Pith Number

pith:G3FI4JAV

pith:2012:G3FI4JAVJJB3VYMC4GYV62SSKK

not attested not anchored not stored refs pending

On the Hardy-Littlewood maximal function for the cube

Jean Bourgain

arxiv:1212.2661 v1 · 2012-12-11 · 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{G3FI4JAVJJB3VYMC4GYV62SSKK}

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	2026-05-18T03:38:35.763948Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

36ca8e24154a43bae182e1b15f6a5252894b8b1212c76976e21d53e58a339c7e

Aliases

arxiv: 1212.2661 · arxiv_version: 1212.2661v1 · doi: 10.48550/arxiv.1212.2661 · pith_short_12: G3FI4JAVJJB3 · pith_short_16: G3FI4JAVJJB3VYMC · pith_short_8: G3FI4JAV

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/G3FI4JAVJJB3VYMC4GYV62SSKK \
  | 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: 36ca8e24154a43bae182e1b15f6a5252894b8b1212c76976e21d53e58a339c7e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65c339798e1fbb0a1916e192eaaa7341d1db672465b322f1d0786301213d38af",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-12-11T21:50:30Z",
    "title_canon_sha256": "fea65e88126fb7f86fbf5acea2ed96883949ae0aabfa674d98e4164bdfb5dfad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.2661",
    "kind": "arxiv",
    "version": 1
  }
}