Pith Number

pith:O72MNMEX

pith:2012:O72MNMEXVW2N6IPWRDHGQAPACI

not attested not anchored not stored refs pending

Limiting Weak Type Estimate for Capacitary Maximal Function

Jie Xiao, Ning Zhang

arxiv:1211.5076 v1 · 2012-11-21 · 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{O72MNMEXVW2N6IPWRDHGQAPACI}

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	2026-05-18T03:40:15.091425Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77f4c6b097adb4df21f688ce6801e0120c6ad0a881b4f1145cafad0d70180ce0

Aliases

arxiv: 1211.5076 · arxiv_version: 1211.5076v1 · doi: 10.48550/arxiv.1211.5076 · pith_short_12: O72MNMEXVW2N · pith_short_16: O72MNMEXVW2N6IPW · pith_short_8: O72MNMEX

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/O72MNMEXVW2N6IPWRDHGQAPACI \
  | 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: 77f4c6b097adb4df21f688ce6801e0120c6ad0a881b4f1145cafad0d70180ce0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3047d69ec8c70800a457da42208bee521b27595d7a7965fa3e36d4fb68daa6d8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-11-21T16:26:07Z",
    "title_canon_sha256": "a9e56df112e8f9c9e8d78a8d4b98ff7785ccb3f0dd55ffdf11a08f69016ed5df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5076",
    "kind": "arxiv",
    "version": 1
  }
}