117",
    "kind": "arxiv",
    "version": 1
  }
}