Pith Number

pith:ZNETGCLP

pith:2016:ZNETGCLPPVL5OBXDVSLC7M5KLJ

not attested not anchored not stored refs pending

Martingale Inequalities in Variable Exponent Hardy spaces with $0<p^-\leq p^+<\infty$

Peide Liu, Wei Chen

arxiv:1612.07160 v1 · 2016-12-21 · 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{ZNETGCLPPVL5OBXDVSLC7M5KLJ}

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	2026-05-18T00:54:14.546264Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb4933096f7d57d706e3ac962fb3aa5a5312aae587193aec55b85931a32cb190

Aliases

arxiv: 1612.07160 · arxiv_version: 1612.07160v1 · doi: 10.48550/arxiv.1612.07160 · pith_short_12: ZNETGCLPPVL5 · pith_short_16: ZNETGCLPPVL5OBXD · pith_short_8: ZNETGCLP

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/ZNETGCLPPVL5OBXDVSLC7M5KLJ \
  | 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: cb4933096f7d57d706e3ac962fb3aa5a5312aae587193aec55b85931a32cb190

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "086c3fac790a91fe3b1514f526ca10cf86603918d150ce66bb98f64da9821c6e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-12-21T15:00:43Z",
    "title_canon_sha256": "1c2bb94e50621b8eb28ea86a0a3c2cb5320f415850d95d6eb85cc9e6ccd4a68a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.07160",
    "kind": "arxiv",
    "version": 1
  }
}