Pith Number

pith:SNZKY64Z

pith:2014:SNZKY64ZTMXRZ2THXVT3MA6B4K

not attested not anchored not stored refs pending

Burkholder-Gundy-Davis Inequality in Martingale Hardy Spaces with Variable Exponent

Maofa Wang, Peide Liu

arxiv:1412.8146 v1 · 2014-12-28 · math.FA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SNZKY64ZTMXRZ2THXVT3MA6B4K}

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	2026-05-18T02:30:23.982524Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9372ac7b999b2f1cea67bd67b603c1e2b37112c5f856372e2c70d73a1257883d

Aliases

arxiv: 1412.8146 · arxiv_version: 1412.8146v1 · doi: 10.48550/arxiv.1412.8146 · pith_short_12: SNZKY64ZTMXR · pith_short_16: SNZKY64ZTMXRZ2TH · pith_short_8: SNZKY64Z

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/SNZKY64ZTMXRZ2THXVT3MA6B4K \
  | 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: 9372ac7b999b2f1cea67bd67b603c1e2b37112c5f856372e2c70d73a1257883d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33fb6f1795d53e1d67c142b21bb052414fd2370259b20576eeec2ada78615481",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-12-28T10:54:48Z",
    "title_canon_sha256": "2482be7ce462ae7ca6409077f44ec2672cda01affc7be94c49bc7f704e1aa31b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.8146",
    "kind": "arxiv",
    "version": 1
  }
}