Pith Number

pith:4KKNXHZV

pith:2011:4KKNXHZVCQCSTPIKCWP67BA4C2

not attested not anchored not stored refs pending

Sharp L^p estimates on BMO

Leonid Slavin, Vasily Vasyunin

arxiv:1110.1771 v1 · 2011-10-08 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4KKNXHZVCQCSTPIKCWP67BA4C2}

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	2026-05-18T04:11:19.653023Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e294db9f35140529bd0a159fef841c1695890d9cbde343e83faef80276b09e33

Aliases

arxiv: 1110.1771 · arxiv_version: 1110.1771v1 · doi: 10.48550/arxiv.1110.1771 · pith_short_12: 4KKNXHZVCQCS · pith_short_16: 4KKNXHZVCQCSTPIK · pith_short_8: 4KKNXHZV

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/4KKNXHZVCQCSTPIKCWP67BA4C2 \
  | 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: e294db9f35140529bd0a159fef841c1695890d9cbde343e83faef80276b09e33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8fd0cc4a997fa73badc1796860823e2240d0a6ab401b7f6efe220ab4830bd490",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-10-08T21:40:28Z",
    "title_canon_sha256": "4d5feafeb44fcc65a46c420fcd913d9630dfebbdba961e243b48ca5817b6d9b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.1771",
    "kind": "arxiv",
    "version": 1
  }
}